In mathematics and classical mechanics, canonical coordinates are particular sets of coordinates on the phase space, or equivalently, on the cotangent bundle of a manifold. Canonical coordinates arise naturally in physics in the study of Hamiltonian mechanics. 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 in terms of cotangent bundles.
This article defines the canonical coordinates as they appear in classical mechanics. A closely related concept also appears in quantum mechanics; see the Stone-von Neumann theorem and canonical commutation relations for details.
Read more about Canonical Coordinates: Definition, in Classical Mechanics, Definition, On Cotangent Bundles, Formal Development, Generalized Coordinates
Famous quotes containing the word canonical:
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