Comment #34 on issue 1816 by ronan.l...@gmail.com: Adding partial derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
In formal mathematics, Lagrangian mechanics is presented in terms of stuff like differential manifolds and tangent bundles. That's not at all what I'm discussing. My point is that in the Euler-Lagrange equation, the derivatives are taken wrt variables and not wrt functions (which would be meaningless). This is discussed fairly often when the Euler-Lagrange equation is introduced, see e.g. http://en.wikibooks.org/wiki/Classical_Mechanics/Lagrangian#Euler-Lagrange_equations or http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation
The Lagranian is *most definitely* a direct function of x(t) and x'(t)
I agree. With the notations above, the Lagrangian is L(x(t), x'(t), t), which obviously depends on x(t) and x'(t). However, I'm talking about L and its partial derivatives. L isn't the Lagrangian, it's the function that expresses the relationship between the Lagrangian and the coordinates.
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