Let (q_1, ..., q_n, p_1, ..., p_n) be any functions of two variables (u, v). Then the expression [u, v] = sum_(r = 1)^n((dq_r)/(du) (dp_r)/(dv) - (dp_r)/(du) (dq_r)/(dv)) is called a Lagrange bracket. The Lagrange brackets are anticommutative, [u_l, u_m] = - [u_m, u_l] (Plummer 1960, p. 136).

Lie bracket | Poisson bracket