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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“Motion or change, and identity or rest, are the first and second secrets of nature: Motion and Rest. The whole code of her laws may be written on the thumbnail, or the signet of a ring.”
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