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:
“I look for the new Teacher that shall follow so far those shining laws that he shall see them come full circle; shall see their rounding complete grace; shall see the world to be the mirror of the soul; shall see the identity of the law of gravitation with purity of the heart; and shall show that the Ought, that Duty, is one thing with Science, with Beauty, and with Joy.”
—Ralph Waldo Emerson (1803–1882)
Related Phrases
Related Words