Lagrange bracket

Lagrange brackets are certain expressions closely related to Poisson brackets that were introduced by Joseph Louis Lagrange in 1808–1810 for the purposes of mathematical formulation of classical mechanics, but unlike the Poisson brackets, have fallen out of use.
Definition.
Suppose that ("q"1, …, "q""n", "p"1, …, "p""n") is a system of canonical coordinates on a phase space. If each of them is expressed as a function of two variables, "u" and "v", then the Lagrange bracket of "u" and "v" is defined by the formula