How can I solve symbolic Lagrange equations of motion numerically?

Question

Alexander Alyukov 2016-1-26

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/265287-how-can-i-solve-symbolic-lagrange-equations-of-motion-numerically

回答： Mischa Kim 2016-4-1

I made a code to obtain the system of Lagrange equations of motion in symbolic form. Now I want to solve it, but the system is huge, so I need to solve it numerically. Here's the code

if true
function fout = deriv(f, g)
% deriv differentiates f with respect to g=g(t)
% the variable g=g(t) is a function of time
b = sym('b');
f1 = subs(f, g, b);
f2 = diff(f1, b);
fout = subs(f2, b, g);
x=sym('x(t)');
tettapl=sym('tettapl(t)');
tettal1=sym('tettal1(t)');
tettal2=sym('tettal2(t)');
%Here is the calculation of the Kinetic and Potential energies
eqn1=diff(deriv(K,diff(x)))-deriv(K,x)+deriv(P,x)
eqn2=diff(deriv(K,diff(tettapl)))-deriv(K,tettapl)+deriv(P,tettapl)
eqn3=diff(deriv(K,diff(tettal1)))-deriv(K,tettal1)+deriv(P,tettal1)-diff(tettal1)
eqn4=diff(deriv(K,diff(tettal2)))-deriv(K,tettal2)+deriv(P,tettal2)-diff(tettal2)
end

I tried to use

if true
  V=odeToVectorField(eqn1,eqn2,eqn3,eqn4)
end

but got:

if true
  Error using symengine (line 58)
Could not extract the differential variables. Try using symbolic functions in contrast to ordinary symbolic objects as dependent ODE variables.
end

How can I define variables so Matlab can see derivatives?