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- Canonical_transformation abstract "In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates (q,p,t) → (Q,P,t) that preserves the form of Hamilton's equations (that is, the new Hamilton's equations resulting from the transformed Hamiltonian may be simply obtained by substituting the new coordinates for the old coordinates), although it might not preserve the Hamiltonian itself. This is sometimes known as form invariance. Canonical transformations are useful in their own right, and also form the basis for the Hamilton–Jacobi equations (a useful method for calculating conserved quantities) and Liouville's theorem (itself the basis for classical statistical mechanics).Since Lagrangian mechanics is based on generalized coordinates, transformations of the coordinates q → Q do not affect the form of Lagrange's equations and, hence, do not affect the form of Hamilton's equations if we simultaneously change the momentum by a Legendre transform intoTherefore, coordinate transformations (also called point transformations) are a type of canonical transformation. However, the class of canonical transformations is much broader, since the old generalized coordinates, momenta and even time may be combined to form the new generalized coordinates and momenta. Canonical transformations that do not include the time explicitly are called restricted canonical transformations (many textbooks consider only this type).For clarity, we restrict the presentation here to calculus and classical mechanics. Readers familiar with more advanced mathematics such as cotangent bundles, exterior derivatives and symplectic manifolds should read the related symplectomorphism article. (Canonical transformations are a special case of a symplectomorphism.) However, a brief introduction to the modern mathematical description is included at the end of this article.".
- Canonical_transformation wikiPageExternalLink Is_the_Lagrangian_unique.3F)..
- Canonical_transformation wikiPageID "514534".
- Canonical_transformation wikiPageRevisionID "598900998".
- Canonical_transformation hasPhotoCollection Canonical_transformation.
- Canonical_transformation subject Category:Concepts_in_physics.
- Canonical_transformation subject Category:Hamiltonian_mechanics.
- Canonical_transformation subject Category:Transforms.
- Canonical_transformation type Abstraction100002137.
- Canonical_transformation type Cognition100023271.
- Canonical_transformation type Concept105835747.
- Canonical_transformation type Content105809192.
- Canonical_transformation type FundamentalPhysicsConcepts.
- Canonical_transformation type Idea105833840.
- Canonical_transformation type PsychologicalFeature100023100.
- Canonical_transformation comment "In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates (q,p,t) → (Q,P,t) that preserves the form of Hamilton's equations (that is, the new Hamilton's equations resulting from the transformed Hamiltonian may be simply obtained by substituting the new coordinates for the old coordinates), although it might not preserve the Hamiltonian itself. This is sometimes known as form invariance.".
- Canonical_transformation label "Canonical transformation".
- Canonical_transformation label "Kanonische Transformation".
- Canonical_transformation label "Transformación canónica".
- Canonical_transformation label "Transformation canonique".
- Canonical_transformation label "Trasformazione canonica".
- Canonical_transformation label "Каноническое преобразование".
- Canonical_transformation label "正則變換".
- Canonical_transformation sameAs Kanonische_Transformation.
- Canonical_transformation sameAs Transformación_canónica.
- Canonical_transformation sameAs Transformation_canonique.
- Canonical_transformation sameAs Trasformazione_canonica.
- Canonical_transformation sameAs 정준_변환.
- Canonical_transformation sameAs m.02kddf.
- Canonical_transformation sameAs Q1366892.
- Canonical_transformation sameAs Q1366892.
- Canonical_transformation sameAs Canonical_transformation.
- Canonical_transformation wasDerivedFrom Canonical_transformation?oldid=598900998.
- Canonical_transformation isPrimaryTopicOf Canonical_transformation.