Poisson bracket

Common card · No. 244278

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. The set of possible canonical transformations is always very rich. For instance, it is often possible to choose the Hamiltonian itself...

Read on Wikipedia · Image François-Séraphin Delpech / After Nicolas Eustache Maurin, Public domain