Equation of Euler-Lagrange

The equation of Euler-Lagrange is a mathematical result which plays a fundamental role in the Calcul of the variations. One finds this equation in many real problems, such as the problem brachistochrone or even the geodetic problems . It is named according to Leonhard Euler and Joseph-Louis Lagrange.

Alternatives

In many problems, F does not depend directly on T , (i.e. $\backslash \; frac\; \{\backslash \; partial\; F\}\; \{\backslash \; partial\; T\}\; =0$) and the preceding equation is simplified in the following form, called Identité of Beltrami:

$f-\; \{\backslash \; dowry\; X\}\; \backslash \; frac\; \{\backslash \; partial\; F\}\; \{\backslash \; partial\; \backslash \; dowry\; X\}\; =C$

With C a Constant of the problem.

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