Poisson bracket

Operation in Hamiltonian mechanics

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 map canonical coordinate systems into other canonical coordinate systems. A "canonical coordinate system" consists of canonical position and momentum variables (below symbolized by q i {\displaystyle q_{i}} and p i {\displaystyle p_{i}} , respectively) that satisfy canonical Poisson bracket relations.

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