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In mathematics and classical mechanics, canonical coordinates are sets of coordinates which can be used to describe a physical system at any given point in time (locating the system within phase space). Canonical coordinates are used in the Hamiltonian formulation of classical mechanics. A closely related concept also appears in quantum mechanics; see the Stone–von Neumann theorem and canonical commutation relations for details. As Hamiltonian mechanics is generalized by symplectic geometry and canonical transformations are generalized by contact transformations, so the 19th century definition of canonical coordinates in classical mechanics may be generalized to a more abstract 20th century definition of coordinates on the cotangent bundle of a manifold. ==Definition, in classical mechanics== In classical mechanics, canonical coordinates are coordinates and in phase space that are used in the Hamiltonian formalism. The canonical coordinates satisfy the fundamental Poisson bracket relations: : A typical example of canonical coordinates is for to be the usual Cartesian coordinates, and to be the components of momentum. Hence in general, the coordinates are referred to as "conjugate momenta." Canonical coordinates can be obtained from the generalized coordinates of the Lagrangian formalism by a Legendre transformation, or from another set of canonical coordinates by a canonical transformation. 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「canonical coordinates」の詳細全文を読む スポンサード リンク
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