Mechanical Hamiltonization of unreduced $ϕ$-simple Chaplygin systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929570952773632 |
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| author | Simoes, Alexandre Anahory Marrero, Juan Carlos de Diego, David Martín |
| author_facet | Simoes, Alexandre Anahory Marrero, Juan Carlos de Diego, David Martín |
| contents | In this paper, we prove that the trajectories of unreduced $ϕ$-simple Chaplygin kinetic systems are reparametrizations of horizontal geodesics with respect to a modified Riemannian metric. Furthermore, our proof is constructive and these Riemannian metrics, which are not unique, are obtained explicitly in interesting examples. We also extend these results to $ϕ$-simple Chaplygin mechanical systems (not necessarily kinetic). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_18648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mechanical Hamiltonization of unreduced $ϕ$-simple Chaplygin systems Simoes, Alexandre Anahory Marrero, Juan Carlos de Diego, David Martín Differential Geometry Mathematical Physics 37J60, 53C22, 70F25, 70G45 In this paper, we prove that the trajectories of unreduced $ϕ$-simple Chaplygin kinetic systems are reparametrizations of horizontal geodesics with respect to a modified Riemannian metric. Furthermore, our proof is constructive and these Riemannian metrics, which are not unique, are obtained explicitly in interesting examples. We also extend these results to $ϕ$-simple Chaplygin mechanical systems (not necessarily kinetic). |
| title | Mechanical Hamiltonization of unreduced $ϕ$-simple Chaplygin systems |
| topic | Differential Geometry Mathematical Physics 37J60, 53C22, 70F25, 70G45 |
| url | https://arxiv.org/abs/2409.18648 |