Partial derivative with Matlab Symbolic Toolbox for Lagrangian equations of motion

Question

I'm trying to derive Lagrangian equations of motion in Matlab using the symbolic toolbox. This involves partial derivatives of a function and your coordinates, but matlab seems to not accept this.

So I would do this in Matlab:

syms t x(t)             % t: time, x(t) position dependent on time
m = sym('m');           % mass, a constant parameter
T = m/2*diff(x,t)^2;    % kinetic energy
dTdx = diff(T,x);
ddTdxDotdt = diff( diff(T,diff(x,t)), t);

But as soon as I try to differentiate anything in x (or diff(x,t)), Matlab complains:

Error using mupadmex
Error in MuPAD command: The variable is invalid. [stdlib::diff]

Error in sym/diff (line 44)
R = mupadmex('symobj::diff', S.s, x.s, int2str(n));

Does anyone know the proper way of handling this?

Answer 1

Matlab ought to be able to do this as you have it written, but I think that it doesn't like taking derivatives with respect to a symfun. Type whos in the command window and you'll see that x is listed as a symfun while t is just a sym. The help for diff kind of indicates this limitation. It won't event try to take the derivative of a constant with respect to x(t): diff(1,x) "complains" just the same. Unless newer versions of Matlab fix this (I'm on R2012b) I think you only option may be to come up with a scheme using two instances of x.