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

Famous quotes containing the word identity:

    During the first formative centuries of its existence, Christianity was separated from and indeed antagonistic to the state, with which it only later became involved. From the lifetime of its founder, Islam was the state, and the identity of religion and government is indelibly stamped on the memories and awareness of the faithful from their own sacred writings, history, and experience.
    Bernard Lewis, U.S. Middle Eastern specialist. Islam and the West, ch. 8, Oxford University Press (1993)