Hamiltonian mechanics and Lie algebroid connections
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908384410730496 |
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| author | Hu, Jiawei Stern, Ari |
| author_facet | Hu, Jiawei Stern, Ari |
| contents | We develop a new, coordinate-free formulation of Hamiltonian mechanics on the dual of a Lie algebroid. Our approach uses a connection, rather than coordinates in a local trivialization, to obtain global expressions for the horizontal and vertical dynamics. We show that these dynamics can be obtained in two equivalent ways: (1) using the canonical Lie-Poisson structure, expressed in terms of the connection; or (2) using a novel variational principle that generalizes Hamilton's phase space principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00579 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hamiltonian mechanics and Lie algebroid connections Hu, Jiawei Stern, Ari Symplectic Geometry Dynamical Systems 53D17 We develop a new, coordinate-free formulation of Hamiltonian mechanics on the dual of a Lie algebroid. Our approach uses a connection, rather than coordinates in a local trivialization, to obtain global expressions for the horizontal and vertical dynamics. We show that these dynamics can be obtained in two equivalent ways: (1) using the canonical Lie-Poisson structure, expressed in terms of the connection; or (2) using a novel variational principle that generalizes Hamilton's phase space principle. |
| title | Hamiltonian mechanics and Lie algebroid connections |
| topic | Symplectic Geometry Dynamical Systems 53D17 |
| url | https://arxiv.org/abs/2304.00579 |