In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time-evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes a certain class of coordinate-transformations, called canonical transformations, which maps canonical coordinate systems into canonical coordinate systems. (A "canonical coordinate system" consists of canonical position and momentum variables (here symbolized by q_i and p_i respectively) that satisfy canonical Poisson-bracket relations.) The set of possible canonical transformations is always very rich. For instance, often it is possible to choose the Hamiltonian itself as one of the new canonical momentum coordinates.