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# Copyright INRIA
with(share):
if SearchText(`Release 3`,interface(version))<>0 then
matadd:=add;
readshare(tex):
readshare(macrofor,numerics):
elif SearchText(`Release 4`,interface(version))<>0 then
readshare(tex,system):
readshare(macrofor,numerics):
else
ERROR(`Unknown Release`)
fi;
#----------------------------------------------------------------------------
# GENERAL PART
#----------------------------------------------------------------------------
#----------------------------------------------------------------------------
# Notation for Tex output
# and TeX output routines
# this routines generates proper derivative notations up to second derivative
# for a set of variable. The TeX name for the variables is also given
# Warning this function will detroy previous values of texsub
# Ex : addnotations( { x = `x` , th = `\\theta`, y =`y` } );
#-----------------------------------------------------------------------------
addnotations:=proc(varlist)
global texsub;
local x,nots:
nots:={};
for x in varlist do
nots:={op(nots),x,
cat(lhs(x),`d`)=cat(`\\dot{`,rhs(x),`}`),
cat(lhs(x),`dd`)=cat(`\\ddot{`,rhs(x),`}`)}
od;
texsub:=nots
end:
sortieinit:=proc(filename)
writeto(filename);
writeto(terminal);
end:
sorties:=proc(filename,comment,exp)
appendto(filename);
lprint(comment);
lprint(` `);
mtex(exp,latex);
writeto(terminal);
end:
sortiesI:=proc(filename,comment)
appendto(filename);
lprint(comment);
writeto(terminal);
end:
sortiesM:=proc(filename,comment,expr)
appendto(filename);
lprint(comment);
lprint(` `);
map(x -> mtex(x,latex),expr);
writeto(terminal);
end:
texwid:=120;
sortieinit(`systeme.tex`);
#---------------------------------------------------------------
# functions for computing euler equations
# L : the Lagrangian,
# q,qd,qdd are the state vector and its derivatives
#---------------------------------------------------------------
with(`linalg`):
euler_equations:=proc(L,q,qd,qdd)
local k,m:
m:=nops(q);
v:=matrix(m,1,0);
for i to m do
v[i,1]:=LL(q[i])=simplify(time_diff(diff(L,qd[i]),q,qd,qdd)
-diff(L,q[i]));
od;
eval(v):
end:
#---------------------------------------------------------------
# Time derivative computation of an expression
# depending on q,qd,qdd
# used to compute Euler equations
#---------------------------------------------------------------
ttvar:=proc(xx)
if type(xx,`indexed`)
then cat(op(0,xx),`d`)[op(xx)]
else cat(xx,`d`) fi
end:
time_diff:=proc(phi,q,qd,qdd)
local phi_copy,k,ttvar,diff_phi:
# subtitution to specify that q,qd ,qdd depends on time
phi_copy:=phi:
phi_copy:=subs(map( xx-> xx=xx(t),[op(q),op(qd)]),phi_copy):
diff_phi:=diff(phi_copy,t):
# subtitution to come back to our variables
diff_phi:=subs(map(xx->diff(xx(t),t)=ttvar(xx),[op(q),op(qd)]),
diff_phi):
diff_phi:=subs(map(xx->xx(t)=xx,[op(q),op(qd),op(qdd)]),diff_phi):
end:
#-----------------------------------------------------
# Rewritting the Euler equations to have a canonical form
# .. .
# El= ME(q) q + CE(q) q^2 + RE(q)
# Computation of ME,CE,RE
# CEuler returns a list [ME,CE,RE];
#-----------------------------------------------------
CEuler:=proc(E,q,qd,qdd)
local Me,Ce,Re:
Me:=MME(E,q,qd,qdd):
Ce:=CCE(E,q,qd,qdd):
Re:=RRE(E,Me,Ce,q,qd,qdd):
[eval(Me),eval(Ce),eval(Re)]:
end:
MME:=proc(E,q,qd,qdd)
local E1:
E1:=eval(E):
genmatrix([seq(E1[i,1],i=1..nops(qdd))],qdd):
end:
#-----------------------------------------------------
# extract the CE(q) matrix El= ME(q) qdd + CE(q) qd^2 + RE(q)
#-----------------------------------------------------
ttvarp:=proc(xx)
if type(xx,`indexed`)
then cat(op(0,xx),`2`)[op(xx)]
else cat(xx,`2`) fi
end:
CCE:=proc(E,q,qd,qdd)
local E_copy,q2d:
E_copy:=eval(E):
q2d:= map(x-> ttvarp(x),qd):
E_copy:=subs( map(x-> x**2=ttvarp(x),qd),eval(E_copy));
genmatrix([seq(E_copy[i,1],i=1..nops(qd))],q2d);
end:
#-----------------------------------------------------
# extract the RE(q) matrix El= ME(q) qdd + CE(q) qd^2 + RE(q)
#-----------------------------------------------------
RRE:=proc(E,ME,CE,q,qd,qdd)
local MM:
MM:=matadd( E,
matadd(multiply(ME,matrix(nops(q),1,qdd)),
multiply(CE,matrix(nops(q),1,map(x->x**2,qd)))),
1,-1);
MM:=map((x)-> simplify(x),eval(MM)):
end:
#
#-----------------------------------------------------
# FORTRAN GENERATION
#-----------------------------------------------------
Gener:=proc(filename,fortranlist)
global optimized;
init_genfor();
optimized:=true:
writeto(filename):
genfor(flist):
writeto(terminal):
end:
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