I am trying to learn the calculus of variations, and I understand the mathematical derivation of the Euler-Lagrange equation.(adsbygoogle = window.adsbygoogle || []).push({});

As I understand it, the calculus of variations seeks to find extrema for functions of the form:

[tex]S[q,\dot{q}, x] = \int_{a}^{b} L(q(x),\dot{q}(x), x) \,dx[/tex].

Here is my question: Why is it necessary to have [itex]\dot{q}[/itex] as an argument of [itex]L[/itex]? Isn't the derivative of the function [itex]q[/itex] "included" with the function itself?

Thanks in advance.

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# A calculus of variations question

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