Text: In mathematics and classical mechanics, the NAME_1 is an important binary operation in Hamiltonian mechanics, playing a central role in NAME_2's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. The NAME_1 also distinguishes a certain class of coordinate transformations, called canonical transformations, which map canonical coordinate systems into canonical coordinate systems. A "canonical coordinate system" consists of canonical position and momentum variables (below symbolized by q_{i} and p_{i}, respectively) that satisfy canonical NAME_1 relations. The set of possible canonical transformations is always very rich. For instance, it is often possible to choose the Hamiltonian itself {\displaystyle H=H(q,p,t)} as one of the new canonical momentum coordinates.

In a more general sense, the NAME_1 is used to define a NAME_3 algebra, of which the algebra of functions on a NAME_4 is a special case. 

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You are an AI that is building a text that explains NAME_1. This is an article on NAME_3 Brackets but some terms must be defined. 

Of the choices listed below, select the THREE that are most central to the text above.

List of concepts: mathematics, classical mechanics, binary operation, Hamiltonian mechanics, dynamical system, canonical transformations, canonical coordinate systems, NAME_3 algebra, NAME_4, lie algebras, tensor algebra, universal enveloping algebra, quantum groups, Siméon Denis NAME_5