Projective geodesic extensions by conformal modifications in nonholonomic mechanics
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914382003306496 |
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| author | Belrhazi, Malika Mestdag, Tom |
| author_facet | Belrhazi, Malika Mestdag, Tom |
| contents | Projective geodesic extensions are reparametrizations of the trajectories of a nonholonomic mechanical system (with only a kinetic energy Lagrangian), in such a way that they can be interpreted as part of the geodesics of a Riemannian metric. We derive necessary and sufficient conditions for the existence of these extensions, in the case where the constrained Lagrangian remains preserved up to a conformal transformation. When the nonholonomic system has a symmetry group (a Chaplygin system), we clarify the relation between projective geodesic extensions and closely related concepts, such as $ϕ$-simplicity, invariant measures and Hamiltonization. Throughout the paper, new and relevant examples illustrate the key differences between all these concepts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Projective geodesic extensions by conformal modifications in nonholonomic mechanics Belrhazi, Malika Mestdag, Tom Differential Geometry 37J06, 37J60, 53Z05, 70G45, 70G65 Projective geodesic extensions are reparametrizations of the trajectories of a nonholonomic mechanical system (with only a kinetic energy Lagrangian), in such a way that they can be interpreted as part of the geodesics of a Riemannian metric. We derive necessary and sufficient conditions for the existence of these extensions, in the case where the constrained Lagrangian remains preserved up to a conformal transformation. When the nonholonomic system has a symmetry group (a Chaplygin system), we clarify the relation between projective geodesic extensions and closely related concepts, such as $ϕ$-simplicity, invariant measures and Hamiltonization. Throughout the paper, new and relevant examples illustrate the key differences between all these concepts. |
| title | Projective geodesic extensions by conformal modifications in nonholonomic mechanics |
| topic | Differential Geometry 37J06, 37J60, 53Z05, 70G45, 70G65 |
| url | https://arxiv.org/abs/2509.15863 |