problem with reduceDifferentialOrder -> massMatrixForm -> odeFunction

Hello.

I am trying to get the Euler-Lagrange equation for a mechanical system and to integrate them numerically. The code is pasted below.

What I get is an error message from 'odeFunction'

Error using mupadengine/feval (line 163) The parameter 'diff(phi(t), t)' is invalid.

Error in sym/odeFunction (line 118) A = feval(symengine, 'daetools::odeFunction', expr, vars, params{:});

I do not understand this error as, at least explicitly, the derivatives diff(phi(t),t), etc are not present neither in M nor in F.

Thank you. Best regards.

    syms R L0 m g real
    for s = [R L0 m g]
        assume(s>0);
    end
    syms phi(t)
    %phi(t) = (L0-s(t))/R;
    urho = [ cos(phi), sin(phi)];
    uphi = [-sin(phi), cos(phi)];
    ux = sym([1 0]);
    uy = sym([0 1]);
    syms l2(t)
    % 
    r1 = R*urho + (L0-l2-phi*R)*uphi;
    r2 = R*ux - l2*uy;
    v1 = diff(r1,t);
    v2 = diff(r2,t);
    T = sym(1/2)*m*( simplify(v1*v1.'+v2*v2.'));
    V = (m*g*r1+m*g*r2)*(uy.');
    L = T-V;
    eqnizq = simplify(functionalDerivative(L,[phi l2]) );
    eqn = eqnizq == 0;
    [newEqs, newVars, R] = reduceDifferentialOrder(eqn, [phi(t) l2(t)]);
    [M,F] = massMatrixForm(newEqs,newVars);
    Mn = odeFunction(M, newVars, m,g,R,L0)
    Fn = odeFunction(F, newVars, m,g,R,L0)

Answer 1

[Mischa Kim]

Carlos, the Euler-Lagrange tool package does exactly what you need.

Answer 2

[Carlos Soria-Hoyo]

Thank you for your answer, Mischa.

I already knew the Euler-Lagrange tool package. It is very good, of course. But I am also interested in improving my use of Symbolic Math Toolbox, both for me and my students. And it is not being easy...

Probably odeToVectorField will work better for this case than reduceDifferentialOrder, etc. But, in any case, I would like to understand why Matlab complains about a variable that, apparently, is not among the inputs.