Poisson Bracket

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics and classical mechanics, the Poisson bracket is an important operator in Hamiltonian mechanics, playing a central role in the definition of the time-evolution of a dynamical system in the Hamiltonian formulation. It places mechanics and dynamics in the context of coordinate-transformations: specifically in coordinate planes such as canonical position/momentum, or canonical-position/canonical transformation. (A so-called "canonical transformation" is a function of the canonical position and momentum satisfying certain Poisson-bracket relations). Note that one example of a canonical transformation is the Hamiltonian itself: H = H(q,p;t). Namely: the Hamiltonian-canonical-transformation transforms canonical position/momenta into the conserved (constant-of-time-integration) quantity known as "energy".