% Copyright INRIA
Lagrangian
 
\begin{eqnarray*} && -m_{2}\,g\left(y_{1}+r_{2}\,\sin({\theta_{2}})
\right) - m_{3}\,g\left(y_{2}+r_{3}\,\sin({\theta_{3}})\right) - m_{4}
\,g\left(y_{3}+r_{4}\,\sin({\theta_{4}})\right) - m_{5}\,g\left(y_{4}+
r_{5}\,\sin({\theta_{5}})\right) \\ &&\quad\mbox{} - m_{6}\,g\left(y_{
5}+r_{6}\,\sin({\theta_{6}})\right) - m_{7}\,g\left(y_{6}+r_{7}\,\sin(
{\theta_{7}})\right) - m_{8}\,g\left(y_{7}+r_{8}\,\sin({\theta_{8}})
\right) - m_{9}\,g\left(y_{8}+r_{9}\,\sin({\theta_{9}})\right)
 \\ &&\quad\mbox{} - m_{10}\,g\left(y_{9}+r_{10}\,\sin({\theta_{10}})
\right) + \frac{m_{1}\left({r_{1}}^2\,{\sin({\theta_{1}})}^2\,{{
\dot{\theta}_{1}}}^2+{r_{1}}^2\,{\cos({\theta_{1}})}^2\,{{\dot{\theta}
_{1}}}^2\right)}{2} \\ &&\quad\mbox{} + \frac{J_{1}\,{{\dot{\theta}_{1
}}}^2}{2} + \frac{m_{2}\left(\left({\dot{x}_{1}}-r_{2}\,\sin({\theta_{
2}})\,{\dot{\theta}_{2}}\right)^2+\left({\dot{y}_{1}}+r_{2}\,\cos({
\theta_{2}})\,{\dot{\theta}_{2}}\right)^2\right)}{2} \\ &&\quad\mbox{}
 + \frac{J_{2}\,{{\dot{\theta}_{2}}}^2}{2} + \frac{m_{3}\left(\left({
\dot{x}_{2}}-r_{3}\,\sin({\theta_{3}})\,{\dot{\theta}_{3}}\right)^2+
\left({\dot{y}_{2}}+r_{3}\,\cos({\theta_{3}})\,{\dot{\theta}_{3}}
\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{J_{3}\,{{\dot{\theta}_{
3}}}^2}{2} + \frac{m_{4}\left(\left({\dot{x}_{3}}-r_{4}\,\sin({\theta
_{4}})\,{\dot{\theta}_{4}}\right)^2+\left({\dot{y}_{3}}+r_{4}\,\cos({
\theta_{4}})\,{\dot{\theta}_{4}}\right)^2\right)}{2} \\ &&\quad\mbox{}
 + \frac{J_{4}\,{{\dot{\theta}_{4}}}^2}{2} + \frac{m_{5}\left(\left({
\dot{x}_{4}}-r_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5}}\right)^2+
\left({\dot{y}_{4}}+r_{5}\,\cos({\theta_{5}})\,{\dot{\theta}_{5}}
\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{J_{5}\,{{\dot{\theta}_{
5}}}^2}{2} + \frac{m_{6}\left(\left({\dot{x}_{5}}-r_{6}\,\sin({\theta
_{6}})\,{\dot{\theta}_{6}}\right)^2+\left({\dot{y}_{5}}+r_{6}\,\cos({
\theta_{6}})\,{\dot{\theta}_{6}}\right)^2\right)}{2} \\ &&\quad\mbox{}
 + \frac{J_{6}\,{{\dot{\theta}_{6}}}^2}{2} + \frac{m_{7}\left(\left({
\dot{x}_{6}}-r_{7}\,\sin({\theta_{7}})\,{\dot{\theta}_{7}}\right)^2+
\left({\dot{y}_{6}}+r_{7}\,\cos({\theta_{7}})\,{\dot{\theta}_{7}}
\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{J_{7}\,{{\dot{\theta}_{
7}}}^2}{2} + \frac{m_{8}\left(\left({\dot{x}_{7}}-r_{8}\,\sin({\theta
_{8}})\,{\dot{\theta}_{8}}\right)^2+\left({\dot{y}_{7}}+r_{8}\,\cos({
\theta_{8}})\,{\dot{\theta}_{8}}\right)^2\right)}{2} \\ &&\quad\mbox{}
 + \frac{J_{8}\,{{\dot{\theta}_{8}}}^2}{2} + \frac{m_{9}\left(\left({
\dot{x}_{8}}-r_{9}\,\sin({\theta_{9}})\,{\dot{\theta}_{9}}\right)^2+
\left({\dot{y}_{8}}+r_{9}\,\cos({\theta_{9}})\,{\dot{\theta}_{9}}
\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{J_{9}\,{{\dot{\theta}_{
9}}}^2}{2} \\ &&\quad\mbox{} + \frac{m_{10}\left(\left({\dot{x}_{9}}-r
_{10}\,\sin({\theta_{10}})\,{\dot{\theta}_{10}}\right)^2+\left({
\dot{y}_{9}}+r_{10}\,\cos({\theta_{10}})\,{\dot{\theta}_{10}}\right)^2
\right)}{2} \\ &&\quad\mbox{} + \frac{J_{10}\,{{\dot{\theta}_{10}}}^2
}{2} - m_{1}\,g\,r_{1}\,\sin({\theta_{1}}) \end{eqnarray*}
Lhs of Euler Equations
 
\[ LL(x_{7}) = m_{8}\,{\ddot{x}_{7}} - m_{8}\,r_{8}\,\cos({\theta_{8}}
)\,{{\dot{\theta}_{8}}}^2 - m_{8}\,r_{8}\,\sin({\theta_{8}})\,{
\ddot{\theta}_{8}} \]
\[ LL(y_{3}) = m_{4}\,{\ddot{y}_{3}} - m_{4}\,r_{4}\,\sin({\theta_{4}}
)\,{{\dot{\theta}_{4}}}^2 + m_{4}\,r_{4}\,\cos({\theta_{4}})\,{
\ddot{\theta}_{4}} + m_{4}\,g \]
\[ LL(y_{5}) = m_{6}\,{\ddot{y}_{5}} - m_{6}\,r_{6}\,\sin({\theta_{6}}
)\,{{\dot{\theta}_{6}}}^2 + m_{6}\,r_{6}\,\cos({\theta_{6}})\,{
\ddot{\theta}_{6}} + m_{6}\,g \]
\[ LL({\theta_{1}}) = m_{1}\,{r_{1}}^2\,{\ddot{\theta}_{1}} + J_{1}\,{
\ddot{\theta}_{1}} + m_{1}\,g\,r_{1}\,\cos({\theta_{1}}) \]
\[ LL(x_{8}) = m_{9}\,{\ddot{x}_{8}} - m_{9}\,r_{9}\,\cos({\theta_{9}}
)\,{{\dot{\theta}_{9}}}^2 - m_{9}\,r_{9}\,\sin({\theta_{9}})\,{
\ddot{\theta}_{9}} \]
\[ LL(y_{4}) = m_{5}\,{\ddot{y}_{4}} - m_{5}\,r_{5}\,\sin({\theta_{5}}
)\,{{\dot{\theta}_{5}}}^2 + m_{5}\,r_{5}\,\cos({\theta_{5}})\,{
\ddot{\theta}_{5}} + m_{5}\,g \]
\begin{eqnarray*} LL({\theta_{9}}) &=& -m_{9}\,r_{9}\,\sin({\theta_{9}
})\,{\ddot{x}_{8}} + m_{9}\,{r_{9}}^2\,{\ddot{\theta}_{9}} + m_{9}\,r
_{9}\,\cos({\theta_{9}})\,{\ddot{y}_{8}} + J_{9}\,{\ddot{\theta}_{9}}
 \\ &&\quad\mbox{} + m_{9}\,g\,r_{9}\,\cos({\theta_{9}})
 \end{eqnarray*}
\begin{eqnarray*} LL({\theta_{2}}) &=& -m_{2}\,r_{2}\,\sin({\theta_{2}
})\,{\ddot{x}_{1}} + m_{2}\,{r_{2}}^2\,{\ddot{\theta}_{2}} + m_{2}\,r
_{2}\,\cos({\theta_{2}})\,{\ddot{y}_{1}} + J_{2}\,{\ddot{\theta}_{2}}
 \\ &&\quad\mbox{} + m_{2}\,g\,r_{2}\,\cos({\theta_{2}})
 \end{eqnarray*}
\[ LL(x_{9}) = m_{10}\,{\ddot{x}_{9}} - m_{10}\,r_{10}\,\cos({\theta_{
10}})\,{{\dot{\theta}_{10}}}^2 - m_{10}\,r_{10}\,\sin({\theta_{10}})\,
{\ddot{\theta}_{10}} \]
\begin{eqnarray*} LL({\theta_{4}}) &=& -m_{4}\,r_{4}\,\sin({\theta_{4}
})\,{\ddot{x}_{3}} + m_{4}\,{r_{4}}^2\,{\ddot{\theta}_{4}} + m_{4}\,r
_{4}\,\cos({\theta_{4}})\,{\ddot{y}_{3}} + J_{4}\,{\ddot{\theta}_{4}}
 \\ &&\quad\mbox{} + m_{4}\,g\,r_{4}\,\cos({\theta_{4}})
 \end{eqnarray*}
\begin{eqnarray*} LL({\theta_{10}}) &=& -m_{10}\,r_{10}\,\sin({\theta
_{10}})\,{\ddot{x}_{9}} + m_{10}\,{r_{10}}^2\,{\ddot{\theta}_{10}} + m
_{10}\,r_{10}\,\cos({\theta_{10}})\,{\ddot{y}_{9}} + J_{10}\,{
\ddot{\theta}_{10}} \\ &&\quad\mbox{} + m_{10}\,g\,r_{10}\,\cos({
\theta_{10}}) \end{eqnarray*}
\[ LL(y_{7}) = m_{8}\,{\ddot{y}_{7}} - m_{8}\,r_{8}\,\sin({\theta_{8}}
)\,{{\dot{\theta}_{8}}}^2 + m_{8}\,r_{8}\,\cos({\theta_{8}})\,{
\ddot{\theta}_{8}} + m_{8}\,g \]
\begin{eqnarray*} LL({\theta_{3}}) &=& -m_{3}\,r_{3}\,\sin({\theta_{3}
})\,{\ddot{x}_{2}} + m_{3}\,{r_{3}}^2\,{\ddot{\theta}_{3}} + m_{3}\,r
_{3}\,\cos({\theta_{3}})\,{\ddot{y}_{2}} + J_{3}\,{\ddot{\theta}_{3}}
 \\ &&\quad\mbox{} + m_{3}\,g\,r_{3}\,\cos({\theta_{3}})
 \end{eqnarray*}
\[ LL(y_{6}) = m_{7}\,{\ddot{y}_{6}} - m_{7}\,r_{7}\,\sin({\theta_{7}}
)\,{{\dot{\theta}_{7}}}^2 + m_{7}\,r_{7}\,\cos({\theta_{7}})\,{
\ddot{\theta}_{7}} + m_{7}\,g \]
\begin{eqnarray*} LL({\theta_{5}}) &=& -m_{5}\,r_{5}\,\sin({\theta_{5}
})\,{\ddot{x}_{4}} + m_{5}\,{r_{5}}^2\,{\ddot{\theta}_{5}} + m_{5}\,r
_{5}\,\cos({\theta_{5}})\,{\ddot{y}_{4}} + J_{5}\,{\ddot{\theta}_{5}}
 \\ &&\quad\mbox{} + m_{5}\,g\,r_{5}\,\cos({\theta_{5}})
 \end{eqnarray*}
\[ LL(x_{2}) = m_{3}\,{\ddot{x}_{2}} - m_{3}\,r_{3}\,\cos({\theta_{3}}
)\,{{\dot{\theta}_{3}}}^2 - m_{3}\,r_{3}\,\sin({\theta_{3}})\,{
\ddot{\theta}_{3}} \]
\[ LL(y_{8}) = m_{9}\,{\ddot{y}_{8}} - m_{9}\,r_{9}\,\sin({\theta_{9}}
)\,{{\dot{\theta}_{9}}}^2 + m_{9}\,r_{9}\,\cos({\theta_{9}})\,{
\ddot{\theta}_{9}} + m_{9}\,g \]
\begin{eqnarray*} LL({\theta_{6}}) &=& -m_{6}\,r_{6}\,\sin({\theta_{6}
})\,{\ddot{x}_{5}} + m_{6}\,{r_{6}}^2\,{\ddot{\theta}_{6}} + m_{6}\,r
_{6}\,\cos({\theta_{6}})\,{\ddot{y}_{5}} + J_{6}\,{\ddot{\theta}_{6}}
 \\ &&\quad\mbox{} + m_{6}\,g\,r_{6}\,\cos({\theta_{6}})
 \end{eqnarray*}
\[ LL(x_{10}) = 0 \]
\[ LL(x_{3}) = m_{4}\,{\ddot{x}_{3}} - m_{4}\,r_{4}\,\cos({\theta_{4}}
)\,{{\dot{\theta}_{4}}}^2 - m_{4}\,r_{4}\,\sin({\theta_{4}})\,{
\ddot{\theta}_{4}} \]
\[ LL(x_{5}) = m_{6}\,{\ddot{x}_{5}} - m_{6}\,r_{6}\,\cos({\theta_{6}}
)\,{{\dot{\theta}_{6}}}^2 - m_{6}\,r_{6}\,\sin({\theta_{6}})\,{
\ddot{\theta}_{6}} \]
\[ LL(y_{1}) = m_{2}\,{\ddot{y}_{1}} - m_{2}\,r_{2}\,\sin({\theta_{2}}
)\,{{\dot{\theta}_{2}}}^2 + m_{2}\,r_{2}\,\cos({\theta_{2}})\,{
\ddot{\theta}_{2}} + m_{2}\,g \]
\[ LL(x_{1}) = m_{2}\,{\ddot{x}_{1}} - m_{2}\,r_{2}\,\cos({\theta_{2}}
)\,{{\dot{\theta}_{2}}}^2 - m_{2}\,r_{2}\,\sin({\theta_{2}})\,{
\ddot{\theta}_{2}} \]
\begin{eqnarray*} LL({\theta_{7}}) &=& -m_{7}\,r_{7}\,\sin({\theta_{7}
})\,{\ddot{x}_{6}} + m_{7}\,{r_{7}}^2\,{\ddot{\theta}_{7}} + m_{7}\,r
_{7}\,\cos({\theta_{7}})\,{\ddot{y}_{6}} + J_{7}\,{\ddot{\theta}_{7}}
 \\ &&\quad\mbox{} + m_{7}\,g\,r_{7}\,\cos({\theta_{7}})
 \end{eqnarray*}
\[ LL(x_{4}) = m_{5}\,{\ddot{x}_{4}} - m_{5}\,r_{5}\,\cos({\theta_{5}}
)\,{{\dot{\theta}_{5}}}^2 - m_{5}\,r_{5}\,\sin({\theta_{5}})\,{
\ddot{\theta}_{5}} \]
\[ LL(y_{9}) = m_{10}\,{\ddot{y}_{9}} - m_{10}\,r_{10}\,\sin({\theta_{
10}})\,{{\dot{\theta}_{10}}}^2 + m_{10}\,r_{10}\,\cos({\theta_{10}})\,
{\ddot{\theta}_{10}} + m_{10}\,g \]
\[ LL(x_{6}) = m_{7}\,{\ddot{x}_{6}} - m_{7}\,r_{7}\,\cos({\theta_{7}}
)\,{{\dot{\theta}_{7}}}^2 - m_{7}\,r_{7}\,\sin({\theta_{7}})\,{
\ddot{\theta}_{7}} \]
\[ LL(y_{2}) = m_{3}\,{\ddot{y}_{2}} - m_{3}\,r_{3}\,\sin({\theta_{3}}
)\,{{\dot{\theta}_{3}}}^2 + m_{3}\,r_{3}\,\cos({\theta_{3}})\,{
\ddot{\theta}_{3}} + m_{3}\,g \]
\begin{eqnarray*} LL({\theta_{8}}) &=& -m_{8}\,r_{8}\,\sin({\theta_{8}
})\,{\ddot{x}_{7}} + m_{8}\,{r_{8}}^2\,{\ddot{\theta}_{8}} + m_{8}\,r
_{8}\,\cos({\theta_{8}})\,{\ddot{y}_{7}} + J_{8}\,{\ddot{\theta}_{8}}
 \\ &&\quad\mbox{} + m_{8}\,g\,r_{8}\,\cos({\theta_{8}})
 \end{eqnarray*}
\[ LL(y_{10}) = 0 \]
$mrc_k=m_k r_k \cos(\theta_k)$
$mrs_k=m_k r_k \sin(\theta_k)$
$M(q)\ddot{q}+C(q)\dot{q}^2 +R(q,\dot{q})$,M:
 
$$ \left( \begin{array}{cccccccccccccccccccccccccccccc} m_{2} & 0 & 0
 & 0 & 0 & -mrs_{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & m_{2} & 0 & 0 & 
0 & mrc_{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & m_{1}\,{r_{1}}^2+J_{
1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & m_{3} & 0 & 0
 & 0 & 0 & -mrs_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & m_{3} & 0 & 0 & 
0 & mrc_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 \cr -mrs_{2} & mrc_{2} & 0 & 0 & 0 & m_{2}\,
{r_{2}}^2+J_{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 
m_{4} & 0 & 0 & 0 & 0 & -mrs_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & m
_{4} & 0 & 0 & 0 & mrc_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & -mrs_{3} & mrc_{3} & 0 & 
0 & 0 & m_{3}\,{r_{3}}^2+J_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & m_{5} & 0 & 0 & 0 & 0 & -mrs_{5} & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & m_{5} & 0 & 0 & 0 & mrc_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & -mrs_{4} & 
mrc_{4} & 0 & 0 & 0 & m_{4}\,{r_{4}}^2+J_{4} & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{6} & 0 & 0 & 0 & 0 & -mrs_{6} & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{6} & 0 & 0 & 0 & mrc_{6} & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & -mrs_{5} & mrc_{5} & 0 & 0 & 0 & m_{5}\,{r_{5}}^2+J_{5} & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{7} & 0 & 0 & 0 & 0 & -
mrs_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{7} & 0 & 0 & 0 & mrc_{7}
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & -mrs_{6} & mrc_{6} & 0 & 0 & 0 & m_{6}\,{r_{6}}^2+J
_{6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{8} & 0
 & 0 & 0 & 0 & -mrs_{8} & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{8} & 0
 & 0 & 0 & mrc_{8} & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -mrs_{7} & mrc_{7} & 0 & 0 & 0
 & m_{7}\,{r_{7}}^2+J_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & m_{9} & 0 & 0 & 0 & 0 & -mrs_{9} & 0 & 0 & 0 \cr 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & m_{9} & 0 & 0 & 0 & mrc_{9} & 0 & 0 & 0 \cr 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -mrs_{8} & 
mrc_{8} & 0 & 0 & 0 & m_{8}\,{r_{8}}^2+J_{8} & 0 & 0 & 0 & 0 & 0 & 0
 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{10} & 0 & 0 & 0 & 0 & -mrs_{10} \cr 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{10} & 0 & 0 & 0 & mrc_{10} \cr 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & -mrs_{9} & mrc_{9} & 0 & 0 & 0 & m_{9}\,{r_{9}}^2+J_{9} & 0
 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & -mrs_{10} & mrc_{10} & 0 & 0 & 0 & m_{10}\,{r_{10}}^2+J_{10}
 \end{array} \right) $$
C~:
 
$$ \left( \begin{array}{cccccccccccccccccccccccccccccc} 0 & 0 & 0 & 0
 & 0 & -m_{2}\,r_{2}\,\cos({\theta_{2}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 \cr 0 & 0 & 0 & 0 & 0 & -m_{2}\,r_{2}\,\sin({\theta_{2}}) & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{3}\,r_{3}\,\cos({\theta_{3}})
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{3}\,r_{3}\,
\sin({\theta_{3}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{4
}\,r_{4}\,\cos({\theta_{4}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & -m_{4}\,r_{4}\,\sin({\theta_{4}}) & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & -m_{5}\,r_{5}\,\cos({\theta_{5}}) & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{5}\,r_{5}\,\sin({\theta_{5}
}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{6}\,r_{6}\,\cos
({\theta_{6}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m
_{6}\,r_{6}\,\sin({\theta_{6}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & -m_{7}\,r_{7}\,\cos({\theta_{7}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & -m_{7}\,r_{7}\,\sin({\theta_{7}}) & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{8}\,r_{8}\,\cos({\theta_{8}})
 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{8}\,r_{8}\,\sin
({\theta_{8}}) & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{9}
\,r_{9}\,\cos({\theta_{9}}) & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & -m_{9}\,r_{9}\,\sin({\theta_{9}}) & 0 & 0 & 0 \cr 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & -m_{10}\,r_{10}\,\cos({\theta_{10}}) \cr 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{10}\,r_{10}\,\sin({
\theta_{10}}) \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 \end{array} \right) $$
R~:
 
$$ \left( \begin{array}{c} 0 \cr m_{2}\,g \cr m_{1}\,g\,r_{1}\,\cos({
\theta_{1}}) \cr 0 \cr m_{3}\,g \cr m_{2}\,g\,r_{2}\,\cos({\theta_{2}}
) \cr 0 \cr m_{4}\,g \cr m_{3}\,g\,r_{3}\,\cos({\theta_{3}}) \cr 0
 \cr m_{5}\,g \cr m_{4}\,g\,r_{4}\,\cos({\theta_{4}}) \cr 0 \cr m_{6}
\,g \cr m_{5}\,g\,r_{5}\,\cos({\theta_{5}}) \cr 0 \cr m_{7}\,g \cr m_{
6}\,g\,r_{6}\,\cos({\theta_{6}}) \cr 0 \cr m_{8}\,g \cr m_{7}\,g\,r_{7
}\,\cos({\theta_{7}}) \cr 0 \cr m_{9}\,g \cr m_{8}\,g\,r_{8}\,\cos({
\theta_{8}}) \cr 0 \cr m_{10}\,g \cr m_{9}\,g\,r_{9}\,\cos({\theta_{9}
}) \cr 0 \cr 0 \cr m_{10}\,g\,r_{10}\,\cos({\theta_{10}})
 \end{array} \right) $$
Constraints 
 
\[ x_{1} - 2\,r_{1}\,\cos({\theta_{1}}) \]
\[ y_{1} - 2\,r_{1}\,\sin({\theta_{1}}) \]
\[ x_{2} - x_{1} - 2\,r_{2}\,\cos({\theta_{2}}) \]
\[ y_{2} - y_{1} - 2\,r_{2}\,\sin({\theta_{2}}) \]
\[ x_{3} - x_{2} - 2\,r_{3}\,\cos({\theta_{3}}) \]
\[ y_{3} - y_{2} - 2\,r_{3}\,\sin({\theta_{3}}) \]
\[ x_{4} - x_{3} - 2\,r_{4}\,\cos({\theta_{4}}) \]
\[ y_{4} - y_{3} - 2\,r_{4}\,\sin({\theta_{4}}) \]
\[ x_{5} - x_{4} - 2\,r_{5}\,\cos({\theta_{5}}) \]
\[ y_{5} - y_{4} - 2\,r_{5}\,\sin({\theta_{5}}) \]
\[ x_{6} - x_{5} - 2\,r_{6}\,\cos({\theta_{6}}) \]
\[ y_{6} - y_{5} - 2\,r_{6}\,\sin({\theta_{6}}) \]
\[ x_{7} - x_{6} - 2\,r_{7}\,\cos({\theta_{7}}) \]
\[ y_{7} - y_{6} - 2\,r_{7}\,\sin({\theta_{7}}) \]
\[ x_{8} - x_{7} - 2\,r_{8}\,\cos({\theta_{8}}) \]
\[ y_{8} - y_{7} - 2\,r_{8}\,\sin({\theta_{8}}) \]
\[ x_{9} - x_{8} - 2\,r_{9}\,\cos({\theta_{9}}) \]
\[ y_{9} - y_{8} - 2\,r_{9}\,\sin({\theta_{9}}) \]
\[ x_{10} - x_{9} - 2\,r_{10}\,\cos({\theta_{10}}) \]
\[ y_{10} - y_{9} - 2\,r_{10}\,\sin({\theta_{10}}) \]
Time derivative of constraints : $A'(q)\dot{q}$
 
$$ \left( \begin{array}{cccccccccccccccccccccccccccccc} 1 & 0 & 2\,r_{
1}\,\sin({\theta_{1}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 1
 & -2\,r_{1}\,\cos({\theta_{1}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 \cr -1 & 0 & 0 & 1 & 0 & 2\,r_{2}\,\sin({\theta_{2}}) & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 \cr 0 & -1 & 0 & 0 & 1 & -2\,r_{2}\,\cos({\theta_{2}}
) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2\,r
_{3}\,\sin({\theta_{3}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & -1 & 0 & 
0 & 1 & -2\,r_{3}\,\cos({\theta_{3}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0
 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2\,r_{4}\,\sin({\theta_{4}}) & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0
 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & -2\,r_{4}\,\cos({\theta_{4
}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2\,
r_{5}\,\sin({\theta_{5}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 
0 & 1 & -2\,r_{5}\,\cos({\theta_{5}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2\,r_{6}\,\sin({\theta_{6}}) & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & -2\,r_{6}\,\cos({\theta_{6
}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2
\,r_{7}\,\sin({\theta_{7}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0
 & 0 & 1 & -2\,r_{7}\,\cos({\theta_{7}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2\,r_{8}\,\sin({\theta_{8}}) & 0
 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & -2\,r_{8}\,\cos({
\theta_{8}}) & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1
 & 0 & 2\,r_{9}\,\sin({\theta_{9}}) & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & -1 & 0 & 0 & 1 & -2\,r_{9}\,\cos({\theta_{9}}) & 0 & 0 & 0 \cr 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2\,r_{10}\,\sin({\theta_{
10}}) \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & -2\,r_{10}\,
\cos({\theta_{10}}) \end{array} \right) $$
N-pendulum energy~:
 
\begin{eqnarray*} && \frac{m_{1}\left({r_{1}}^2\,{\sin({\theta_{1}})}^
2\,{{\dot{\theta}_{1}}}^2+{r_{1}}^2\,{\cos({\theta_{1}})}^2\,{{
\dot{\theta}_{1}}}^2\right)}{2} + \frac{J_{1}\,{{\dot{\theta}_{1}}}^2
}{2} + \frac{J_{2}\,{{\dot{\theta}_{2}}}^2}{2} \\ &&\quad\mbox{} + 
\frac{J_{3}\,{{\dot{\theta}_{3}}}^2}{2} + \frac{J_{4}\,{{\dot{\theta}
_{4}}}^2}{2} + \frac{J_{5}\,{{\dot{\theta}_{5}}}^2}{2} + \frac{J_{6}\,
{{\dot{\theta}_{6}}}^2}{2} + \frac{J_{7}\,{{\dot{\theta}_{7}}}^2}{2}
 + \frac{J_{8}\,{{\dot{\theta}_{8}}}^2}{2} \\ &&\quad\mbox{} + \frac{J
_{9}\,{{\dot{\theta}_{9}}}^2}{2} + \frac{J_{10}\,{{\dot{\theta}_{10}}}
^2}{2} + m_{1}\,g\,r_{1}\,\sin({\theta_{1}}) \\ &&\quad\mbox{} + 
\frac{m_{2}\left(\left(-2\,r_{1}\,\sin({\theta_{1}})\,{\dot{\theta}_{1
}}-r_{2}\,\sin({\theta_{2}})\,{\dot{\theta}_{2}}\right)^2+\left(2\,r_{
1}\,\cos({\theta_{1}})\,{\dot{\theta}_{1}}+r_{2}\,\cos({\theta_{2}})\,
{\dot{\theta}_{2}}\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{m_{3}
\left(\left(-2\,r_{1}\,\sin({\theta_{1}})\,{\dot{\theta}_{1}}-2\,r_{2}
\,\sin({\theta_{2}})\,{\dot{\theta}_{2}}-r_{3}\,\sin({\theta_{3}})\,{
\dot{\theta}_{3}}\right)^2+\left(2\,r_{1}\,\cos({\theta_{1}})\,{
\dot{\theta}_{1}}+2\,r_{2}\,\cos({\theta_{2}})\,{\dot{\theta}_{2}}+r_{
3}\,\cos({\theta_{3}})\,{\dot{\theta}_{3}}\right)^2\right)}{2}
 \\ &&\quad\mbox{} + \frac{m_{4}\left(\left(-2\,r_{3}\,\sin({\theta_{3
}})\,{\dot{\theta}_{3}}-2\,r_{1}\,\sin({\theta_{1}})\,{\dot{\theta}_{1
}}-2\,r_{2}\,\sin({\theta_{2}})\,{\dot{\theta}_{2}}-r_{4}\,\sin({
\theta_{4}})\,{\dot{\theta}_{4}}\right)^2+\left(2\,r_{3}\,\cos({\theta
_{3}})\,{\dot{\theta}_{3}}+2\,r_{1}\,\cos({\theta_{1}})\,{\dot{\theta}
_{1}}+2\,r_{2}\,\cos({\theta_{2}})\,{\dot{\theta}_{2}}+r_{4}\,\cos({
\theta_{4}})\,{\dot{\theta}_{4}}\right)^2\right)}{2} \\ &&\quad\mbox{}
 + \frac{m_{5}\left(\left(-2\,r_{1}\,\sin({\theta_{1}})\,{\dot{\theta}
_{1}}-2\,r_{3}\,\sin({\theta_{3}})\,{\dot{\theta}_{3}}-2\,r_{2}\,\sin(
{\theta_{2}})\,{\dot{\theta}_{2}}-2\,r_{4}\,\sin({\theta_{4}})\,{
\dot{\theta}_{4}}-r_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5}}\right)
^2+\left(2\,r_{3}\,\cos({\theta_{3}})\,{\dot{\theta}_{3}}+2\,r_{4}\,
\cos({\theta_{4}})\,{\dot{\theta}_{4}}+2\,r_{1}\,\cos({\theta_{1}})\,{
\dot{\theta}_{1}}+2\,r_{2}\,\cos({\theta_{2}})\,{\dot{\theta}_{2}}+r_{
5}\,\cos({\theta_{5}})\,{\dot{\theta}_{5}}\right)^2\right)}{2}
 \\ &&\quad\mbox{} + m_{6}\,g\left(2\,r_{1}\,\sin({\theta_{1}})+2\,r_{
5}\,\sin({\theta_{5}})+2\,r_{3}\,\sin({\theta_{3}})+2\,r_{2}\,\sin({
\theta_{2}})+2\,r_{4}\,\sin({\theta_{4}})+r_{6}\,\sin({\theta_{6}})
\right) \\ &&\quad\mbox{} + m_{8}\,g\left(2\,r_{7}\,\sin({\theta_{7}})
+2\,r_{1}\,\sin({\theta_{1}})+2\,r_{6}\,\sin({\theta_{6}})+2\,r_{5}\,
\sin({\theta_{5}})+2\,r_{3}\,\sin({\theta_{3}})+2\,r_{2}\,\sin({\theta
_{2}})+2\,r_{4}\,\sin({\theta_{4}})+r_{8}\,\sin({\theta_{8}})\right)
 \\ &&\quad\mbox{} + m_{9}\,g\left(2\,r_{7}\,\sin({\theta_{7}})+2\,r_{
8}\,\sin({\theta_{8}})+2\,r_{1}\,\sin({\theta_{1}})+2\,r_{6}\,\sin({
\theta_{6}})+2\,r_{5}\,\sin({\theta_{5}})+2\,r_{3}\,\sin({\theta_{3}})
+2\,r_{2}\,\sin({\theta_{2}})+2\,r_{4}\,\sin({\theta_{4}})+r_{9}\,\sin
({\theta_{9}})\right) \\ &&\quad\mbox{} + m_{10}\,g\left(2\,r_{7}\,
\sin({\theta_{7}})+2\,r_{9}\,\sin({\theta_{9}})+2\,r_{8}\,\sin({\theta
_{8}})+2\,r_{1}\,\sin({\theta_{1}})+2\,r_{6}\,\sin({\theta_{6}})+2\,r
_{5}\,\sin({\theta_{5}})+2\,r_{3}\,\sin({\theta_{3}})+2\,r_{2}\,\sin({
\theta_{2}})+2\,r_{4}\,\sin({\theta_{4}})+r_{10}\,\sin({\theta_{10}})
\right) \\ &&\quad\mbox{} + m_{7}\,g\left(2\,r_{1}\,\sin({\theta_{1}})
+2\,r_{6}\,\sin({\theta_{6}})+2\,r_{5}\,\sin({\theta_{5}})+2\,r_{3}\,
\sin({\theta_{3}})+2\,r_{2}\,\sin({\theta_{2}})+2\,r_{4}\,\sin({\theta
_{4}})+r_{7}\,\sin({\theta_{7}})\right) \\ &&\quad\mbox{} + m_{3}\,g
\left(2\,r_{1}\,\sin({\theta_{1}})+2\,r_{2}\,\sin({\theta_{2}})+r_{3}
\,\sin({\theta_{3}})\right) \\ &&\quad\mbox{} + m_{4}\,g\left(2\,r_{3}
\,\sin({\theta_{3}})+2\,r_{1}\,\sin({\theta_{1}})+2\,r_{2}\,\sin({
\theta_{2}})+r_{4}\,\sin({\theta_{4}})\right) \\ &&\quad\mbox{} + m_{5
}\,g\left(2\,r_{1}\,\sin({\theta_{1}})+2\,r_{3}\,\sin({\theta_{3}})+2
\,r_{2}\,\sin({\theta_{2}})+2\,r_{4}\,\sin({\theta_{4}})+r_{5}\,\sin({
\theta_{5}})\right) \\ &&\quad\mbox{} + m_{2}\,g\left(2\,r_{1}\,\sin({
\theta_{1}})+r_{2}\,\sin({\theta_{2}})\right) \\ &&\quad\mbox{} + 
\frac{m_{10}\left(\left(-2\,r_{7}\,\sin({\theta_{7}})\,{\dot{\theta}_{
7}}-2\,r_{9}\,\sin({\theta_{9}})\,{\dot{\theta}_{9}}-2\,r_{8}\,\sin({
\theta_{8}})\,{\dot{\theta}_{8}}-2\,r_{1}\,\sin({\theta_{1}})\,{
\dot{\theta}_{1}}-2\,r_{6}\,\sin({\theta_{6}})\,{\dot{\theta}_{6}}-2\,
r_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5}}-2\,r_{3}\,\sin({\theta_{
3}})\,{\dot{\theta}_{3}}-2\,r_{2}\,\sin({\theta_{2}})\,{\dot{\theta}_{
2}}-2\,r_{4}\,\sin({\theta_{4}})\,{\dot{\theta}_{4}}-r_{10}\,\sin({
\theta_{10}})\,{\dot{\theta}_{10}}\right)^2+\left(2\,r_{7}\,\cos({
\theta_{7}})\,{\dot{\theta}_{7}}+2\,r_{9}\,\cos({\theta_{9}})\,{
\dot{\theta}_{9}}+2\,r_{8}\,\cos({\theta_{8}})\,{\dot{\theta}_{8}}+2\,
r_{1}\,\cos({\theta_{1}})\,{\dot{\theta}_{1}}+2\,r_{6}\,\cos({\theta_{
6}})\,{\dot{\theta}_{6}}+2\,r_{3}\,\cos({\theta_{3}})\,{\dot{\theta}_{
3}}+2\,r_{4}\,\cos({\theta_{4}})\,{\dot{\theta}_{4}}+2\,r_{2}\,\cos({
\theta_{2}})\,{\dot{\theta}_{2}}+2\,r_{5}\,\cos({\theta_{5}})\,{
\dot{\theta}_{5}}+r_{10}\,\cos({\theta_{10}})\,{\dot{\theta}_{10}}
\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{m_{7}\left(\left(-2\,r
_{1}\,\sin({\theta_{1}})\,{\dot{\theta}_{1}}-2\,r_{6}\,\sin({\theta_{6
}})\,{\dot{\theta}_{6}}-2\,r_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5
}}-2\,r_{3}\,\sin({\theta_{3}})\,{\dot{\theta}_{3}}-2\,r_{2}\,\sin({
\theta_{2}})\,{\dot{\theta}_{2}}-2\,r_{4}\,\sin({\theta_{4}})\,{
\dot{\theta}_{4}}-r_{7}\,\sin({\theta_{7}})\,{\dot{\theta}_{7}}\right)
^2+\left(2\,r_{1}\,\cos({\theta_{1}})\,{\dot{\theta}_{1}}+2\,r_{6}\,
\cos({\theta_{6}})\,{\dot{\theta}_{6}}+2\,r_{3}\,\cos({\theta_{3}})\,{
\dot{\theta}_{3}}+2\,r_{4}\,\cos({\theta_{4}})\,{\dot{\theta}_{4}}+2\,
r_{2}\,\cos({\theta_{2}})\,{\dot{\theta}_{2}}+2\,r_{5}\,\cos({\theta_{
5}})\,{\dot{\theta}_{5}}+r_{7}\,\cos({\theta_{7}})\,{\dot{\theta}_{7}}
\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{m_{8}\left(\left(-2\,r
_{7}\,\sin({\theta_{7}})\,{\dot{\theta}_{7}}-2\,r_{1}\,\sin({\theta_{1
}})\,{\dot{\theta}_{1}}-2\,r_{6}\,\sin({\theta_{6}})\,{\dot{\theta}_{6
}}-2\,r_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5}}-2\,r_{3}\,\sin({
\theta_{3}})\,{\dot{\theta}_{3}}-2\,r_{2}\,\sin({\theta_{2}})\,{
\dot{\theta}_{2}}-2\,r_{4}\,\sin({\theta_{4}})\,{\dot{\theta}_{4}}-r_{
8}\,\sin({\theta_{8}})\,{\dot{\theta}_{8}}\right)^2+\left(2\,r_{7}\,
\cos({\theta_{7}})\,{\dot{\theta}_{7}}+2\,r_{1}\,\cos({\theta_{1}})\,{
\dot{\theta}_{1}}+2\,r_{6}\,\cos({\theta_{6}})\,{\dot{\theta}_{6}}+2\,
r_{3}\,\cos({\theta_{3}})\,{\dot{\theta}_{3}}+2\,r_{4}\,\cos({\theta_{
4}})\,{\dot{\theta}_{4}}+2\,r_{2}\,\cos({\theta_{2}})\,{\dot{\theta}_{
2}}+2\,r_{5}\,\cos({\theta_{5}})\,{\dot{\theta}_{5}}+r_{8}\,\cos({
\theta_{8}})\,{\dot{\theta}_{8}}\right)^2\right)}{2} \\ &&\quad\mbox{}
 + \frac{m_{9}\left(\left(-2\,r_{7}\,\sin({\theta_{7}})\,{\dot{\theta}
_{7}}-2\,r_{8}\,\sin({\theta_{8}})\,{\dot{\theta}_{8}}-2\,r_{1}\,\sin(
{\theta_{1}})\,{\dot{\theta}_{1}}-2\,r_{6}\,\sin({\theta_{6}})\,{
\dot{\theta}_{6}}-2\,r_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5}}-2\,
r_{3}\,\sin({\theta_{3}})\,{\dot{\theta}_{3}}-2\,r_{2}\,\sin({\theta_{
2}})\,{\dot{\theta}_{2}}-2\,r_{4}\,\sin({\theta_{4}})\,{\dot{\theta}_{
4}}-r_{9}\,\sin({\theta_{9}})\,{\dot{\theta}_{9}}\right)^2+\left(2\,r
_{7}\,\cos({\theta_{7}})\,{\dot{\theta}_{7}}+2\,r_{8}\,\cos({\theta_{8
}})\,{\dot{\theta}_{8}}+2\,r_{1}\,\cos({\theta_{1}})\,{\dot{\theta}_{1
}}+2\,r_{6}\,\cos({\theta_{6}})\,{\dot{\theta}_{6}}+2\,r_{3}\,\cos({
\theta_{3}})\,{\dot{\theta}_{3}}+2\,r_{4}\,\cos({\theta_{4}})\,{
\dot{\theta}_{4}}+2\,r_{2}\,\cos({\theta_{2}})\,{\dot{\theta}_{2}}+2\,
r_{5}\,\cos({\theta_{5}})\,{\dot{\theta}_{5}}+r_{9}\,\cos({\theta_{9}}
)\,{\dot{\theta}_{9}}\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{m
_{6}\left(\left(-2\,r_{1}\,\sin({\theta_{1}})\,{\dot{\theta}_{1}}-2\,r
_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5}}-2\,r_{3}\,\sin({\theta_{3
}})\,{\dot{\theta}_{3}}-2\,r_{2}\,\sin({\theta_{2}})\,{\dot{\theta}_{2
}}-2\,r_{4}\,\sin({\theta_{4}})\,{\dot{\theta}_{4}}-r_{6}\,\sin({
\theta_{6}})\,{\dot{\theta}_{6}}\right)^2+\left(2\,r_{1}\,\cos({\theta
_{1}})\,{\dot{\theta}_{1}}+2\,r_{3}\,\cos({\theta_{3}})\,{\dot{\theta}
_{3}}+2\,r_{4}\,\cos({\theta_{4}})\,{\dot{\theta}_{4}}+2\,r_{2}\,\cos(
{\theta_{2}})\,{\dot{\theta}_{2}}+2\,r_{5}\,\cos({\theta_{5}})\,{
\dot{\theta}_{5}}+r_{6}\,\cos({\theta_{6}})\,{\dot{\theta}_{6}}\right)
^2\right)}{2} \end{eqnarray*}
$\dot{q}=S(q)\eta$ Kernel of $A(q)'$~:
 
$$ \left( \begin{array}{cccccccccc} -2\,r_{1}\,\sin({\theta_{1}}) & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
 & 0 \cr -2\,r_{1}\,\sin({\theta_{1}}) & -2\,r_{2}\,\sin({\theta_{2}})
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2
\,r_{2}\,\cos({\theta_{2}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 1
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr -2\,r_{1}\,\sin({\theta_{1}}) & -
2\,r_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta_{3}}) & 0 & 0
 & 0 & 0 & 0 & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2\,r_{2}\,\cos
({\theta_{2}}) & 2\,r_{3}\,\cos({\theta_{3}}) & 0 & 0 & 0 & 0 & 0 & 0
 & 0 \cr 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr -2\,r_{1}\,\sin({
\theta_{1}}) & -2\,r_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta
_{3}}) & -2\,r_{4}\,\sin({\theta_{4}}) & 0 & 0 & 0 & 0 & 0 & 0 \cr 2\,
r_{1}\,\cos({\theta_{1}}) & 2\,r_{2}\,\cos({\theta_{2}}) & 2\,r_{3}\,
\cos({\theta_{3}}) & 2\,r_{4}\,\cos({\theta_{4}}) & 0 & 0 & 0 & 0 & 0
 & 0 \cr 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \cr -2\,r_{1}\,\sin({
\theta_{1}}) & -2\,r_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta
_{3}}) & -2\,r_{4}\,\sin({\theta_{4}}) & -2\,r_{5}\,\sin({\theta_{5}})
 & 0 & 0 & 0 & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2\,r_{2}\,\cos
({\theta_{2}}) & 2\,r_{3}\,\cos({\theta_{3}}) & 2\,r_{4}\,\cos({\theta
_{4}}) & 2\,r_{5}\,\cos({\theta_{5}}) & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 
0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \cr -2\,r_{1}\,\sin({\theta_{1}}) & -2\,
r_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta_{3}}) & -2\,r_{4}
\,\sin({\theta_{4}}) & -2\,r_{5}\,\sin({\theta_{5}}) & -2\,r_{6}\,\sin
({\theta_{6}}) & 0 & 0 & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2\,r
_{2}\,\cos({\theta_{2}}) & 2\,r_{3}\,\cos({\theta_{3}}) & 2\,r_{4}\,
\cos({\theta_{4}}) & 2\,r_{5}\,\cos({\theta_{5}}) & 2\,r_{6}\,\cos({
\theta_{6}}) & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0
 \cr -2\,r_{1}\,\sin({\theta_{1}}) & -2\,r_{2}\,\sin({\theta_{2}}) & -
2\,r_{3}\,\sin({\theta_{3}}) & -2\,r_{4}\,\sin({\theta_{4}}) & -2\,r_{
5}\,\sin({\theta_{5}}) & -2\,r_{6}\,\sin({\theta_{6}}) & -2\,r_{7}\,
\sin({\theta_{7}}) & 0 & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2\,r
_{2}\,\cos({\theta_{2}}) & 2\,r_{3}\,\cos({\theta_{3}}) & 2\,r_{4}\,
\cos({\theta_{4}}) & 2\,r_{5}\,\cos({\theta_{5}}) & 2\,r_{6}\,\cos({
\theta_{6}}) & 2\,r_{7}\,\cos({\theta_{7}}) & 0 & 0 & 0 \cr 0 & 0 & 0
 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \cr -2\,r_{1}\,\sin({\theta_{1}}) & -2\,r
_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta_{3}}) & -2\,r_{4}\,
\sin({\theta_{4}}) & -2\,r_{5}\,\sin({\theta_{5}}) & -2\,r_{6}\,\sin({
\theta_{6}}) & -2\,r_{7}\,\sin({\theta_{7}}) & -2\,r_{8}\,\sin({\theta
_{8}}) & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2\,r_{2}\,\cos({
\theta_{2}}) & 2\,r_{3}\,\cos({\theta_{3}}) & 2\,r_{4}\,\cos({\theta_{
4}}) & 2\,r_{5}\,\cos({\theta_{5}}) & 2\,r_{6}\,\cos({\theta_{6}}) & 2
\,r_{7}\,\cos({\theta_{7}}) & 2\,r_{8}\,\cos({\theta_{8}}) & 0 & 0
 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \cr -2\,r_{1}\,\sin({\theta
_{1}}) & -2\,r_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta_{3}})
 & -2\,r_{4}\,\sin({\theta_{4}}) & -2\,r_{5}\,\sin({\theta_{5}}) & -2
\,r_{6}\,\sin({\theta_{6}}) & -2\,r_{7}\,\sin({\theta_{7}}) & -2\,r_{8
}\,\sin({\theta_{8}}) & -2\,r_{9}\,\sin({\theta_{9}}) & 0 \cr 2\,r_{1}
\,\cos({\theta_{1}}) & 2\,r_{2}\,\cos({\theta_{2}}) & 2\,r_{3}\,\cos({
\theta_{3}}) & 2\,r_{4}\,\cos({\theta_{4}}) & 2\,r_{5}\,\cos({\theta_{
5}}) & 2\,r_{6}\,\cos({\theta_{6}}) & 2\,r_{7}\,\cos({\theta_{7}}) & 2
\,r_{8}\,\cos({\theta_{8}}) & 2\,r_{9}\,\cos({\theta_{9}}) & 0 \cr 0
 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \cr -2\,r_{1}\,\sin({\theta_{1}})
 & -2\,r_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta_{3}}) & -2
\,r_{4}\,\sin({\theta_{4}}) & -2\,r_{5}\,\sin({\theta_{5}}) & -2\,r_{6
}\,\sin({\theta_{6}}) & -2\,r_{7}\,\sin({\theta_{7}}) & -2\,r_{8}\,
\sin({\theta_{8}}) & -2\,r_{9}\,\sin({\theta_{9}}) & -2\,r_{10}\,\sin(
{\theta_{10}}) \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2\,r_{2}\,\cos({
\theta_{2}}) & 2\,r_{3}\,\cos({\theta_{3}}) & 2\,r_{4}\,\cos({\theta_{
4}}) & 2\,r_{5}\,\cos({\theta_{5}}) & 2\,r_{6}\,\cos({\theta_{6}}) & 2
\,r_{7}\,\cos({\theta_{7}}) & 2\,r_{8}\,\cos({\theta_{8}}) & 2\,r_{9}
\,\cos({\theta_{9}}) & 2\,r_{10}\,\cos({\theta_{10}}) \cr 0 & 0 & 0 & 
0 & 0 & 0 & 0 & 0 & 0 & 1 \end{array} \right) $$
$S(q)^T E$ simplified with $\dot{q}=S(q)\eta $
 
\begin{eqnarray*} && m_{8}\,g\,r_{8}\,\cos({\theta_{8}}) + 4\,{r_{8}}^
2\,m_{9}\,{\dot{\eta}_{8}} + 2\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,g
 + 2\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,g \\ &&\quad\mbox{} + 4\,r_{8}
\,\sin({\theta_{8}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^
2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{
\dot{\eta}_{9}} \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{
10}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{8}\,\sin({
\theta_{8}})\,m_{10}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{6}\,\cos
({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}
\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} - 4\,r
_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1
}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{1}\,\cos({\theta_{1}}
)\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,
m_{10}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{8}\,\cos({
\theta_{8}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{2}\,\sin
({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}
\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r
_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4
}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{4}\,\cos({\theta_{4}}
)\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,
m_{10}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{8}\,\cos({
\theta_{8}})\,m_{10}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{9}\,\sin
({\theta_{9}})\,{{\eta_{9}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}
\,r_{9}\,\cos({\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} - 4\,r
_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7
}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})
\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m
_{9}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{8}\,\cos({
\theta_{8}})\,m_{9}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}}
 \\ &&\quad\mbox{} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r_{1}\,\cos(
{\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r
_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 2\,m_{8
}\,r_{8}\,\sin({\theta_{8}})\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^
2 + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r_{4}\,\sin({\theta_{4}})\,{
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}}
)\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 2\,m_{8}\,r_{8}\,\sin({
\theta_{8}})\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r_{2}\,\cos(
{\theta_{2}})\,{{\eta_{2}}}^2 + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r
_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 2\,m_{8
}\,r_{8}\,\cos({\theta_{8}})\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^
2 + 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,r_{5}\,\cos({\theta_{5}})\,{
\dot{\eta}_{5}} \\ &&\quad\mbox{} - 2\,m_{8}\,r_{8}\,\cos({\theta_{8}}
)\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 2\,m_{8}\,r_{8}\,\cos({
\theta_{8}})\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} - 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,r_{6}\,\sin(
{\theta_{6}})\,{{\eta_{6}}}^2 + 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,r
_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{8
}\,\sin({\theta_{8}})\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}
^2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,
{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{
10}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{8}\,\sin({
\theta_{8}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{3}\,\cos
({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}
\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r
_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2
}}}^2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{2}\,\sin({\theta_{2}}
)\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,
m_{10}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{8}\,\sin({
\theta_{8}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{6}\,\sin
({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}
\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r
_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{
\dot{\eta}_{7}} + 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,r_{2}\,\cos({
\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 2\,m_{8}\,r_{8}\,
\cos({\theta_{8}})\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 + 2\,m_{
8}\,r_{8}\,\cos({\theta_{8}})\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}
_{4}} \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{5}
\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 2\,m_{8}\,r_{8}\,\sin({\theta
_{8}})\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 
4\,r_{8}\,\sin({\theta_{8}})\,m_{9}\,r_{7}\,\sin({\theta_{7}})\,{
\dot{\eta}_{7}} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{9}\,r_{2}\,\cos({
\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({
\theta_{8}})\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} + 4\,
r_{8}\,\sin({\theta_{8}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5
}}}^2 \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{9}\,r_{6}\,
\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{
9}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} - 4
\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})\,{{\eta
_{1}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{1}\,\cos({\theta_{1
}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})
\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{8}\,\cos({
\theta_{8}})\,m_{9}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{2}\,\sin(
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r
_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{8
}\,\cos({\theta_{8}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^
2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})\,{
\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m_{9
}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{8}\,\cos({\theta
_{8}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{7}\,\sin(
{\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{9}\,r
_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{8
}\,\sin({\theta_{8}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^
2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})\,{
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{9
}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{8}\,\sin({\theta
_{8}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r_{5}\,\sin(
{\theta_{5}})\,{\dot{\eta}_{5}} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})
\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 2\,m_{
8}\,r_{8}\,\sin({\theta_{8}})\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}
_{7}} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r_{6}\,\cos({\theta_{6}})
\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}
})\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} - 2\,m_{8}\,r_{8}\,
\cos({\theta_{8}})\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,r_{1}\,\cos(
{\theta_{1}})\,{\dot{\eta}_{1}} - 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 2\,m_{
8}\,r_{8}\,\cos({\theta_{8}})\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}
_{3}} - 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,r_{2}\,\sin({\theta_{2}})
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{
9}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{8}\,\sin({
\theta_{8}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + J_{8}
\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,{r_{8}}^2\,m_{10}\,{
\dot{\eta}_{8}} + m_{8}\,{r_{8}}^2\,{\dot{\eta}_{8}} + 2\,r_{8}\,\sin(
{\theta_{8}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}}
 \\ &&\quad\mbox{} + 2\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{9}\,\cos(
{\theta_{9}})\,{\dot{\eta}_{9}} + 2\,r_{8}\,\sin({\theta_{8}})\,m_{10}
\,r_{10}\,\sin({\theta_{10}})\,{\dot{\eta}_{10}} \\ &&\quad\mbox{} + 2
\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{
\dot{\eta}_{10}} + 2\,r_{8}\,\sin({\theta_{8}})\,m_{9}\,r_{9}\,\cos({
\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} - 2\,r_{8}\,\cos({
\theta_{8}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 + 2\,r
_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{{\eta
_{10}}}^2 \\ &&\quad\mbox{} - 2\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r
_{10}\,\sin({\theta_{10}})\,{{\eta_{10}}}^2 \end{eqnarray*}
\begin{eqnarray*} && m_{3}\,g\,r_{3}\,\cos({\theta_{3}}) + 2\,r_{3}\,
\cos({\theta_{3}})\,m_{5}\,g + 2\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,g
 + 2\,r_{3}\,\cos({\theta_{3}})\,m_{4}\,g + 2\,r_{3}\,\cos({\theta_{3}
})\,m_{10}\,g \\ &&\quad\mbox{} + 2\,r_{3}\,\cos({\theta_{3}})\,m_{8}
\,g + 2\,r_{3}\,\cos({\theta_{3}})\,m_{6}\,g + 2\,r_{3}\,\cos({\theta
_{3}})\,m_{7}\,g + 4\,{r_{3}}^2\,m_{8}\,{\dot{\eta}_{3}} + 4\,{r_{3}}^
2\,m_{6}\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,{r_{3}}^2\,m_{9}\,{
\dot{\eta}_{3}} + 4\,{r_{3}}^2\,m_{5}\,{\dot{\eta}_{3}} + 4\,{r_{3}}^2
\,m_{7}\,{\dot{\eta}_{3}} + 4\,{r_{3}}^2\,m_{4}\,{\dot{\eta}_{3}} + J
_{3}\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,{r_{3}}^2\,m_{10}\,{
\dot{\eta}_{3}} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{6}\,r_{2}\,\sin({
\theta_{2}})\,{\dot{\eta}_{2}} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{7}\,
r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{
3}\,\sin({\theta_{3}})\,m_{7}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}
^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{7}\,r_{5}\,\sin({\theta_{5}})\,{
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{7
}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{3}\,\sin({\theta
_{3}})\,m_{7}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}}
 \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{7}\,r_{1}\,\sin(
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{7}\,r
_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{3
}\,\cos({\theta_{3}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^
2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{7}\,r_{2}\,\cos({\theta_{2}})\,{
\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{7
}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\cos({\theta
_{3}})\,m_{7}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{7}\,r_{5}\,\sin(
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{7}\,r
_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{3
}\,\cos({\theta_{3}})\,m_{7}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^
2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{7}\,r_{6}\,\cos({\theta_{6}})\,{
\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8
}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{3}\,\sin({\theta
_{3}})\,m_{8}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}}
 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{4}\,\cos(
{\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r
_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{3
}\,\sin({\theta_{3}})\,m_{8}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^
2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{2}\,\sin({\theta_{2}})\,{
\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8
}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{3}\,\sin({\theta
_{3}})\,m_{8}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{6}\,r_{5}\,\cos(
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{6}\,r
_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{3
}\,\cos({\theta_{3}})\,m_{6}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^
2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{6}\,r_{1}\,\cos({\theta_{1}})\,{
\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{6
}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{3}\,\cos({\theta
_{3}})\,m_{6}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{6}\,r_{4}\,\sin(
{\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{6}\,r
_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{3
}\,\cos({\theta_{3}})\,m_{6}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^
2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{6}\,r_{5}\,\cos({\theta_{5}})\,{
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{7
}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{3}\,\sin({\theta
_{3}})\,m_{7}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}}
 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{7}\,r_{4}\,\cos(
{\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{7}\,r
_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{3
}\,\sin({\theta_{3}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^
2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{7}\,\sin({\theta_{7}})\,{
\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9
}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{3}\,\sin({\theta
_{3}})\,m_{9}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}}
 \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{8}\,\sin(
{\theta_{8}})\,{\dot{\eta}_{8}} + 2\,r_{3}\,\cos({\theta_{3}})\,m_{8}
\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r
_{3}\,\cos({\theta_{3}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{
\dot{\eta}_{9}} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{9}\,\sin({
\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({
\theta_{3}})\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{\dot{\eta}_{10}}
 + 2\,r_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,
{\dot{\eta}_{10}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m
_{4}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{3}\,\sin({
\theta_{3}})\,m_{4}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{8}\,r_{1}\,\cos(
{\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{8}
\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
3}\,\cos({\theta_{3}})\,m_{8}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
_{2}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{8}\,r_{4}\,\sin({\theta_{4}})
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{
8}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{3}\,\cos({
\theta_{3}})\,m_{8}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2
 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{8}\,r_{5}\,\cos(
{\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{8}
\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{
3}\,\cos({\theta_{3}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}
_{7}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{8}\,r_{6}\,\sin({\theta_{6}})
\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{
8}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} - 4\,r_{3}\,\cos({
\theta_{3}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,r_{1}\,\cos(
{\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}
\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
3}\,\cos({\theta_{3}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
_{2}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{
9}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} + 2\,m_{3}\,r_{3}\,
\sin({\theta_{3}})\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 2\,m_{3}\,r_{3}\,\sin({\theta_{3}})\,r_{1}\,\sin(
{\theta_{1}})\,{\dot{\eta}_{1}} + 2\,m_{3}\,r_{3}\,\sin({\theta_{3}})
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 2\,m_{
3}\,r_{3}\,\sin({\theta_{3}})\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
_{2}} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{4}\,r_{1}\,\cos({\theta_{1}})
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{
4}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{3}\,\cos({
\theta_{3}})\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}}
 \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{2}\,\sin
({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}
\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r
_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4
}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{4}\,\cos({\theta_{4}}
)\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,
m_{10}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{3}\,\cos({
\theta_{3}})\,m_{10}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{8}\,\sin
({\theta_{8}})\,{{\eta_{8}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}
\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} - 4\,r
_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9
}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{9}\,\cos({\theta_{9}}
)\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,
m_{10}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{3}\,\cos({
\theta_{3}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{6}\,\sin
({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}
\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r
_{3}\,\sin({\theta_{3}})\,m_{6}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}
}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{6}\,r_{1}\,\sin({\theta_{1}})
\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m
_{6}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\sin({
\theta_{3}})\,m_{6}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{6}\,r_{2}\,\cos(
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,r
_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{3
}\,\cos({\theta_{3}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^
2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{
\dot{\eta}_{8}} \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{9
}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{3}\,\cos({\theta
_{3}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,r_{6}\,\sin(
{\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,r
_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{3
}\,\sin({\theta_{3}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^
2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})\,{
\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9
}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\sin({\theta
_{3}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{2}\,\cos(
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9}\,r
_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{3
}\,\sin({\theta_{3}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^
2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{5}\,\sin({\theta_{5}})\,{
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9
}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 - 4\,r_{3}\,\cos({\theta
_{3}})\,m_{4}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{4}\,r_{1}\,\cos(
{\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{4}
\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
3}\,\cos({\theta_{3}})\,m_{4}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
_{2}} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{5}\,r_{1}\,\cos({\theta_{1}})
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{
5}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{3}\,\sin({
\theta_{3}})\,m_{5}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2
 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{5}\,r_{4}\,\sin(
{\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{5}
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
3}\,\sin({\theta_{3}})\,m_{5}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
_{2}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{5}\,r_{1}\,\sin({\theta_{1}})
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{
5}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{3}\,\cos({
\theta_{3}})\,m_{5}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2
 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{5}\,r_{2}\,\cos(
{\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{5}
\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{
3}\,\cos({\theta_{3}})\,m_{5}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}
_{4}} - 2\,m_{3}\,r_{3}\,\cos({\theta_{3}})\,r_{1}\,\sin({\theta_{1}})
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 2\,m_{3}\,r_{3}\,\cos({\theta_{3}
})\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} - 2\,m_{3}\,r_{3}\,
\cos({\theta_{3}})\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2
 \\ &&\quad\mbox{} + 2\,m_{3}\,r_{3}\,\cos({\theta_{3}})\,r_{2}\,\cos(
{\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}
\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} - 4\,r_{
3}\,\cos({\theta_{3}})\,m_{8}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}
^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{
{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}
\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{3}\,\sin({\theta
_{3}})\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2
 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{6}\,\sin
({\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8}
\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r
_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}
}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{6}\,\sin({\theta_{6}})
\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m
_{10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{3}\,\sin({
\theta_{3}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}}
 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{4}\,\cos
({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}
\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r
_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2
}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{2}\,\sin({\theta_{2}}
)\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,
m_{10}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{3}\,\sin({
\theta_{3}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{9}\,\cos
({\theta_{9}})\,{{\eta_{9}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}
\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 4\,r
_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8
}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{8}\,\sin({\theta_{8}}
)\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,
m_{10}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{3}\,\sin({
\theta_{3}})\,m_{7}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + m_{3}
\,{r_{3}}^2\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({
\theta_{3}})\,m_{9}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r
_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{
\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{4
}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 - 2\,r_{3}\,\cos({\theta
_{3}})\,m_{4}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
 \\ &&\quad\mbox{} - 2\,r_{3}\,\cos({\theta_{3}})\,m_{5}\,r_{5}\,\sin(
{\theta_{5}})\,{{\eta_{5}}}^2 + 2\,r_{3}\,\sin({\theta_{3}})\,m_{5}\,r
_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 2\,r_{3}
\,\sin({\theta_{3}})\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2
 - 2\,r_{3}\,\cos({\theta_{3}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,{{
\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{7}\,
r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 - 2\,r_{3}\,\cos({\theta_{3}
})\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{}
 - 2\,r_{3}\,\cos({\theta_{3}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{{
\eta_{8}}}^2 + 2\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{8}\,\cos({
\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} - 2\,r_{3}\,\cos({
\theta_{3}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 + 2\,r
_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}
}}^2 \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{10}
\,\cos({\theta_{10}})\,{{\eta_{10}}}^2 - 2\,r_{3}\,\cos({\theta_{3}})
\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{{\eta_{10}}}^2
 \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{4}\,r_{4}\,\sin(
{\theta_{4}})\,{\dot{\eta}_{4}} + 2\,r_{3}\,\cos({\theta_{3}})\,m_{4}
\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 2\,r
_{3}\,\cos({\theta_{3}})\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,{
\dot{\eta}_{5}} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{5}\,r_{5}\,\sin({
\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({
\theta_{3}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} + 2\,
r_{3}\,\cos({\theta_{3}})\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,{
\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{7
}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 2\,r_{3}\,\cos({
\theta_{3}})\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
 \end{eqnarray*}
\begin{eqnarray*} && 4\,{r_{6}}^2\,m_{7}\,{\dot{\eta}_{6}} + 4\,{r_{6}
}^2\,m_{10}\,{\dot{\eta}_{6}} + m_{6}\,g\,r_{6}\,\cos({\theta_{6}}) + 
4\,{r_{6}}^2\,m_{8}\,{\dot{\eta}_{6}} + 4\,{r_{6}}^2\,m_{9}\,{
\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r_{6}\,\cos({\theta_{6}})\,m_{9
}\,g + 2\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,g + 2\,r_{6}\,\cos({
\theta_{6}})\,m_{7}\,g + 2\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,g
 \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{1}\,\sin
({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10
}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r
_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{
\dot{\eta}_{4}} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{7}\,r_{3}\,\cos({
\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({
\theta_{6}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,
r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{
1}}}^2 + J_{6}\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r_{6}\,\sin({
\theta_{6}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}} + 2\,
r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,{
\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r_{6}\,\sin({\theta_{6}})\,m_{9
}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} + 2\,r_{6}\,\cos({
\theta_{6}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{\dot{\eta}_{9}}
 \\ &&\quad\mbox{} + 2\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{10}\,
\sin({\theta_{10}})\,{\dot{\eta}_{10}} + 2\,r_{6}\,\cos({\theta_{6}})
\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{\dot{\eta}_{10}}
 \\ &&\quad\mbox{} - 2\,r_{6}\,\cos({\theta_{6}})\,m_{7}\,r_{7}\,\sin(
{\theta_{7}})\,{{\eta_{7}}}^2 + 2\,r_{6}\,\sin({\theta_{6}})\,m_{7}\,r
_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 2\,r_{6}
\,\sin({\theta_{6}})\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2
 - 2\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{{
\eta_{8}}}^2 \\ &&\quad\mbox{} - 2\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,
r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 + 2\,r_{6}\,\sin({\theta_{6}
})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{}
 + 2\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,
{{\eta_{10}}}^2 - 2\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{10}\,\sin({
\theta_{10}})\,{{\eta_{10}}}^2 + m_{6}\,{r_{6}}^2\,{\dot{\eta}_{6}}
 \\ &&\quad\mbox{} + 2\,r_{6}\,\cos({\theta_{6}})\,m_{7}\,r_{7}\,\cos(
{\theta_{7}})\,{\dot{\eta}_{7}} + 2\,r_{6}\,\sin({\theta_{6}})\,m_{7}
\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r
_{6}\,\sin({\theta_{6}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}
}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})
\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m
_{7}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{6}\,\sin({
\theta_{6}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,r_{1}\,\cos(
{\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,r
_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{6
}\,\sin({\theta_{6}})\,m_{7}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^
2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{7}\,r_{1}\,\sin({\theta_{1}})\,{
\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{7
}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{6}\,\sin({\theta
_{6}})\,m_{7}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8}\,r_{1}\,\cos(
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8}\,r
_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{6
}\,\sin({\theta_{6}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^
2 - 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,{
{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}
\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{6}\,\cos({\theta
_{6}})\,m_{10}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{3}\,\cos
({\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{10
}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r
_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{
\dot{\eta}_{2}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{4}\,\sin({
\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({
\theta_{6}})\,m_{10}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} - 4
\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{{\eta
_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{
5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{6}\,\cos({\theta_{6}}
)\,m_{10}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{}
 + 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{
\dot{\eta}_{8}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{9}\,\sin({
\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({
\theta_{6}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{\dot{\eta}_{9}} - 4
\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{7}\,\sin({\theta_{7}})\,{{\eta
_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{
7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} - 4\,r_{6}\,\cos({\theta_{6}}
)\,m_{8}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{}
 + 4\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{1}\,\cos({\theta_{1}})\,{
\dot{\eta}_{1}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{3}\,\sin({
\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({
\theta_{6}})\,m_{8}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 4\,
r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2
}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{2}\,
\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{6}\,\cos({\theta_{6}})\,m
_{8}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4
\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})\,{
\dot{\eta}_{4}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{5}\,\sin({
\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({
\theta_{6}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} - 4\,
r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7
}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{7}\,
\cos({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{6}\,\sin({\theta_{6}})\,m
_{7}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4
\,r_{6}\,\sin({\theta_{6}})\,m_{7}\,r_{5}\,\sin({\theta_{5}})\,{
\dot{\eta}_{5}} + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,r_{4}\,\cos({
\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 2\,m_{6}\,r_{6}\,\sin
({\theta_{6}})\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 2\,m_{6}
\,r_{6}\,\sin({\theta_{6}})\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,r_{3}\,\sin(
{\theta_{3}})\,{\dot{\eta}_{3}} + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}})
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 2\,m_{
6}\,r_{6}\,\sin({\theta_{6}})\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
_{2}} + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,r_{5}\,\cos({\theta_{5}})
\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}
})\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{6}\,\cos({
\theta_{6}})\,m_{7}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{7}\,r_{1}\,\cos(
{\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{7}
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
6}\,\cos({\theta_{6}})\,m_{7}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}
_{3}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{
7}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{6}\,\cos({
\theta_{6}})\,m_{7}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{7}\,r_{4}\,\cos(
{\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{7}
\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{
6}\,\cos({\theta_{6}})\,m_{7}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}
_{5}} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8}\,r_{4}\,\sin({\theta_{4}})
\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m
_{8}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{6}\,\sin({
\theta_{6}})\,m_{8}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8}\,r_{2}\,\cos(
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8}\,r
_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{6
}\,\sin({\theta_{6}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^
2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8}\,r_{5}\,\sin({\theta_{5}})\,{
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8
}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{6}\,\sin({\theta
_{6}})\,m_{8}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} - 2\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,r_{1}\,\sin(
{\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,r
_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 2\,m_{6
}\,r_{6}\,\cos({\theta_{6}})\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^
2 + 2\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,r_{3}\,\cos({\theta_{3}})\,{
\dot{\eta}_{3}} \\ &&\quad\mbox{} - 2\,m_{6}\,r_{6}\,\cos({\theta_{6}}
)\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 2\,m_{6}\,r_{6}\,\cos({
\theta_{6}})\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} - 2\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,r_{4}\,\sin(
{\theta_{4}})\,{{\eta_{4}}}^2 + 2\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,r
_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 2\,m_{6
}\,r_{6}\,\cos({\theta_{6}})\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^
2 + 2\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,r_{5}\,\cos({\theta_{5}})\,{
\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{9
}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{6}\,\cos({\theta
_{6}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}}
 \\ &&\quad\mbox{} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,r_{3}\,\sin(
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,r
_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r_{6
}\,\cos({\theta_{6}})\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^
2 + 4\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})\,{
\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{9
}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{6}\,\cos({\theta
_{6}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,r_{5}\,\sin(
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,r
_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{6
}\,\cos({\theta_{6}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^
2 + 4\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{
\dot{\eta}_{8}} \\ &&\quad\mbox{} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{9
}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{6}\,\cos({\theta
_{6}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9}\,r_{4}\,\cos(
{\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9}\,r
_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{6
}\,\sin({\theta_{6}})\,m_{9}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^
2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{
\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{6}\,\sin({\theta
_{6}})\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9}\,r_{5}\,\cos(
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9}\,r
_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{6
}\,\sin({\theta_{6}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^
2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{
\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9
}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{6}\,\sin({\theta
_{6}})\,m_{9}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{3}\,\cos
({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}
\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r
_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2
}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{2}\,\sin({\theta_{2}}
)\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,
m_{10}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{6}\,\sin({
\theta_{6}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{9}\,\cos
({\theta_{9}})\,{{\eta_{9}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}
\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 4\,r
_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8
}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{8}\,\sin({\theta_{8}}
)\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,
m_{10}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{6}\,\sin({
\theta_{6}})\,m_{10}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}}
 \end{eqnarray*}
\begin{eqnarray*} && m_{9}\,g\,r_{9}\,\cos({\theta_{9}}) + 2\,r_{9}\,
\cos({\theta_{9}})\,m_{10}\,g + J_{9}\,{\dot{\eta}_{9}} + m_{9}\,{r_{9
}}^2\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,r_{9}\,\sin({\theta_{9}}
)\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{\dot{\eta}_{10}} + 2\,r_{9}\,
\cos({\theta_{9}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{\dot{\eta}_{
10}} \\ &&\quad\mbox{} + 2\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{10}
\,\cos({\theta_{10}})\,{{\eta_{10}}}^2 - 2\,r_{9}\,\cos({\theta_{9}})
\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{{\eta_{10}}}^2
 \\ &&\quad\mbox{} + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{1}\,\cos
({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}
\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r
_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4
}}}^2 + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{4}\,\sin({\theta_{4}}
)\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{9}\,\sin({\theta_{9}})\,
m_{10}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{9}\,\sin({
\theta_{9}})\,m_{10}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{2}\,\cos
({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}
\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r
_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5
}}}^2 + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{5}\,\sin({\theta_{5}}
)\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{9}\,\sin({\theta_{9}})\,
m_{10}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 + 4\,r_{9}\,\sin({
\theta_{9}})\,m_{10}\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}}
 \\ &&\quad\mbox{} + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{7}\,\cos
({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}
\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r
_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6
}}}^2 + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{6}\,\sin({\theta_{6}}
)\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} - 4\,r_{9}\,\cos({\theta_{9}})\,
m_{10}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{9}\,\cos({
\theta_{9}})\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}}
 \\ &&\quad\mbox{} - 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{3}\,\sin
({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}
\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r
_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2
}}}^2 + 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{2}\,\cos({\theta_{2}}
)\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{9}\,\cos({\theta_{9}})\,
m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{9}\,\cos({
\theta_{9}})\,m_{10}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} - 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{5}\,\sin
({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}
\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r
_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8
}}}^2 + 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{8}\,\cos({\theta_{8}}
)\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} - 4\,r_{9}\,\cos({\theta_{9}})\,
m_{10}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{9}\,\cos({
\theta_{9}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} - 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{6}\,\sin
({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}
\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,m
_{9}\,r_{9}\,\sin({\theta_{9}})\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}
}}^2 + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r_{1}\,\sin({\theta_{1}})
\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\sin({\theta_{
9}})\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 2\,m_{9}\,r_{9}\,
\sin({\theta_{9}})\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r_{3}\,\cos(
{\theta_{3}})\,{{\eta_{3}}}^2 + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r
_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 2\,m_{9
}\,r_{9}\,\sin({\theta_{9}})\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^
2 + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r_{2}\,\sin({\theta_{2}})\,{
\dot{\eta}_{2}} \\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}}
)\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 2\,m_{9}\,r_{9}\,\sin({
\theta_{9}})\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r_{8}\,\cos(
{\theta_{8}})\,{{\eta_{8}}}^2 + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r
_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,m_{9
}\,r_{9}\,\sin({\theta_{9}})\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^
2 + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r_{7}\,\sin({\theta_{7}})\,{
\dot{\eta}_{7}} \\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}}
)\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 2\,m_{9}\,r_{9}\,\sin({
\theta_{9}})\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}}
 \\ &&\quad\mbox{} - 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r_{1}\,\sin(
{\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r
_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 2\,m_{9
}\,r_{9}\,\cos({\theta_{9}})\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^
2 + 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r_{3}\,\cos({\theta_{3}})\,{
\dot{\eta}_{3}} \\ &&\quad\mbox{} - 2\,m_{9}\,r_{9}\,\cos({\theta_{9}}
)\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 2\,m_{9}\,r_{9}\,\cos({
\theta_{9}})\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} - 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r_{4}\,\sin(
{\theta_{4}})\,{{\eta_{4}}}^2 - 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r
_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 2\,m_{9}
\,r_{9}\,\cos({\theta_{9}})\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5
}} - 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r_{8}\,\sin({\theta_{8}})\,{
{\eta_{8}}}^2 \\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})
\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} - 2\,m_{9}\,r_{9}\,\cos(
{\theta_{9}})\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2
 \\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r_{7}\,\cos(
{\theta_{7}})\,{\dot{\eta}_{7}} - 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})
\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,m_{
9}\,r_{9}\,\cos({\theta_{9}})\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}
_{6}} + 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r_{4}\,\cos({\theta_{4}})
\,{\dot{\eta}_{4}} + 4\,{r_{9}}^2\,m_{10}\,{\dot{\eta}_{9}}
 \end{eqnarray*}
\begin{eqnarray*} && 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{8}\,\cos
({\theta_{8}})\,{\dot{\eta}_{8}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{10
}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} + 4\,r
_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{
\dot{\eta}_{9}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{7}\,\sin({
\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\cos({
\theta_{4}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} - 4
\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{{\eta
_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{
6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} + m_{4}\,g\,r_{4}\,\cos({
\theta_{4}}) + 4\,r_{4}\,\sin({\theta_{4}})\,m_{7}\,r_{5}\,\cos({
\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({
\theta_{4}})\,m_{7}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,
r_{4}\,\sin({\theta_{4}})\,m_{7}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6
}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{7}\,r_{6}\,
\sin({\theta_{6}})\,{\dot{\eta}_{6}} - 4\,r_{4}\,\cos({\theta_{4}})\,m
_{9}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4
\,r_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})\,{
\dot{\eta}_{2}} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{1}\,\cos({
\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({
\theta_{4}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 2\,m
_{4}\,r_{4}\,\sin({\theta_{4}})\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}
}}^2 \\ &&\quad\mbox{} + 2\,m_{4}\,r_{4}\,\sin({\theta_{4}})\,r_{2}\,
\sin({\theta_{2}})\,{\dot{\eta}_{2}} - 2\,m_{4}\,r_{4}\,\cos({\theta_{
4}})\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} - 4
\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{1}\,\sin({\theta_{1}})\,{{\eta
_{1}}}^2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{1}\,\cos({\theta_{1
}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})
\,m_{6}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{4}\,\sin({
\theta_{4}})\,m_{7}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 2\,m_{4}\,r_{4}\,\cos({\theta_{4}})\,r_{2}\,\cos(
{\theta_{2}})\,{\dot{\eta}_{2}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{7}
\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r
_{4}\,\sin({\theta_{4}})\,m_{7}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}
}}^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})
\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m
_{7}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 - 2\,m_{4}\,r_{4}\,
\cos({\theta_{4}})\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 2\,m_{4}\,r_{4}\,\cos({\theta_{4}})\,r_{1}\,\cos(
{\theta_{1}})\,{\dot{\eta}_{1}} - 2\,m_{4}\,r_{4}\,\cos({\theta_{4}})
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
4}\,\sin({\theta_{4}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
_{2}} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{3}\,\cos({\theta_{3}})
\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m
_{6}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\cos({
\theta_{4}})\,m_{6}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{1}\,\sin(
{\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}
\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r
_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}
}}^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{7}\,\sin({\theta_{7}})
\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m
_{9}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{4}\,\sin({
\theta_{4}})\,m_{9}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}}
 \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{7}\,\sin(
{\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{9}\,r
_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} - 4\,r_{4
}\,\cos({\theta_{4}})\,m_{9}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^
2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{6}\,\cos({\theta_{6}})\,{
\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{8
}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} + 4\,r_{4}\,\sin({
\theta_{4}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2
 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{5}\,\sin(
{\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{7}
\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{
4}\,\cos({\theta_{4}})\,m_{7}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}
_{6}} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{7}\,r_{5}\,\cos({\theta_{5}})
\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m
_{10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{4}\,\cos({
\theta_{4}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r_{6}\,\sin(
{\theta_{6}})\,{{\eta_{6}}}^2 - 4\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r
_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}
\,\cos({\theta_{4}})\,m_{8}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1
}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})\,{
{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}
\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{4}\,\sin({\theta
_{4}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2
 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{8}\,\sin(
{\theta_{8}})\,{\dot{\eta}_{8}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}
\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
4}\,\sin({\theta_{4}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}
_{3}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{
8}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{4}\,\sin({
\theta_{4}})\,m_{8}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2
 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{1}\,\cos(
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r
_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{4
}\,\sin({\theta_{4}})\,m_{8}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{
1}} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r_{3}\,\cos({\theta_{3}})\,
{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{
8}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\cos({\theta
_{4}})\,m_{8}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r_{3}\,\sin(
{\theta_{3}})\,{{\eta_{3}}}^2 - 4\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r
_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}
\,\cos({\theta_{4}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5
}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{6}\,r_{2}\,\sin({\theta_{2}})\,{
\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{6
}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{4}\,\sin({\theta
_{4}})\,m_{6}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}}
 \\ &&\quad\mbox{} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{5}\,\cos(
{\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{6}
\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
4}\,\sin({\theta_{4}})\,m_{6}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}
^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{5}\,r_{1}\,\cos({\theta_{1}})\,{
{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{5}
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\sin({\theta_{
4}})\,m_{5}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{5}\,r_{2}\,\sin(
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{5}\,r
_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 2\,m_{4
}\,r_{4}\,\sin({\theta_{4}})\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^
2 + 2\,m_{4}\,r_{4}\,\sin({\theta_{4}})\,r_{1}\,\sin({\theta_{1}})\,{
\dot{\eta}_{1}} \\ &&\quad\mbox{} + 2\,m_{4}\,r_{4}\,\sin({\theta_{4}}
)\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{4}\,\sin({\theta
_{4}})\,m_{5}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}}
 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{5}\,r_{3}\,\cos(
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{5}\,r
_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{4
}\,\sin({\theta_{4}})\,m_{6}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{
5}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{6}\,r_{3}\,\sin({\theta_{3}})\,
{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{
10}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{4}\,\sin({
\theta_{4}})\,m_{10}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2
 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{5}\,\sin
({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{10
}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} + 4\,r
_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{
\dot{\eta}_{9}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{8}\,\cos({
\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({
\theta_{4}})\,m_{10}\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}} - 4
\,r_{4}\,\cos({\theta_{4}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})\,{{\eta
_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{
7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{4}\,\sin({\theta_{4}}
)\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{}
 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{
\dot{\eta}_{6}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{7}\,\cos({
\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({
\theta_{4}})\,m_{8}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,
r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6
}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{6}\,
\sin({\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{4}\,\sin({\theta_{4}})\,m
_{10}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} - 4
\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,{{\eta
_{1}}}^2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{1}\,\cos({\theta_{
1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}}
)\,m_{10}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{4}\,\cos(
{\theta_{4}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{2}\,\sin
({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}
\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r
_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3
}}}^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{3}\,\sin({\theta_{3}}
)\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,
m_{10}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\sin({
\theta_{4}})\,m_{10}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{7}\,r_{3}\,\cos(
{\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{7}
\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
4}\,\cos({\theta_{4}})\,m_{7}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
_{2}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{7}\,r_{5}\,\sin({\theta_{5}})
\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{
7}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 + 2\,r_{4}\,\cos({\theta
_{4}})\,m_{8}\,g + 2\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,g + 2\,r_{4}
\,\cos({\theta_{4}})\,m_{7}\,g \\ &&\quad\mbox{} + 2\,r_{4}\,\cos({
\theta_{4}})\,m_{9}\,g + 2\,r_{4}\,\cos({\theta_{4}})\,m_{5}\,g + 2\,r
_{4}\,\cos({\theta_{4}})\,m_{6}\,g - 4\,r_{4}\,\cos({\theta_{4}})\,m_{
10}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 2\,
m_{4}\,r_{4}\,\cos({\theta_{4}})\,r_{3}\,\cos({\theta_{3}})\,{
\dot{\eta}_{3}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{3}\,\sin({
\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({
\theta_{4}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 - 4\,r
_{4}\,\cos({\theta_{4}})\,m_{5}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}
}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{6}\,r_{2}\,
\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{
8}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} - 4\,r
_{4}\,\cos({\theta_{4}})\,m_{8}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}
}}^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{
10}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{4}\,\cos({
\theta_{4}})\,m_{7}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}}
 \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{5}\,\sin
({\theta_{5}})\,{{\eta_{5}}}^2 + J_{4}\,{\dot{\eta}_{4}} + 2\,r_{4}\,
\cos({\theta_{4}})\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}}
 \\ &&\quad\mbox{} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{8}\,\sin(
{\theta_{8}})\,{\dot{\eta}_{8}} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{9}
\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,r
_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{
\dot{\eta}_{9}} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{10}\,\sin({
\theta_{10}})\,{\dot{\eta}_{10}} \\ &&\quad\mbox{} + 2\,r_{4}\,\cos({
\theta_{4}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{\dot{\eta}_{10}}
 + 2\,m_{4}\,r_{4}\,\sin({\theta_{4}})\,r_{3}\,\sin({\theta_{3}})\,{
\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{9
}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{4}\,\cos({
\theta_{4}})\,m_{9}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2
 \\ &&\quad\mbox{} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{5}\,\cos(
{\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{9}
\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{
4}\,\cos({\theta_{4}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}
_{8}} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{5}\,r_{1}\,\cos({\theta_{1}})
\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m
_{5}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{4}\,\cos({
\theta_{4}})\,m_{5}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{5}\,r_{5}\,\cos(
{\theta_{5}})\,{{\eta_{5}}}^2 - 2\,r_{4}\,\cos({\theta_{4}})\,m_{5}\,r
_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 2\,r_{4}
\,\sin({\theta_{4}})\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2
 - 2\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,{{
\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{7}\,
r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 - 2\,r_{4}\,\cos({\theta_{4}
})\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{}
 - 2\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{{
\eta_{8}}}^2 + 2\,r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{8}\,\cos({
\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 2\,r_{4}\,\sin({
\theta_{4}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 - 2\,r
_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}
}}^2 \\ &&\quad\mbox{} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{10}
\,\cos({\theta_{10}})\,{{\eta_{10}}}^2 - 2\,r_{4}\,\cos({\theta_{4}})
\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{{\eta_{10}}}^2 + 4\,{r_{4}}^2
\,m_{6}\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,{r_{4}}^2\,m_{9}\,{
\dot{\eta}_{4}} + 4\,{r_{4}}^2\,m_{10}\,{\dot{\eta}_{4}} + 4\,{r_{4}}^
2\,m_{7}\,{\dot{\eta}_{4}} + 4\,{r_{4}}^2\,m_{8}\,{\dot{\eta}_{4}} + 4
\,{r_{4}}^2\,m_{5}\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + m_{4}\,{r_{4}
}^2\,{\dot{\eta}_{4}} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{5}\,r_{5}\,
\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 2\,r_{4}\,\cos({\theta_{4}})\,m
_{5}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 
2\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,{
\dot{\eta}_{6}} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{6}\,r_{6}\,\sin({
\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r_{4}\,\sin({
\theta_{4}})\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 2\,
r_{4}\,\cos({\theta_{4}})\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,{
\dot{\eta}_{7}} \end{eqnarray*}
\begin{eqnarray*} && m_{7}\,g\,r_{7}\,\cos({\theta_{7}}) + 4\,{r_{7}}^
2\,m_{8}\,{\dot{\eta}_{7}} + 4\,{r_{7}}^2\,m_{9}\,{\dot{\eta}_{7}} + 4
\,{r_{7}}^2\,m_{10}\,{\dot{\eta}_{7}} + 2\,r_{7}\,\cos({\theta_{7}})\,
m_{9}\,g \\ &&\quad\mbox{} + 2\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,g
 + 2\,r_{7}\,\cos({\theta_{7}})\,m_{8}\,g + J_{7}\,{\dot{\eta}_{7}} + 
2\,r_{7}\,\sin({\theta_{7}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{
\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r_{7}\,\cos({\theta_{7}})\,m_{8
}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} + 2\,r_{7}\,\sin({
\theta_{7}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}}
 \\ &&\quad\mbox{} + 2\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{9}\,\cos(
{\theta_{9}})\,{\dot{\eta}_{9}} + 2\,r_{7}\,\sin({\theta_{7}})\,m_{10}
\,r_{10}\,\sin({\theta_{10}})\,{\dot{\eta}_{10}} \\ &&\quad\mbox{} + 2
\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{
\dot{\eta}_{10}} + 2\,r_{7}\,\sin({\theta_{7}})\,m_{8}\,r_{8}\,\cos({
\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} - 2\,r_{7}\,\cos({
\theta_{7}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 + 2\,r
_{7}\,\sin({\theta_{7}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}
}}^2 \\ &&\quad\mbox{} - 2\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{9}\,
\sin({\theta_{9}})\,{{\eta_{9}}}^2 + 2\,r_{7}\,\sin({\theta_{7}})\,m_{
10}\,r_{10}\,\cos({\theta_{10}})\,{{\eta_{10}}}^2 \\ &&\quad\mbox{} - 
2\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{{
\eta_{10}}}^2 + m_{7}\,{r_{7}}^2\,{\dot{\eta}_{7}} + 4\,r_{7}\,\sin({
\theta_{7}})\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{1}\,\sin
({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{8}
\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{
7}\,\sin({\theta_{7}})\,m_{8}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}
_{1}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{
8}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{7}\,\sin({
\theta_{7}})\,m_{8}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{8}\,r_{3}\,\sin(
{\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{8}
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
7}\,\sin({\theta_{7}})\,m_{8}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
_{2}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})
\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{
8}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{7}\,\sin({
\theta_{7}})\,m_{8}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2
 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{8}\,r_{6}\,\sin(
{\theta_{6}})\,{\dot{\eta}_{6}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{8}
\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{
7}\,\cos({\theta_{7}})\,m_{8}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}
_{1}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{8}\,r_{3}\,\sin({\theta_{3}})
\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{
8}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{7}\,\cos({
\theta_{7}})\,m_{8}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2
 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{8}\,r_{2}\,\cos(
{\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{8}
\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{
7}\,\cos({\theta_{7}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}
_{4}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{8}\,r_{5}\,\sin({\theta_{5}})
\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{
8}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{7}\,\cos({
\theta_{7}})\,m_{8}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2
 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{8}\,r_{6}\,\cos(
{\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}
\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{
7}\,\sin({\theta_{7}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}
_{1}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{
9}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{7}\,\sin({
\theta_{7}})\,m_{9}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}\,r_{3}\,\sin(
{\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
7}\,\sin({\theta_{7}})\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
_{2}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})
\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{
9}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{7}\,\sin({
\theta_{7}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2
 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}\,r_{8}\,\sin(
{\theta_{8}})\,{\dot{\eta}_{8}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}
\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{
7}\,\sin({\theta_{7}})\,m_{9}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}
_{6}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{4}\,\cos({\theta_{4}}
)\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m
_{10}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{7}\,\sin({
\theta_{7}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{3}\,\sin
({\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r
_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{2}\,\sin({\theta_{2}})\,{
\dot{\eta}_{2}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{5}\,\cos({
\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({
\theta_{7}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4
\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{{\eta
_{9}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{
9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} + 4\,r_{7}\,\sin({\theta_{7}}
)\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{}
 + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{8}\,\sin({\theta_{8}})\,{
\dot{\eta}_{8}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{6}\,\cos({
\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({
\theta_{7}})\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} - 4
\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,{{\eta
_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{
1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{7}\,\cos({\theta_{7}}
)\,m_{10}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{}
 + 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{
\dot{\eta}_{3}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{2}\,\sin({
\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({
\theta_{7}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4
\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta
_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{
4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{7}\,\cos({\theta_{7}}
)\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{}
 + 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{5}\,\cos({\theta_{5}})\,{
\dot{\eta}_{5}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{8}\,\sin({
\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({
\theta_{7}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} - 4
\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{{\eta
_{9}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{
9}\,\cos({\theta_{9}})\,{\dot{\eta}_{9}} - 4\,r_{7}\,\cos({\theta_{7}}
)\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{}
 + 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{
\dot{\eta}_{6}} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,r_{1}\,\cos({
\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\sin
({\theta_{7}})\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 2\,m_{7}
\,r_{7}\,\sin({\theta_{7}})\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2
 \\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,r_{4}\,\sin(
{\theta_{4}})\,{\dot{\eta}_{4}} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}})
\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 2\,m_{
7}\,r_{7}\,\sin({\theta_{7}})\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}
_{3}} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,r_{2}\,\cos({\theta_{2}})
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}
})\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} + 2\,m_{7}\,r_{7}\,
\sin({\theta_{7}})\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2
 \\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,r_{5}\,\sin(
{\theta_{5}})\,{\dot{\eta}_{5}} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}})
\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,m_{
7}\,r_{7}\,\sin({\theta_{7}})\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}
_{6}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{
9}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{7}\,\cos({
\theta_{7}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{3}\,\cos(
{\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}
\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
7}\,\cos({\theta_{7}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
_{2}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{
9}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{7}\,\cos({
\theta_{7}})\,m_{9}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2
 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{5}\,\cos(
{\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}
\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{
7}\,\cos({\theta_{7}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}
_{8}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{6}\,\sin({\theta_{6}})
\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{
9}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} - 2\,m_{7}\,r_{7}\,
\cos({\theta_{7}})\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,r_{1}\,\cos(
{\theta_{1}})\,{\dot{\eta}_{1}} - 2\,m_{7}\,r_{7}\,\cos({\theta_{7}})
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 2\,m_{
7}\,r_{7}\,\cos({\theta_{7}})\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}
_{3}} - 2\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,r_{2}\,\sin({\theta_{2}})
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\cos({\theta_{7}
})\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 2\,m_{7}\,r_{7}\,
\cos({\theta_{7}})\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
 \\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,r_{4}\,\cos(
{\theta_{4}})\,{\dot{\eta}_{4}} - 2\,m_{7}\,r_{7}\,\cos({\theta_{7}})
\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 2\,m_{
7}\,r_{7}\,\cos({\theta_{7}})\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}
_{5}} - 2\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,r_{6}\,\sin({\theta_{6}})
\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\cos({\theta_{7}
})\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \end{eqnarray*}
\begin{eqnarray*} && m_{2}\,g\,r_{2}\,\cos({\theta_{2}}) + 2\,r_{2}\,
\cos({\theta_{2}})\,m_{6}\,g + 2\,r_{2}\,\cos({\theta_{2}})\,m_{3}\,g
 + 2\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,g + 2\,r_{2}\,\cos({\theta_{2}
})\,m_{5}\,g \\ &&\quad\mbox{} + 2\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,
g + 2\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,g + 2\,r_{2}\,\cos({\theta_{2
}})\,m_{7}\,g + 2\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,g + 4\,{r_{2}}^2
\,m_{10}\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,{r_{2}}^2\,m_{5}\,{
\dot{\eta}_{2}} + 4\,{r_{2}}^2\,m_{4}\,{\dot{\eta}_{2}} + 4\,{r_{2}}^2
\,m_{3}\,{\dot{\eta}_{2}} + 4\,{r_{2}}^2\,m_{7}\,{\dot{\eta}_{2}} + 4
\,{r_{2}}^2\,m_{6}\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,{r_{2}}^2
\,m_{8}\,{\dot{\eta}_{2}} + 4\,{r_{2}}^2\,m_{9}\,{\dot{\eta}_{2}} + J
_{2}\,{\dot{\eta}_{2}} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,r_{1}\,
\cos({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{2}\,
\cos({\theta_{2}})\,m_{3}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{3}\,r_{1}\,\cos({\theta_{1}})\,{
\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{4
}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{2}\,\cos({
\theta_{2}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{3}\,\sin
({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{10}
\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r
_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4
}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{1}\,\sin({\theta_{1}}
)\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m
_{10}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{2}\,\cos({
\theta_{2}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2
 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{5}\,\cos
({\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{10
}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r
_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{4}\,\cos({\theta_{4}})\,{
\dot{\eta}_{4}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{5}\,\cos({
\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({
\theta_{2}})\,m_{10}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r
_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{
10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 - 4\,r_{2}\,\cos({
\theta_{2}})\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{3}\,\sin
({\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{10
}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,
r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{
\dot{\eta}_{8}} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{7}\,\sin({
\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({
\theta_{2}})\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} + 4
\,r_{2}\,\sin({\theta_{2}})\,m_{3}\,r_{1}\,\cos({\theta_{1}})\,{{\eta
_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,r_{3
}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} + 2\,m_{2}\,r_{2}\,\sin({
\theta_{2}})\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,r_{1}\,\sin(
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}\,
r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}
\,\sin({\theta_{2}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{
9}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})
\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{
10}\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}} + 4\,r_{2}\,\sin({
\theta_{2}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{7}\,\cos
({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}
\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r
_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6
}}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{6}\,\sin({\theta_{6}}
)\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,
m_{10}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\sin({
\theta_{2}})\,m_{4}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{4}\,r_{1}\,\cos(
{\theta_{1}})\,{{\eta_{1}}}^2 + 2\,r_{2}\,\sin({\theta_{2}})\,m_{8}\,r
_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r_{2
}\,\cos({\theta_{2}})\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{
8}} + 2\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,
{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{
9}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} + 2\,r_{2}\,\sin({
\theta_{2}})\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{\dot{\eta}_{10}}
 \\ &&\quad\mbox{} + 2\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{10}\,
\cos({\theta_{10}})\,{\dot{\eta}_{10}} + 4\,r_{2}\,\sin({\theta_{2}})
\,m_{4}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{}
 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,r_{3}\,\sin({\theta_{3}})\,{{
\eta_{3}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{5}\,r_{4}\,\sin({
\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({
\theta_{2}})\,m_{5}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r
_{2}\,\sin({\theta_{2}})\,m_{5}\,r_{4}\,\sin({\theta_{4}})\,{
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{5
}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\sin({\theta
_{2}})\,m_{5}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{6}\,r_{5}\,\cos(
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{7}\,r
_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{2
}\,\sin({\theta_{2}})\,m_{7}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{
1}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{7}\,r_{4}\,\cos({\theta_{4}})\,
{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{7}
\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{2}\,\sin({\theta
_{2}})\,m_{7}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{7}\,r_{3}\,\cos(
{\theta_{3}})\,{{\eta_{3}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{7}\,r
_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}
\,\sin({\theta_{2}})\,m_{8}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6
}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{
{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{7}
\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{2}\,\cos({\theta
_{2}})\,m_{7}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 + m_{2}\,{r_{
2}}^2\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}
})\,m_{6}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{2}\,
\sin({\theta_{2}})\,m_{6}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{6}\,r_{3}\,\sin(
{\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{6}
\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{
2}\,\cos({\theta_{2}})\,m_{6}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}
_{5}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{6}\,r_{1}\,\cos({\theta_{1}})
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{
6}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{2}\,\cos({
\theta_{2}})\,m_{6}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{6}\,r_{3}\,\cos(
{\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{6}
\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r
_{2}\,\cos({\theta_{2}})\,m_{6}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}
}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})
\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m
_{7}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{2}\,\sin({
\theta_{2}})\,m_{7}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{7}\,r_{6}\,\cos(
{\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{7}\,r
_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} - 4\,r_{2
}\,\cos({\theta_{2}})\,m_{6}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^
2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{6}\,r_{5}\,\sin({\theta_{5}})\,{
\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{5
}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{2}\,\cos({\theta
_{2}})\,m_{5}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}}
 \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{5}\,r_{3}\,\sin(
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{5}\,r
_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{2
}\,\sin({\theta_{2}})\,m_{6}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{
1}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{6}\,r_{4}\,\cos({\theta_{4}})\,
{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{5}
\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{2}\,\sin({\theta
_{2}})\,m_{5}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{5}\,r_{1}\,\sin(
{\theta_{1}})\,{\dot{\eta}_{1}} + 2\,m_{2}\,r_{2}\,\sin({\theta_{2}})
\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r
_{2}\,\sin({\theta_{2}})\,m_{3}\,r_{1}\,\sin({\theta_{1}})\,{
\dot{\eta}_{1}} - 2\,r_{2}\,\cos({\theta_{2}})\,m_{3}\,r_{3}\,\sin({
\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({
\theta_{2}})\,m_{3}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 2\,r
_{2}\,\sin({\theta_{2}})\,m_{4}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}
}}^2 \\ &&\quad\mbox{} - 2\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,r_{4}\,
\sin({\theta_{4}})\,{{\eta_{4}}}^2 + 2\,r_{2}\,\sin({\theta_{2}})\,m_{
5}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} - 2\,r
_{2}\,\cos({\theta_{2}})\,m_{5}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}
}}^2 - 2\,r_{2}\,\cos({\theta_{2}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})
\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{
6}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 - 2\,r_{2}\,\cos({\theta
_{2}})\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2
 \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{7}\,r_{7}\,\cos(
{\theta_{7}})\,{{\eta_{7}}}^2 + 2\,r_{2}\,\sin({\theta_{2}})\,m_{8}\,r
_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} - 2\,r_{2}
\,\cos({\theta_{2}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2
 - 2\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{{
\eta_{9}}}^2 \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,
r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 + 2\,r_{2}\,\sin({\theta_{2}
})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{{\eta_{10}}}^2
 \\ &&\quad\mbox{} - 2\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{10}\,
\sin({\theta_{10}})\,{{\eta_{10}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m
_{10}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} + 4
\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{
\dot{\eta}_{9}} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r_{5}\,\cos({
\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({
\theta_{2}})\,m_{8}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m
_{2}\,r_{2}\,\cos({\theta_{2}})\,r_{1}\,\cos({\theta_{1}})\,{
\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{8
}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 2\,m_{2}\,r_{2}\,\cos
({\theta_{2}})\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r_{4}\,\cos(
{\theta_{4}})\,{{\eta_{4}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r
_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}
\,\cos({\theta_{2}})\,m_{9}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6
}} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})\,{
\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{9
}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\cos({\theta
_{2}})\,m_{9}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r_{3}\,\sin(
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r
_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}
\,\sin({\theta_{2}})\,m_{9}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5
}} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r_{4}\,\sin({\theta_{4}})\,{
{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}
\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{2}\,\cos({\theta
_{2}})\,m_{8}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2
 \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r_{1}\,\sin(
{\theta_{1}})\,{{\eta_{1}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r
_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}
\,\cos({\theta_{2}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7
}} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r_{6}\,\sin({\theta_{6}})\,{
{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8}
\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{2}\,\cos({\theta
_{2}})\,m_{8}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}}
 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r_{1}\,\cos(
{\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}
\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{
2}\,\sin({\theta_{2}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}
_{8}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})
\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{
9}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{2}\,\sin({
\theta_{2}})\,m_{9}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r_{6}\,\sin(
{\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8}
\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r
_{2}\,\sin({\theta_{2}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}
}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8}\,r_{4}\,\sin({\theta_{4}})
\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m
_{8}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\sin({
\theta_{2}})\,m_{8}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8}\,r_{5}\,\cos(
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{7}\,r
_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{2
}\,\cos({\theta_{2}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^
2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8}\,r_{7}\,\sin({\theta_{7}})\,{
\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8
}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{2}\,\cos({\theta
_{2}})\,m_{7}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{7}\,r_{5}\,\sin(
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{7}\,r
_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{2
}\,\cos({\theta_{2}})\,m_{7}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^
2 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{
\dot{\eta}_{7}} \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{9
}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 - 4\,r_{2}\,\cos({\theta
_{2}})\,m_{9}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2
 \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r_{1}\,\sin(
{\theta_{1}})\,{{\eta_{1}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r
_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}
\,\cos({\theta_{2}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5
}} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{
{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}
\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} + 4\,r_{2}\,\sin({\theta
_{2}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r_{3}\,\cos(
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r
_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{2
}\,\cos({\theta_{2}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{
4}} + 2\,r_{2}\,\cos({\theta_{2}})\,m_{3}\,r_{3}\,\cos({\theta_{3}})\,
{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{
3}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} + 2\,r_{2}\,\sin({
\theta_{2}})\,m_{4}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} + 2\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,r_{4}\,\cos(
{\theta_{4}})\,{\dot{\eta}_{4}} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{5}
\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 2\,r
_{2}\,\cos({\theta_{2}})\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,{
\dot{\eta}_{5}} + 2\,r_{2}\,\cos({\theta_{2}})\,m_{6}\,r_{6}\,\cos({
\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({
\theta_{2}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} + 2\,
r_{2}\,\cos({\theta_{2}})\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,{
\dot{\eta}_{7}} \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{7
}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{2}\,\sin({
\theta_{2}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r_{1}\,\sin(
{\theta_{1}})\,{\dot{\eta}_{1}} \end{eqnarray*}
\begin{eqnarray*} && 4\,{r_{1}}^2\,m_{3}\,{\dot{\eta}_{1}} + 4\,{r_{1}
}^2\,m_{8}\,{\dot{\eta}_{1}} + m_{1}\,g\,r_{1}\,\cos({\theta_{1}}) + 4
\,{r_{1}}^2\,m_{5}\,{\dot{\eta}_{1}} + 4\,{r_{1}}^2\,m_{10}\,{
\dot{\eta}_{1}} \\ &&\quad\mbox{} - 2\,r_{1}\,\cos({\theta_{1}})\,m_{9
}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 + 2\,r_{1}\,\sin({\theta
_{1}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 + 4\,{r_{1}}^
2\,m_{4}\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,{r_{1}}^2\,m_{7}\,{
\dot{\eta}_{1}} + 4\,{r_{1}}^2\,m_{6}\,{\dot{\eta}_{1}} + 4\,{r_{1}}^2
\,m_{9}\,{\dot{\eta}_{1}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{4
}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,
\sin({\theta_{1}})\,m_{3}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2
 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{3}\,r_{2}\,\sin({\theta_{2}})\,{
\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{3
}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\cos({\theta
_{1}})\,m_{3}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r_{3}\,\sin(
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r
_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r_{1
}\,\cos({\theta_{1}})\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^
2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})\,{
\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{9
}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{1}\,\cos({\theta
_{1}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r_{5}\,\sin(
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r
_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{1
}\,\cos({\theta_{1}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^
2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{
\dot{\eta}_{8}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{9
}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{1}\,\sin({\theta
_{1}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}\,r_{2}\,\cos(
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}\,r
_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{1
}\,\sin({\theta_{1}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}\,r_{5}\,\sin({\theta_{5}})\,{
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9
}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 + 4\,r_{1}\,\sin({\theta
_{1}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}}
 \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}\,r_{7}\,\cos(
{\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}\,r
_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{1
}\,\sin({\theta_{1}})\,m_{9}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}\,r_{6}\,\sin({\theta_{6}})\,{
\dot{\eta}_{6}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{8
}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\cos({\theta
_{1}})\,m_{8}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r_{4}\,\sin(
{\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r
_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{1
}\,\cos({\theta_{1}})\,m_{8}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^
2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})\,{
\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{8
}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{1}\,\cos({\theta
_{1}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r_{6}\,\sin(
{\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r
_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{1
}\,\sin({\theta_{1}})\,m_{6}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{6}\,r_{4}\,\sin({\theta_{4}})\,{
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{6
}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\sin({\theta
_{1}})\,m_{6}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{6}\,r_{2}\,\cos(
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{6}\,r
_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{1
}\,\sin({\theta_{1}})\,m_{6}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{6}\,r_{5}\,\sin({\theta_{5}})\,{
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9
}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{1}\,\sin({\theta
_{1}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r_{3}\,\cos(
{\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}
\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1}\,\sin({\theta_{1}})\,m_{7}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}
^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{7}\,r_{5}\,\sin({\theta_{5}})\,{
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{7
}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{1}\,\sin({\theta
_{1}})\,m_{7}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}}
 \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{4}\,r_{3}\,\sin(
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{4}\,r
_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r_{1
}\,\cos({\theta_{1}})\,m_{4}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^
2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{4}\,r_{2}\,\cos({\theta_{2}})\,{
\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{6
}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\cos({\theta
_{1}})\,m_{6}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{6}\,r_{2}\,\sin(
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{6}\,r
_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{1
}\,\cos({\theta_{1}})\,m_{6}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^
2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{6}\,r_{4}\,\cos({\theta_{4}})\,{
\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{6
}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{1}\,\cos({\theta
_{1}})\,m_{6}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{7}\,r_{4}\,\cos(
{\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{8}\,r
_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{1
}\,\sin({\theta_{1}})\,m_{8}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{8}\,r_{6}\,\sin({\theta_{6}})\,{
\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{5
}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{1}\,\cos({
\theta_{1}})\,m_{5}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{5}\,r_{4}\,\cos(
{\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1}\,\cos({\theta_{1}})\,m_{7}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}
_{3}} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{
7}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{1}\,\cos({
\theta_{1}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2
 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{5}\,\cos
({\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{10
}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r
_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{
\dot{\eta}_{8}} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{9}\,\sin({
\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({
\theta_{1}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{\dot{\eta}_{9}} - 4
\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{7}\,\sin({\theta_{7}})\,{{\eta
_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{
7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} - 4\,r_{1}\,\cos({\theta_{1}}
)\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{}
 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{
\dot{\eta}_{6}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{3}\,\sin({
\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({
\theta_{1}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r
_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{2}\,\sin({\theta_{2}})\,{
\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{
10}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{1}\,\sin({
\theta_{1}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{9}\,\cos
({\theta_{9}})\,{{\eta_{9}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10}
\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 4\,r
_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8
}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{8}\,\sin({\theta_{8}}
)\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,
m_{9}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{1}\,\cos({
\theta_{1}})\,m_{9}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}}
 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}\,r_{5}\,\cos(
{\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}
\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1}\,\cos({\theta_{1}})\,m_{7}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}
_{6}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{
8}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{1}\,\sin({
\theta_{1}})\,m_{8}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{8}\,r_{3}\,\sin(
{\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{8}
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1}\,\sin({\theta_{1}})\,m_{8}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
_{2}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})
\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{
8}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{1}\,\sin({
\theta_{1}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2
 \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{7}\,\sin
({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10
}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r
_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{
\dot{\eta}_{6}} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{3}\,\sin({
\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({
\theta_{1}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 4
\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{2}\,\sin({\theta_{2}})\,{{\eta
_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r_{7
}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{1}\,\sin({\theta_{1}})
\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{}
 - 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}\,r_{4}\,\sin({\theta_{4}})\,{{
\eta_{4}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}\,r_{4}\,\cos({
\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({
\theta_{1}})\,m_{5}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r
_{1}\,\sin({\theta_{1}})\,m_{5}\,r_{4}\,\sin({\theta_{4}})\,{
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{5
}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\sin({\theta
_{1}})\,m_{5}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{5}\,r_{2}\,\cos(
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{5}\,r
_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{1
}\,\sin({\theta_{1}})\,m_{4}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{4}\,r_{3}\,\sin({\theta_{3}})\,{
\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{4
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\sin({\theta
_{1}})\,m_{4}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{5}\,r_{3}\,\sin(
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{5}\,r
_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{1
}\,\sin({\theta_{1}})\,m_{7}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})\,{
\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{7
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\sin({\theta
_{1}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} + 2\,r_{1}
\,\cos({\theta_{1}})\,m_{9}\,g \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({
\theta_{1}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4
\,r_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{{\eta
_{3}}}^2 \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r_{3
}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,
m_{7}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{}
 - 4\,r_{1}\,\cos({\theta_{1}})\,m_{5}\,r_{2}\,\sin({\theta_{2}})\,{{
\eta_{2}}}^2 - 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}\,r_{5}\,\sin({
\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({
\theta_{1}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4
\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta
_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{
4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} + 2\,r_{1}\,\cos({\theta_{1}}
)\,m_{2}\,g + 2\,r_{1}\,\cos({\theta_{1}})\,m_{4}\,g + 2\,r_{1}\,\cos(
{\theta_{1}})\,m_{3}\,g \\ &&\quad\mbox{} + 2\,r_{1}\,\cos({\theta_{1}
})\,m_{8}\,g + 2\,r_{1}\,\cos({\theta_{1}})\,m_{7}\,g + 2\,r_{1}\,\cos
({\theta_{1}})\,m_{6}\,g + 2\,r_{1}\,\cos({\theta_{1}})\,m_{5}\,g + 2
\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,g \\ &&\quad\mbox{} + J_{1}\,{
\dot{\eta}_{1}} + 2\,r_{1}\,\sin({\theta_{1}})\,m_{8}\,r_{8}\,\sin({
\theta_{8}})\,{\dot{\eta}_{8}} + 2\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,
r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r_{
1}\,\sin({\theta_{1}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}
_{9}} + 2\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})
\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,r_{1}\,\cos({\theta_{1}})\,m
_{10}\,r_{10}\,\cos({\theta_{10}})\,{\dot{\eta}_{10}} + 2\,r_{1}\,\sin
({\theta_{1}})\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{\dot{\eta}_{10}}
 \\ &&\quad\mbox{} + m_{1}\,{r_{1}}^2\,{\dot{\eta}_{1}} + 2\,r_{1}\,
\cos({\theta_{1}})\,m_{2}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
 + 2\,r_{1}\,\sin({\theta_{1}})\,m_{2}\,r_{2}\,\sin({\theta_{2}})\,{
\dot{\eta}_{2}} \\ &&\quad\mbox{} + 2\,r_{1}\,\sin({\theta_{1}})\,m_{2
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 - 2\,r_{1}\,\cos({\theta
_{1}})\,m_{2}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2
 \\ &&\quad\mbox{} + 2\,r_{1}\,\sin({\theta_{1}})\,m_{3}\,r_{3}\,\cos(
{\theta_{3}})\,{{\eta_{3}}}^2 - 2\,r_{1}\,\cos({\theta_{1}})\,m_{3}\,r
_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} - 2\,r_{1}
\,\cos({\theta_{1}})\,m_{4}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
 + 2\,r_{1}\,\sin({\theta_{1}})\,m_{4}\,r_{4}\,\cos({\theta_{4}})\,{{
\eta_{4}}}^2 \\ &&\quad\mbox{} - 2\,r_{1}\,\cos({\theta_{1}})\,m_{5}\,
r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 2\,r_{1}\,\sin({\theta_{1}
})\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{}
 + 2\,r_{1}\,\sin({\theta_{1}})\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,{{
\eta_{6}}}^2 - 2\,r_{1}\,\cos({\theta_{1}})\,m_{6}\,r_{6}\,\sin({
\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,r_{1}\,\sin({
\theta_{1}})\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 - 2\,r
_{1}\,\cos({\theta_{1}})\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}
}}^2 \\ &&\quad\mbox{} - 2\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r_{8}\,
\sin({\theta_{8}})\,{{\eta_{8}}}^2 + 2\,r_{1}\,\sin({\theta_{1}})\,m_{
8}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 2\,r
_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{{\eta
_{10}}}^2 - 2\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{10}\,\sin({\theta
_{10}})\,{{\eta_{10}}}^2 \\ &&\quad\mbox{} + 2\,r_{1}\,\sin({\theta_{1
}})\,m_{3}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} + 2\,r_{1}\,
\cos({\theta_{1}})\,m_{3}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 2\,r_{1}\,\cos({\theta_{1}})\,m_{4}\,r_{4}\,\cos(
{\theta_{4}})\,{\dot{\eta}_{4}} + 2\,r_{1}\,\sin({\theta_{1}})\,m_{4}
\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 2\,r
_{1}\,\cos({\theta_{1}})\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,{
\dot{\eta}_{5}} + 2\,r_{1}\,\sin({\theta_{1}})\,m_{5}\,r_{5}\,\sin({
\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 2\,r_{1}\,\sin({
\theta_{1}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} + 2\,
r_{1}\,\cos({\theta_{1}})\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,{
\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r_{1}\,\sin({\theta_{1}})\,m_{7
}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 2\,r_{1}\,\cos({
\theta_{1}})\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,
{r_{1}}^2\,m_{2}\,{\dot{\eta}_{1}} \end{eqnarray*}
\begin{eqnarray*} && m_{10}\,g\,r_{10}\,\cos({\theta_{10}}) + J_{10}\,
{\dot{\eta}_{10}} + m_{10}\,{r_{10}}^2\,{\dot{\eta}_{10}} + 2\,m_{10}
\,r_{10}\,\cos({\theta_{10}})\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
_{2}} \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{2
}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 2\,m_{10}\,r_{10}\,\sin({
\theta_{10}})\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{5}\,
\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 2\,m_{10}\,r_{10}\,\sin({\theta_{
10}})\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{}
 + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{9}\,\cos({\theta_{9}})\,
{{\eta_{9}}}^2 + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{9}\,\sin({
\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,
\sin({\theta_{10}})\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 + 2\,m
_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{8}\,\sin({\theta_{8}})\,{
\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,\sin({\theta_{
10}})\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 2\,m_{10}\,r_{10}\,
\sin({\theta_{10}})\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{6}\,
\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 2\,m_{10}\,r_{10}\,\sin({\theta_{
10}})\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{}
 - 2\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{1}\,\sin({\theta_{1}})\,
{{\eta_{1}}}^2 + 2\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{1}\,\cos({
\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 2\,m_{10}\,r_{10}\,
\cos({\theta_{10}})\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 2\,m
_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{4}\,\cos({\theta_{4}})\,{
\dot{\eta}_{4}} \\ &&\quad\mbox{} - 2\,m_{10}\,r_{10}\,\cos({\theta_{
10}})\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 2\,m_{10}\,r_{10}\,
\cos({\theta_{10}})\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} - 2\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{8}\,
\sin({\theta_{8}})\,{{\eta_{8}}}^2 + 2\,m_{10}\,r_{10}\,\cos({\theta_{
10}})\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{}
 - 2\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{9}\,\sin({\theta_{9}})\,
{{\eta_{9}}}^2 + 2\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{9}\,\cos({
\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} - 2\,m_{10}\,r_{10}\,
\cos({\theta_{10}})\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 2\,m
_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{7}\,\cos({\theta_{7}})\,{
\dot{\eta}_{7}} \\ &&\quad\mbox{} - 2\,m_{10}\,r_{10}\,\cos({\theta_{
10}})\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 + 2\,m_{10}\,r_{10}\,
\cos({\theta_{10}})\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}}
 \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{1}\,
\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{10}\,r_{10}\,\sin({\theta_{
10}})\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{}
 + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{4}\,\cos({\theta_{4}})\,
{{\eta_{4}}}^2 + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{4}\,\sin({
\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,
\sin({\theta_{10}})\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 - 2\,m
_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{4}\,\sin({\theta_{4}})\,{{\eta
_{4}}}^2 \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r
_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} + 2\,m_{10}\,r_{10}\,\cos({
\theta_{10}})\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} - 2\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{2}\,
\sin({\theta_{2}})\,{{\eta_{2}}}^2 \end{eqnarray*}
\begin{eqnarray*} && m_{5}\,g\,r_{5}\,\cos({\theta_{5}}) + 2\,r_{5}\,
\cos({\theta_{5}})\,m_{10}\,g + 2\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,g
 + 2\,r_{5}\,\cos({\theta_{5}})\,m_{8}\,g + 2\,r_{5}\,\cos({\theta_{5}
})\,m_{9}\,g \\ &&\quad\mbox{} + 2\,r_{5}\,\cos({\theta_{5}})\,m_{6}\,
g + 4\,{r_{5}}^2\,m_{7}\,{\dot{\eta}_{5}} + 4\,{r_{5}}^2\,m_{6}\,{
\dot{\eta}_{5}} + 4\,{r_{5}}^2\,m_{8}\,{\dot{\eta}_{5}} + 4\,{r_{5}}^2
\,m_{9}\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,{r_{5}}^2\,m_{10}\,{
\dot{\eta}_{5}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,r_{3}\,\sin({
\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,
r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}
\,\sin({\theta_{5}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2
}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,r_{4}\,\sin({\theta_{4}})\,{
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{7
}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{5}\,\sin({\theta
_{5}})\,m_{7}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}}
 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{6}\,r_{1}\,\cos(
{\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{6}
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
5}\,\cos({\theta_{5}})\,m_{6}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}
_{3}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{6}\,r_{2}\,\sin({\theta_{2}})
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{
6}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{5}\,\cos({
\theta_{5}})\,m_{6}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{6}\,r_{4}\,\cos(
{\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{6}
\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{
5}\,\sin({\theta_{5}})\,m_{7}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}
^2 - 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,r_{6}\,\sin({\theta_{6}})\,{
{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}
\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{5}\,\cos({\theta
_{5}})\,m_{8}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{8}\,r_{2}\,\sin(
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,r
_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{5
}\,\cos({\theta_{5}})\,m_{8}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^
2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,r_{4}\,\cos({\theta_{4}})\,{{
\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,
r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{5}\,\sin({\theta_{
5}})\,m_{6}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,r_{1}\,\cos(
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,r
_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{5
}\,\sin({\theta_{5}})\,m_{6}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^
2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,r_{2}\,\sin({\theta_{2}})\,{
\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{8
}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{5}\,r_{5}\,\sin({
\theta_{5}})\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 2\,m_{5}\,r_{5}\,\sin({\theta_{5}})\,r_{2}\,\cos(
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{8}\,r
_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} - 4\,r_{5
}\,\cos({\theta_{5}})\,m_{8}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^
2 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})\,{
\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{8
}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{5}\,\cos({\theta
_{5}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{8}\,r_{2}\,\cos(
{\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{8}
\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{
5}\,\cos({\theta_{5}})\,m_{8}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}
_{1}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{2}\,\sin({\theta_{2}}
)\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m
_{10}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{5}\,\cos({
\theta_{5}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{3}\,\cos
({\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{10
}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,
r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{
8}}}^2 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{8}\,\cos({\theta_{8}
})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})
\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{5}\,\cos({
\theta_{5}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{\dot{\eta}_{9}}
 \\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{7}\,\sin
({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}
\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r
_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{
\dot{\eta}_{6}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{6}\,\sin({
\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} - 4\,r_{5}\,\cos({
\theta_{5}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 - 4\,r
_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1
}}}^2 \\ &&\quad\mbox{} + 2\,m_{5}\,r_{5}\,\sin({\theta_{5}})\,r_{2}\,
\sin({\theta_{2}})\,{\dot{\eta}_{2}} + 4\,r_{5}\,\cos({\theta_{5}})\,m
_{10}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{}
 - 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{3}\,\sin({\theta_{3}})\,{{
\eta_{3}}}^2 + 2\,m_{5}\,r_{5}\,\sin({\theta_{5}})\,r_{4}\,\cos({
\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 2\,m_{5}\,r_{5}\,\sin
({\theta_{5}})\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 2\,m_{5}
\,r_{5}\,\sin({\theta_{5}})\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{4}\,\cos(
{\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{10}
\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r
_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4
}}}^2 - 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{
10}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{5}\,\sin({
\theta_{5}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{3}\,\sin
({\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{10
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r
_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{2}\,\sin({\theta_{2}})\,{
\dot{\eta}_{2}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{6}\,\cos({
\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({
\theta_{5}})\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} + 4
\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{{\eta
_{9}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{3
}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{5}\,\cos({\theta_{5}})
\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{}
 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})\,{
\dot{\eta}_{2}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{8}\,\sin({
\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({
\theta_{5}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r
_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{7}\,\sin({\theta_{7}})\,{
\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{5}\,\sin({\theta
_{5}})\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
 \\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{1}\,\sin(
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}\,r
_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}
\,\sin({\theta_{5}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4
}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}\,r_{3}\,\cos({\theta_{3}})\,{
{\eta_{3}}}^2 \\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}
\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{5}\,\sin({\theta_{
5}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{1}\,\cos(
{\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
5}\,\sin({\theta_{5}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}
_{9}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{8}\,\cos({\theta_{8}}
)\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m
_{9}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{5}\,\cos({
\theta_{5}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}}
 \\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{7}\,\sin(
{\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r
_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} - 4\,r_{5
}\,\cos({\theta_{5}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^
2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{{
\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}\,
r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{5}\,\sin({\theta_{
5}})\,m_{8}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{8}\,r_{6}\,\sin(
{\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}
\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} - 4\,r_{
5}\,\cos({\theta_{5}})\,m_{7}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}
^2 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,r_{1}\,\cos({\theta_{1}})\,{
\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9
}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{5}\,\sin({
\theta_{5}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2
 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{8}\,r_{4}\,\sin(
{\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}
\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,r
_{5}\,\sin({\theta_{5}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}
}}^2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}\,r_{7}\,\sin({\theta_{7}})
\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m
_{8}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} + 4\,r_{5}\,\sin({
\theta_{5}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2
 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{8}\,r_{7}\,\sin(
{\theta_{7}})\,{\dot{\eta}_{7}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}
\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
5}\,\cos({\theta_{5}})\,m_{7}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
_{2}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,r_{4}\,\sin({\theta_{4}})
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{
7}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{5}\,\sin({
\theta_{5}})\,m_{8}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,r_{3}\,\cos(
{\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{8}
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
5}\,\sin({\theta_{5}})\,m_{8}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}
^2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{8}\,r_{1}\,\cos({\theta_{1}})\,{
{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{8}
\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{5}\,\sin({\theta
_{5}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2
 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,r_{1}\,\cos(
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,r
_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{5
}\,\sin({\theta_{5}})\,m_{7}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^
2 - 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})\,{{
\eta_{3}}}^2 \\ &&\quad\mbox{} + 2\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,
r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 2\,m_{5}\,r_{5}\,\cos({
\theta_{5}})\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2
 \\ &&\quad\mbox{} - 2\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,r_{3}\,\sin(
{\theta_{3}})\,{{\eta_{3}}}^2 - 2\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,r
_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 2\,m_{5}
\,r_{5}\,\cos({\theta_{5}})\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4
}} + 2\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,r_{2}\,\cos({\theta_{2}})\,{
\dot{\eta}_{2}} \\ &&\quad\mbox{} + 2\,m_{5}\,r_{5}\,\sin({\theta_{5}}
)\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{5}\,r_{5}\,\sin({
\theta_{5}})\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}}
 \\ &&\quad\mbox{} - 2\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,r_{1}\,\sin(
{\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,r
_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} + J_{5}\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} + 2\,r_{5}\,\sin({\theta_{5}})\,m_{8}\,r_{8}\,\sin(
{\theta_{8}})\,{\dot{\eta}_{8}} + 2\,r_{5}\,\cos({\theta_{5}})\,m_{8}
\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r
_{5}\,\sin({\theta_{5}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{
\dot{\eta}_{9}} + 2\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{9}\,\cos({
\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,r_{5}\,\cos({
\theta_{5}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{\dot{\eta}_{10}}
 + 2\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,
{\dot{\eta}_{10}} \\ &&\quad\mbox{} + 2\,r_{5}\,\sin({\theta_{5}})\,m
_{6}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 - 2\,r_{5}\,\cos({
\theta_{5}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2
 \\ &&\quad\mbox{} + 2\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,r_{7}\,\cos(
{\theta_{7}})\,{{\eta_{7}}}^2 - 2\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,r
_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 2\,r_{5}
\,\sin({\theta_{5}})\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2
 - 2\,r_{5}\,\cos({\theta_{5}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{{
\eta_{8}}}^2 \\ &&\quad\mbox{} + 2\,r_{5}\,\sin({\theta_{5}})\,m_{9}\,
r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 - 2\,r_{5}\,\cos({\theta_{5}
})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{}
 - 2\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,
{{\eta_{10}}}^2 + 2\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{10}\,\cos({
\theta_{10}})\,{{\eta_{10}}}^2 + m_{5}\,{r_{5}}^2\,{\dot{\eta}_{5}}
 \\ &&\quad\mbox{} + 2\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,r_{6}\,\sin(
{\theta_{6}})\,{\dot{\eta}_{6}} + 2\,r_{5}\,\cos({\theta_{5}})\,m_{6}
\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r
_{5}\,\cos({\theta_{5}})\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,{
\dot{\eta}_{7}} + 2\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,r_{7}\,\sin({
\theta_{7}})\,{\dot{\eta}_{7}} \end{eqnarray*}
a cononical form $M(q)\dot{t}+C(q)t^2 +R$,M:
 
$$ \left( \begin{array}{cccccccccc} 4\,{r_{1}}^2\,m_{8}+4\,{r_{1}}^2\,
m_{10}+m_{1}\,{r_{1}}^2+4\,{r_{1}}^2\,m_{6}+4\,{r_{1}}^2\,m_{9}+4\,{r
_{1}}^2\,m_{7}+4\,{r_{1}}^2\,m_{2}+J_{1}+4\,{r_{1}}^2\,m_{5}+4\,{r_{1}
}^2\,m_{4}+4\,{r_{1}}^2\,m_{3} & 2\,r_{1}\,r_{2}\,\cos({\theta_{1}}-{
\theta_{2}})\,(2\,m_{3}+m_{2}+2\,m_{4}+2\,m_{7}+2\,m_{10}+2\,m_{5}+2\,
m_{6}+2\,m_{9}+2\,m_{8}) & 2\,r_{1}\,r_{3}\,\cos({\theta_{1}}-{\theta
_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m_{7}+m_{3}+2\,m_{9}+
2\,m_{6}) & 2\,r_{1}\,r_{4}\,\cos({\theta_{1}}-{\theta_{4}})\,(2\,m_{8
}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,m_{6}) & 2\,r_{1}\,r_{
5}\,\cos({\theta_{1}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m
_{7}+m_{5}+2\,m_{10}) & 2\,r_{1}\,r_{6}\,\cos({\theta_{1}}-{\theta_{6}
})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{1}\,r_{7}\,
\cos({\theta_{1}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9})
 & 2\,r_{1}\,r_{8}\,\cos({\theta_{1}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+
2\,m_{9}) & 2\,r_{1}\,r_{9}\,\cos({\theta_{1}}-{\theta_{9}})\,(m_{9}+2
\,m_{10}) & 2\,r_{1}\,m_{10}\,r_{10}\,\cos({\theta_{1}}-{\theta_{10}})
 \cr 2\,r_{1}\,r_{2}\,\cos({\theta_{1}}-{\theta_{2}})\,(2\,m_{3}+m_{2}
+2\,m_{4}+2\,m_{7}+2\,m_{10}+2\,m_{5}+2\,m_{6}+2\,m_{9}+2\,m_{8}) & J
_{2}+4\,{r_{2}}^2\,m_{3}+4\,{r_{2}}^2\,m_{4}+4\,{r_{2}}^2\,m_{7}+4\,{r
_{2}}^2\,m_{8}+m_{2}\,{r_{2}}^2+4\,{r_{2}}^2\,m_{9}+4\,{r_{2}}^2\,m_{5
}+4\,{r_{2}}^2\,m_{10}+4\,{r_{2}}^2\,m_{6} & 2\,r_{2}\,r_{3}\,\cos({
\theta_{2}}-{\theta_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m
_{7}+m_{3}+2\,m_{9}+2\,m_{6}) & 2\,r_{2}\,r_{4}\,\cos({\theta_{2}}-{
\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,
m_{6}) & 2\,r_{2}\,r_{5}\,\cos({\theta_{2}}-{\theta_{5}})\,(2\,m_{6}+2
\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 2\,r_{2}\,r_{6}\,\cos({
\theta_{2}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}
) & 2\,r_{2}\,r_{7}\,\cos({\theta_{2}}-{\theta_{7}})\,(2\,m_{10}+m_{7}
+2\,m_{8}+2\,m_{9}) & 2\,r_{2}\,r_{8}\,\cos({\theta_{2}}-{\theta_{8}})
\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{2}\,r_{9}\,\cos({\theta_{2}}-{
\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{2}\,m_{10}\,r_{10}\,\cos({
\theta_{2}}-{\theta_{10}}) \cr 2\,r_{1}\,r_{3}\,\cos({\theta_{1}}-{
\theta_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m_{7}+m_{3}+2\,
m_{9}+2\,m_{6}) & 2\,r_{2}\,r_{3}\,\cos({\theta_{2}}-{\theta_{3}})\,(2
\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m_{7}+m_{3}+2\,m_{9}+2\,m_{6})
 & 4\,{r_{3}}^2\,m_{4}+4\,{r_{3}}^2\,m_{10}+4\,{r_{3}}^2\,m_{9}+4\,{r
_{3}}^2\,m_{5}+4\,{r_{3}}^2\,m_{6}+m_{3}\,{r_{3}}^2+J_{3}+4\,{r_{3}}^2
\,m_{7}+4\,{r_{3}}^2\,m_{8} & 2\,r_{3}\,r_{4}\,\cos({\theta_{3}}-{
\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,
m_{6}) & 2\,r_{3}\,r_{5}\,\cos({\theta_{3}}-{\theta_{5}})\,(2\,m_{6}+2
\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 2\,r_{3}\,r_{6}\,\cos({
\theta_{3}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}
) & 2\,r_{3}\,r_{7}\,\cos({\theta_{3}}-{\theta_{7}})\,(2\,m_{10}+m_{7}
+2\,m_{8}+2\,m_{9}) & 2\,r_{3}\,r_{8}\,\cos({\theta_{3}}-{\theta_{8}})
\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{3}\,r_{9}\,\cos({\theta_{3}}-{
\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{3}\,m_{10}\,r_{10}\,\cos({
\theta_{3}}-{\theta_{10}}) \cr 2\,r_{1}\,r_{4}\,\cos({\theta_{1}}-{
\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,
m_{6}) & 2\,r_{2}\,r_{4}\,\cos({\theta_{2}}-{\theta_{4}})\,(2\,m_{8}+m
_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,m_{6}) & 2\,r_{3}\,r_{4}
\,\cos({\theta_{3}}-{\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2
\,m_{7}+2\,m_{10}+2\,m_{6}) & 4\,{r_{4}}^2\,m_{10}+4\,{r_{4}}^2\,m_{9}
+4\,{r_{4}}^2\,m_{6}+4\,{r_{4}}^2\,m_{5}+4\,{r_{4}}^2\,m_{7}+J_{4}+m_{
4}\,{r_{4}}^2+4\,{r_{4}}^2\,m_{8} & 2\,r_{4}\,r_{5}\,\cos({\theta_{4}}
-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10})
 & 2\,r_{4}\,r_{6}\,\cos({\theta_{4}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2
\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{4}\,r_{7}\,\cos({\theta_{4}}-{
\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{4}\,r_{8}\,
\cos({\theta_{4}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{4}
\,r_{9}\,\cos({\theta_{4}}-{\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{4}
\,m_{10}\,r_{10}\,\cos({\theta_{4}}-{\theta_{10}}) \cr 2\,r_{1}\,r_{5}
\,\cos({\theta_{1}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7
}+m_{5}+2\,m_{10}) & 2\,r_{2}\,r_{5}\,\cos({\theta_{2}}-{\theta_{5}})
\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 2\,r_{3}\,r
_{5}\,\cos({\theta_{3}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,
m_{7}+m_{5}+2\,m_{10}) & 2\,r_{4}\,r_{5}\,\cos({\theta_{4}}-{\theta_{5
}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 4\,{r_{5}
}^2\,m_{8}+4\,{r_{5}}^2\,m_{10}+4\,{r_{5}}^2\,m_{7}+4\,{r_{5}}^2\,m_{9
}+4\,{r_{5}}^2\,m_{6}+J_{5}+m_{5}\,{r_{5}}^2 & 2\,r_{5}\,r_{6}\,\cos({
\theta_{5}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}
) & 2\,r_{5}\,r_{7}\,\cos({\theta_{5}}-{\theta_{7}})\,(2\,m_{10}+m_{7}
+2\,m_{8}+2\,m_{9}) & 2\,r_{5}\,r_{8}\,\cos({\theta_{5}}-{\theta_{8}})
\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{5}\,r_{9}\,\cos({\theta_{5}}-{
\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{5}\,m_{10}\,r_{10}\,\cos({
\theta_{5}}-{\theta_{10}}) \cr 2\,r_{1}\,r_{6}\,\cos({\theta_{1}}-{
\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{2}
\,r_{6}\,\cos({\theta_{2}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2
\,m_{7}+2\,m_{8}) & 2\,r_{3}\,r_{6}\,\cos({\theta_{3}}-{\theta_{6}})\,
(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{4}\,r_{6}\,\cos({
\theta_{4}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}
) & 2\,r_{5}\,r_{6}\,\cos({\theta_{5}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+
2\,m_{10}+2\,m_{7}+2\,m_{8}) & m_{6}\,{r_{6}}^2+4\,{r_{6}}^2\,m_{7}+4
\,{r_{6}}^2\,m_{8}+J_{6}+4\,{r_{6}}^2\,m_{9}+4\,{r_{6}}^2\,m_{10} & 2
\,r_{6}\,r_{7}\,\cos({\theta_{6}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m
_{8}+2\,m_{9}) & 2\,r_{6}\,r_{8}\,\cos({\theta_{6}}-{\theta_{8}})\,(m
_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{6}\,r_{9}\,\cos({\theta_{6}}-{\theta
_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{6}\,m_{10}\,r_{10}\,\cos({\theta_{6}
}-{\theta_{10}}) \cr 2\,r_{1}\,r_{7}\,\cos({\theta_{1}}-{\theta_{7}})
\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{2}\,r_{7}\,\cos({\theta
_{2}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{3}\,r
_{7}\,\cos({\theta_{3}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m
_{9}) & 2\,r_{4}\,r_{7}\,\cos({\theta_{4}}-{\theta_{7}})\,(2\,m_{10}+m
_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{5}\,r_{7}\,\cos({\theta_{5}}-{\theta_{
7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{6}\,r_{7}\,\cos({
\theta_{6}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 4\,{r
_{7}}^2\,m_{9}+4\,{r_{7}}^2\,m_{10}+4\,{r_{7}}^2\,m_{8}+J_{7}+m_{7}\,{
r_{7}}^2 & 2\,r_{7}\,r_{8}\,\cos({\theta_{7}}-{\theta_{8}})\,(m_{8}+2
\,m_{10}+2\,m_{9}) & 2\,r_{7}\,r_{9}\,\cos({\theta_{7}}-{\theta_{9}})
\,(m_{9}+2\,m_{10}) & 2\,r_{7}\,m_{10}\,r_{10}\,\cos({\theta_{7}}-{
\theta_{10}}) \cr 2\,r_{1}\,r_{8}\,\cos({\theta_{1}}-{\theta_{8}})\,(m
_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{2}\,r_{8}\,\cos({\theta_{2}}-{\theta
_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{3}\,r_{8}\,\cos({\theta_{3}
}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{4}\,r_{8}\,\cos({
\theta_{4}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{5}\,r_{8
}\,\cos({\theta_{5}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r
_{6}\,r_{8}\,\cos({\theta_{6}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9
}) & 2\,r_{7}\,r_{8}\,\cos({\theta_{7}}-{\theta_{8}})\,(m_{8}+2\,m_{10
}+2\,m_{9}) & 4\,{r_{8}}^2\,m_{9}+J_{8}+m_{8}\,{r_{8}}^2+4\,{r_{8}}^2
\,m_{10} & 2\,r_{8}\,r_{9}\,\cos({\theta_{8}}-{\theta_{9}})\,(m_{9}+2
\,m_{10}) & 2\,r_{8}\,m_{10}\,r_{10}\,\cos({\theta_{8}}-{\theta_{10}})
 \cr 2\,r_{1}\,r_{9}\,\cos({\theta_{1}}-{\theta_{9}})\,(m_{9}+2\,m_{10
}) & 2\,r_{2}\,r_{9}\,\cos({\theta_{2}}-{\theta_{9}})\,(m_{9}+2\,m_{10
}) & 2\,r_{3}\,r_{9}\,\cos({\theta_{3}}-{\theta_{9}})\,(m_{9}+2\,m_{10
}) & 2\,r_{4}\,r_{9}\,\cos({\theta_{4}}-{\theta_{9}})\,(m_{9}+2\,m_{10
}) & 2\,r_{5}\,r_{9}\,\cos({\theta_{5}}-{\theta_{9}})\,(m_{9}+2\,m_{10
}) & 2\,r_{6}\,r_{9}\,\cos({\theta_{6}}-{\theta_{9}})\,(m_{9}+2\,m_{10
}) & 2\,r_{7}\,r_{9}\,\cos({\theta_{7}}-{\theta_{9}})\,(m_{9}+2\,m_{10
}) & 2\,r_{8}\,r_{9}\,\cos({\theta_{8}}-{\theta_{9}})\,(m_{9}+2\,m_{10
}) & 4\,{r_{9}}^2\,m_{10}+J_{9}+m_{9}\,{r_{9}}^2 & 2\,r_{9}\,m_{10}\,r
_{10}\,\cos({\theta_{9}}-{\theta_{10}}) \cr 2\,r_{1}\,m_{10}\,r_{10}\,
\cos({\theta_{1}}-{\theta_{10}}) & 2\,r_{2}\,m_{10}\,r_{10}\,\cos({
\theta_{2}}-{\theta_{10}}) & 2\,r_{3}\,m_{10}\,r_{10}\,\cos({\theta_{3
}}-{\theta_{10}}) & 2\,r_{4}\,m_{10}\,r_{10}\,\cos({\theta_{4}}-{
\theta_{10}}) & 2\,r_{5}\,m_{10}\,r_{10}\,\cos({\theta_{5}}-{\theta_{
10}}) & 2\,r_{6}\,m_{10}\,r_{10}\,\cos({\theta_{6}}-{\theta_{10}}) & 2
\,r_{7}\,m_{10}\,r_{10}\,\cos({\theta_{7}}-{\theta_{10}}) & 2\,r_{8}\,
m_{10}\,r_{10}\,\cos({\theta_{8}}-{\theta_{10}}) & 2\,r_{9}\,m_{10}\,r
_{10}\,\cos({\theta_{9}}-{\theta_{10}}) & m_{10}\,{r_{10}}^2+J_{10}
 \end{array} \right) $$
C:
 
$$ \left( \begin{array}{cccccccccc} 0 & 2\,r_{1}\,r_{2}\,\sin({\theta
_{1}}-{\theta_{2}})\,(2\,m_{3}+m_{2}+2\,m_{4}+2\,m_{7}+2\,m_{10}+2\,m
_{5}+2\,m_{6}+2\,m_{9}+2\,m_{8}) & 2\,r_{1}\,r_{3}\,\sin({\theta_{1}}-
{\theta_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m_{7}+m_{3}+2
\,m_{9}+2\,m_{6}) & 2\,r_{1}\,r_{4}\,\sin({\theta_{1}}-{\theta_{4}})\,
(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,m_{6}) & 2\,r
_{1}\,r_{5}\,\sin({\theta_{1}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m
_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 2\,r_{1}\,r_{6}\,\sin({\theta_{1}}-{
\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{1}
\,r_{7}\,\sin({\theta_{1}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2
\,m_{9}) & 2\,r_{1}\,r_{8}\,\sin({\theta_{1}}-{\theta_{8}})\,(m_{8}+2
\,m_{10}+2\,m_{9}) & 2\,r_{1}\,r_{9}\,\sin({\theta_{1}}-{\theta_{9}})
\,(m_{9}+2\,m_{10}) & 2\,r_{1}\,m_{10}\,r_{10}\,\sin({\theta_{1}}-{
\theta_{10}}) \cr -2\,r_{1}\,r_{2}\,\sin({\theta_{1}}-{\theta_{2}})\,(
2\,m_{3}+m_{2}+2\,m_{4}+2\,m_{7}+2\,m_{10}+2\,m_{5}+2\,m_{6}+2\,m_{9}+
2\,m_{8}) & 0 & 2\,r_{2}\,r_{3}\,\sin({\theta_{2}}-{\theta_{3}})\,(2\,
m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m_{7}+m_{3}+2\,m_{9}+2\,m_{6}) & 
2\,r_{2}\,r_{4}\,\sin({\theta_{2}}-{\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m
_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,m_{6}) & 2\,r_{2}\,r_{5}\,\sin({
\theta_{2}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+
2\,m_{10}) & 2\,r_{2}\,r_{6}\,\sin({\theta_{2}}-{\theta_{6}})\,(m_{6}+
2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{2}\,r_{7}\,\sin({\theta
_{2}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{2}\,r
_{8}\,\sin({\theta_{2}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2
\,r_{2}\,r_{9}\,\sin({\theta_{2}}-{\theta_{9}})\,(m_{9}+2\,m_{10}) & 2
\,r_{2}\,m_{10}\,r_{10}\,\sin({\theta_{2}}-{\theta_{10}}) \cr -2\,r_{1
}\,r_{3}\,\sin({\theta_{1}}-{\theta_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10
}+2\,m_{8}+2\,m_{7}+m_{3}+2\,m_{9}+2\,m_{6}) & -2\,r_{2}\,r_{3}\,\sin(
{\theta_{2}}-{\theta_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m
_{7}+m_{3}+2\,m_{9}+2\,m_{6}) & 0 & 2\,r_{3}\,r_{4}\,\sin({\theta_{3}}
-{\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2
\,m_{6}) & 2\,r_{3}\,r_{5}\,\sin({\theta_{3}}-{\theta_{5}})\,(2\,m_{6}
+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 2\,r_{3}\,r_{6}\,\sin({
\theta_{3}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}
) & 2\,r_{3}\,r_{7}\,\sin({\theta_{3}}-{\theta_{7}})\,(2\,m_{10}+m_{7}
+2\,m_{8}+2\,m_{9}) & 2\,r_{3}\,r_{8}\,\sin({\theta_{3}}-{\theta_{8}})
\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{3}\,r_{9}\,\sin({\theta_{3}}-{
\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{3}\,m_{10}\,r_{10}\,\sin({
\theta_{3}}-{\theta_{10}}) \cr -2\,r_{1}\,r_{4}\,\sin({\theta_{1}}-{
\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,
m_{6}) & -2\,r_{2}\,r_{4}\,\sin({\theta_{2}}-{\theta_{4}})\,(2\,m_{8}+
m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,m_{6}) & -2\,r_{3}\,r_{4
}\,\sin({\theta_{3}}-{\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+
2\,m_{7}+2\,m_{10}+2\,m_{6}) & 0 & 2\,r_{4}\,r_{5}\,\sin({\theta_{4}}-
{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10})
 & 2\,r_{4}\,r_{6}\,\sin({\theta_{4}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2
\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{4}\,r_{7}\,\sin({\theta_{4}}-{
\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{4}\,r_{8}\,
\sin({\theta_{4}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{4}
\,r_{9}\,\sin({\theta_{4}}-{\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{4}
\,m_{10}\,r_{10}\,\sin({\theta_{4}}-{\theta_{10}}) \cr -2\,r_{1}\,r_{5
}\,\sin({\theta_{1}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{
7}+m_{5}+2\,m_{10}) & -2\,r_{2}\,r_{5}\,\sin({\theta_{2}}-{\theta_{5}}
)\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & -2\,r_{3}\,
r_{5}\,\sin({\theta_{3}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2
\,m_{7}+m_{5}+2\,m_{10}) & -2\,r_{4}\,r_{5}\,\sin({\theta_{4}}-{\theta
_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 0 & 2
\,r_{5}\,r_{6}\,\sin({\theta_{5}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m
_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{5}\,r_{7}\,\sin({\theta_{5}}-{\theta
_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{5}\,r_{8}\,\sin({
\theta_{5}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{5}\,r_{9
}\,\sin({\theta_{5}}-{\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{5}\,m_{
10}\,r_{10}\,\sin({\theta_{5}}-{\theta_{10}}) \cr -2\,r_{1}\,r_{6}\,
\sin({\theta_{1}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2
\,m_{8}) & -2\,r_{2}\,r_{6}\,\sin({\theta_{2}}-{\theta_{6}})\,(m_{6}+2
\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & -2\,r_{3}\,r_{6}\,\sin({\theta
_{3}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & -2
\,r_{4}\,r_{6}\,\sin({\theta_{4}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m
_{10}+2\,m_{7}+2\,m_{8}) & -2\,r_{5}\,r_{6}\,\sin({\theta_{5}}-{\theta
_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & 0 & 2\,r_{6}\,r
_{7}\,\sin({\theta_{6}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m
_{9}) & 2\,r_{6}\,r_{8}\,\sin({\theta_{6}}-{\theta_{8}})\,(m_{8}+2\,m
_{10}+2\,m_{9}) & 2\,r_{6}\,r_{9}\,\sin({\theta_{6}}-{\theta_{9}})\,(m
_{9}+2\,m_{10}) & 2\,r_{6}\,m_{10}\,r_{10}\,\sin({\theta_{6}}-{\theta
_{10}}) \cr -2\,r_{1}\,r_{7}\,\sin({\theta_{1}}-{\theta_{7}})\,(2\,m_{
10}+m_{7}+2\,m_{8}+2\,m_{9}) & -2\,r_{2}\,r_{7}\,\sin({\theta_{2}}-{
\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & -2\,r_{3}\,r_{7}\,
\sin({\theta_{3}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9})
 & -2\,r_{4}\,r_{7}\,\sin({\theta_{4}}-{\theta_{7}})\,(2\,m_{10}+m_{7}
+2\,m_{8}+2\,m_{9}) & -2\,r_{5}\,r_{7}\,\sin({\theta_{5}}-{\theta_{7}}
)\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & -2\,r_{6}\,r_{7}\,\sin({
\theta_{6}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 0 & 2
\,r_{7}\,r_{8}\,\sin({\theta_{7}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m
_{9}) & 2\,r_{7}\,r_{9}\,\sin({\theta_{7}}-{\theta_{9}})\,(m_{9}+2\,m
_{10}) & 2\,r_{7}\,m_{10}\,r_{10}\,\sin({\theta_{7}}-{\theta_{10}})
 \cr -2\,r_{1}\,r_{8}\,\sin({\theta_{1}}-{\theta_{8}})\,(m_{8}+2\,m_{
10}+2\,m_{9}) & -2\,r_{2}\,r_{8}\,\sin({\theta_{2}}-{\theta_{8}})\,(m
_{8}+2\,m_{10}+2\,m_{9}) & -2\,r_{3}\,r_{8}\,\sin({\theta_{3}}-{\theta
_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & -2\,r_{4}\,r_{8}\,\sin({\theta_{4
}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & -2\,r_{5}\,r_{8}\,\sin(
{\theta_{5}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & -2\,r_{6}\,r
_{8}\,\sin({\theta_{6}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & -2
\,r_{7}\,r_{8}\,\sin({\theta_{7}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m
_{9}) & 0 & 2\,r_{8}\,r_{9}\,\sin({\theta_{8}}-{\theta_{9}})\,(m_{9}+2
\,m_{10}) & 2\,r_{8}\,m_{10}\,r_{10}\,\sin({\theta_{8}}-{\theta_{10}})
 \cr -2\,r_{1}\,r_{9}\,\sin({\theta_{1}}-{\theta_{9}})\,(m_{9}+2\,m_{
10}) & -2\,r_{2}\,r_{9}\,\sin({\theta_{2}}-{\theta_{9}})\,(m_{9}+2\,m
_{10}) & -2\,r_{3}\,r_{9}\,\sin({\theta_{3}}-{\theta_{9}})\,(m_{9}+2\,
m_{10}) & -2\,r_{4}\,r_{9}\,\sin({\theta_{4}}-{\theta_{9}})\,(m_{9}+2
\,m_{10}) & -2\,r_{5}\,r_{9}\,\sin({\theta_{5}}-{\theta_{9}})\,(m_{9}+
2\,m_{10}) & -2\,r_{6}\,r_{9}\,\sin({\theta_{6}}-{\theta_{9}})\,(m_{9}
+2\,m_{10}) & -2\,r_{7}\,r_{9}\,\sin({\theta_{7}}-{\theta_{9}})\,(m_{9
}+2\,m_{10}) & -2\,r_{8}\,r_{9}\,\sin({\theta_{8}}-{\theta_{9}})\,(m_{
9}+2\,m_{10}) & 0 & 2\,r_{9}\,m_{10}\,r_{10}\,\sin({\theta_{9}}-{
\theta_{10}}) \cr -2\,r_{1}\,m_{10}\,r_{10}\,\sin({\theta_{1}}-{\theta
_{10}}) & -2\,r_{2}\,m_{10}\,r_{10}\,\sin({\theta_{2}}-{\theta_{10}})
 & -2\,r_{3}\,m_{10}\,r_{10}\,\sin({\theta_{3}}-{\theta_{10}}) & -2\,r
_{4}\,m_{10}\,r_{10}\,\sin({\theta_{4}}-{\theta_{10}}) & -2\,r_{5}\,m
_{10}\,r_{10}\,\sin({\theta_{5}}-{\theta_{10}}) & -2\,r_{6}\,m_{10}\,r
_{10}\,\sin({\theta_{6}}-{\theta_{10}}) & -2\,r_{7}\,m_{10}\,r_{10}\,
\sin({\theta_{7}}-{\theta_{10}}) & -2\,r_{8}\,m_{10}\,r_{10}\,\sin({
\theta_{8}}-{\theta_{10}}) & -2\,r_{9}\,m_{10}\,r_{10}\,\sin({\theta_{
9}}-{\theta_{10}}) & 0 \end{array} \right) $$
R:
 
$$ \left( \begin{array}{c} g\,r_{1}\,\cos({\theta_{1}})\,(m_{1}+2\,m_{
9}+2\,m_{2}+2\,m_{4}+2\,m_{3}+2\,m_{8}+2\,m_{7}+2\,m_{6}+2\,m_{5}+2\,m
_{10}) \cr g\,r_{2}\,\cos({\theta_{2}})\,(2\,m_{3}+m_{2}+2\,m_{4}+2\,m
_{7}+2\,m_{10}+2\,m_{5}+2\,m_{6}+2\,m_{9}+2\,m_{8}) \cr g\,r_{3}\,\cos
({\theta_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m_{7}+m_{3}+2
\,m_{9}+2\,m_{6}) \cr g\,r_{4}\,\cos({\theta_{4}})\,(2\,m_{8}+m_{4}+2
\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,m_{6}) \cr g\,r_{5}\,\cos({
\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10})
 \cr g\,r_{6}\,\cos({\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+
2\,m_{8}) \cr g\,r_{7}\,\cos({\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+
2\,m_{9}) \cr g\,\cos({\theta_{8}})\,r_{8}\,(m_{8}+2\,m_{10}+2\,m_{9})
 \cr g\,r_{9}\,\cos({\theta_{9}})\,(m_{9}+2\,m_{10}) \cr m_{10}\,g\,r
_{10}\,\cos({\theta_{10}}) \end{array} \right) $$
Since $M,C,R$ only depends on $\theta$ 
,we can forget $x_i,y_i$ in the dynamical system 
 and just keep the $\dot{theta}=\eta$ in the	constraints