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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 qi and pi 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 ''H'' = ''H''(''q'', ''p''; ''t'') as one of the new canonical momentum coordinates. In a more general sense: the Poisson bracket is used to define a Poisson algebra, of which the algebra of functions on a Poisson manifold is a special case. These are all named in honour of Siméon Denis Poisson. ==Properties== For any functions of phase space and time: * ''Anticommutativity'': * ''Distributivity'': * ''Product rule'': * ''Jacobi identity'': Also, if a function is time-dependent but constant over phase space, then for any . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Poisson bracket」の詳細全文を読む スポンサード リンク
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