Classical relativistic nonholonomic mechanics and time-dependent $G$-Chaplygin systems with affine constraints
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916316213936128 |
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| author | Jovanovic, Bozidar |
| author_facet | Jovanovic, Bozidar |
| contents | We study the relativistic formulation of a classical time-dependent nonholonomic Lagrangian mechanics from the perspective of moving frames. We also introduce time-dependent $G$-Chaplygin systems with affine constraints, which are natural objects for the invariant formulation of nonholonomic systems with symmetries. As far as the author is aware, the Hamiltonization problem for time-dependent constraints has not yet been studied. As a first step in this direction, we consider a rolling without sliding of a balanced disc of radius $r$ over a vertical circle of variable radius $R(t)$. We modify the Chaplygin multiplier method and prove that the reduced system becomes the usual Lagrangian system with respect to the new time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classical relativistic nonholonomic mechanics and time-dependent $G$-Chaplygin systems with affine constraints Jovanovic, Bozidar Mathematical Physics Differential Geometry 37J06, 37J60, 70F25, 70G45, 70H40 We study the relativistic formulation of a classical time-dependent nonholonomic Lagrangian mechanics from the perspective of moving frames. We also introduce time-dependent $G$-Chaplygin systems with affine constraints, which are natural objects for the invariant formulation of nonholonomic systems with symmetries. As far as the author is aware, the Hamiltonization problem for time-dependent constraints has not yet been studied. As a first step in this direction, we consider a rolling without sliding of a balanced disc of radius $r$ over a vertical circle of variable radius $R(t)$. We modify the Chaplygin multiplier method and prove that the reduced system becomes the usual Lagrangian system with respect to the new time. |
| title | Classical relativistic nonholonomic mechanics and time-dependent $G$-Chaplygin systems with affine constraints |
| topic | Mathematical Physics Differential Geometry 37J06, 37J60, 70F25, 70G45, 70H40 |
| url | https://arxiv.org/abs/2407.06231 |