Calculus of Variations - Beltrami Identity

Beltrami Identity

In physics problems it frequently turns out that ∂L / ∂x = 0. In that case, the Euler-Lagrange equation can be simplified to the Beltrami identity:

where C is a constant. The left hand side is the Legendre transformation of L with respect to f ′.

Read more about this topic:  Calculus Of Variations

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