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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“Let it be an alliance of two large, formidable natures, mutually beheld, mutually feared, before yet they recognize the deep identity which beneath these disparities unites them.”
—Ralph Waldo Emerson (1803–1882)
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