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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A calculus of variations question

**Physics Forums | Science Articles, Homework Help, Discussion**