Generalized hybrid momentum maps and reduction by symmetries of forced mechanical systems with inelastic collisions
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908408109596672 |
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| author | Colombo, Leonardo J. de León, Manuel Irazú, María Emma Eyrea López-Gordón, Asier |
| author_facet | Colombo, Leonardo J. de León, Manuel Irazú, María Emma Eyrea López-Gordón, Asier |
| contents | This paper discusses reduction by symmetries for autonomous and non-autonomous forced mechanical systems with inelastic collisions. In particular, we introduce the notion of generalized hybrid momentum map and hybrid constants of the motion to give general conditions on whether it is possible to perform symmetry reduction for Hamiltonian and Lagrangian systems subject to non-conservative external forces and non-elastic impacts, as well as its extension to time-dependent mechanical systems subject to time-dependent external forces and time-dependent inelastic collisions. We illustrate the applicability of the method with examples and numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_02573 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Generalized hybrid momentum maps and reduction by symmetries of forced mechanical systems with inelastic collisions Colombo, Leonardo J. de León, Manuel Irazú, María Emma Eyrea López-Gordón, Asier Systems and Control Dynamical Systems Symplectic Geometry 53Z05, 70F35, 70F40, 93C30 This paper discusses reduction by symmetries for autonomous and non-autonomous forced mechanical systems with inelastic collisions. In particular, we introduce the notion of generalized hybrid momentum map and hybrid constants of the motion to give general conditions on whether it is possible to perform symmetry reduction for Hamiltonian and Lagrangian systems subject to non-conservative external forces and non-elastic impacts, as well as its extension to time-dependent mechanical systems subject to time-dependent external forces and time-dependent inelastic collisions. We illustrate the applicability of the method with examples and numerical simulations. |
| title | Generalized hybrid momentum maps and reduction by symmetries of forced mechanical systems with inelastic collisions |
| topic | Systems and Control Dynamical Systems Symplectic Geometry 53Z05, 70F35, 70F40, 93C30 |
| url | https://arxiv.org/abs/2112.02573 |