A summary on symmetries and conserved quantities of autonomous Hamiltonian systems
A complete geometric classification of symmetries of autonomous Hamiltonian systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results and properties about the symmetries of the Hamiltonian and of the symplec...
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| Tipo de documento: | artigo |
| Data de publicação: | 2020 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/363198 |
| Acesso em linha: | https://hdl.handle.net/2117/363198 https://dx.doi.org/10.3934/jgm.2020009 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Nonlinear systems Hamiltonian systems Field theory (Physics) Symmetries Conserved quantities Noether theorem Symplectic manifolds Sistemes no lineals Hamilton, Sistemes de Camps, Teoria dels (Física) Classificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamics Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
| Resumo: | A complete geometric classification of symmetries of autonomous Hamiltonian systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results and properties about the symmetries of the Hamiltonian and of the symplectic form and then some new kinds of non-symplectic symmetries and their conserved quantities are introduced and studied. |
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