Let u and v be any functions of a set of variables (q_1, ..., q_n, p_1, ..., p_n). Then the expression (u, v) = sum_(r = 1)^n((du)/(dq_r) (dv)/(dp_r) - (du)/(dp_r) (dv)/(dq_r)) is called a Poisson bracket. Plummer uses the alternate notation {u, v}. The Poisson brackets are anticommutative, (u_l, u_m) = - (u_m, u_l) (Plummer 1960, p. 136).

Lagrange bracket | Lie bracket