Geodesic extensions of mechanical systems with nonholonomic constraints
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909994800119808 |
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| author | Belrhazi, Malika Mestdag, Tom |
| author_facet | Belrhazi, Malika Mestdag, Tom |
| contents | For a Lagrangian system with nonholonomic constraints, we construct extensions of the equations of motion to sets of second-order ordinary differential equations. In the case of a purely kinetic Lagrangian, we investigate the conditions under which the nonholonomic trajectories are geodesics of a Riemannian metric, while preserving the constrained Lagrangian. We interpret the algebraic and PDE conditions of this problem as infinitesimal versions of the relation between the nonholonomic exponential map and the Riemannian metric. We discuss the special case of a Chaplygin system with symmetries and we end the paper with a worked-out example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11997 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geodesic extensions of mechanical systems with nonholonomic constraints Belrhazi, Malika Mestdag, Tom Differential Geometry Mathematical Physics 37J06, 37J60, 53Z05, 70G45, 70G65 For a Lagrangian system with nonholonomic constraints, we construct extensions of the equations of motion to sets of second-order ordinary differential equations. In the case of a purely kinetic Lagrangian, we investigate the conditions under which the nonholonomic trajectories are geodesics of a Riemannian metric, while preserving the constrained Lagrangian. We interpret the algebraic and PDE conditions of this problem as infinitesimal versions of the relation between the nonholonomic exponential map and the Riemannian metric. We discuss the special case of a Chaplygin system with symmetries and we end the paper with a worked-out example. |
| title | Geodesic extensions of mechanical systems with nonholonomic constraints |
| topic | Differential Geometry Mathematical Physics 37J06, 37J60, 53Z05, 70G45, 70G65 |
| url | https://arxiv.org/abs/2404.11997 |