Comment #28 on issue 1816 by elliso...@gmail.com: Adding partial derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816

The "Falling Mass" example here shows this, in that diff(L, x(t)) == mg, which assumes that the derivative you give is zero:

http://en.wikipedia.org/wiki/Lagrangian_mechanics

I will update the docs and finish up the coding to address the comments of renato.

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