Reduction by Symmetries of Contact Mechanical Systems on Lie Groups
We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus, we obtain Euler-Poincar\'e-Herglotz equations on the ext...
| Autores: | , , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/381563 |
| Acceso en línea: | http://hdl.handle.net/10261/381563 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85201598106&doi=10.1137%2f23M1616935&partnerID=40&md5=94217f9e5294d175020b799815c097e0 |
| Access Level: | acceso abierto |
| Palabra clave: | Contact mechanical systems Euler-Poincar\'e equations Jacobi structures in mechanics Lie–Poisson equations Herglotz principle Reduction by symmetries |
| Sumario: | We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus, we obtain Euler-Poincar\'e-Herglotz equations on the extended reduced phase space \frakg \times \BbbR associated with the extended phase space TG \times \BbbR, where the configuration manifold G is a Lie group and \frakg its Lie algebra. Furthermore, we obtain the Hamiltonian counterpart of these equations by studying the underlying Jacobi structure. Finally, we extend the reduction process to the case of symmetry-breaking systems which are invariant under a Lie subgroup of symmetries. © 2024 Society for Industrial and Applied Mathematics. |
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