Hamiltonian mechanics | Symplectic geometry | Differential topology

Canonical coordinates

In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time. 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 are 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 (the mathematical notion of phase space). (Wikipedia).

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Related pages

Tangent bundle | Generalized coordinates | Hamiltonian mechanics | Symplectomorphism | Hamilton–Jacobi equation | Momentum | Phase space | Poisson bracket | Symplectic vector field | Cotangent bundle | Stone–von Neumann theorem | Mathematics | Linear discriminant analysis | Symplectic geometry | Section (fiber bundle) | Canonical transformation | Lagrangian mechanics | Legendre transformation | Manifold | Atlas (topology) | Symplectic manifold | Vector field