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# pendulum on a cart
# uses DAE solver to solve for x'', th1''
#
# pend-cart1.ode
#
# masses of cart and pendulum (kg)
par mc=5,mp=1
# length (m) and gravity
par l=1,g=9.8
# simple linear friction
par muc=0,mup=0
# set up DAEs
0=(mc+mp)*xdd+mp*l*cos(th1)*th1dd-mp*l*sin(th1)*th1p^2+muc*xp
0=cos(th1)*xdd+l*th1dd+g*sin(th1)+mup*th1p
solv xdd=0
solv th1dd=0
#
# dynamics
x'=xp
xp'=xdd
th1'=th1p
th1p'=th1dd
# track accelerations
aux xpp=xdd
aux th1pp=th1dd
@ dt=.02
# nice ICs
init th1=1.5
done
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