Affine generalizations of the nonholonomic problem of a convex body rolling without slipping on the plane
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929498876805120 |
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| author | Villegas, M. Costa García-Naranjo, L. C. |
| author_facet | Villegas, M. Costa García-Naranjo, L. C. |
| contents | We introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body rolling without slipping on the plane. We investigate dynamical aspects of the system such as existence of first integrals, smooth invariant measure and integrability, giving special attention to the cases in which the convex body is a dynamically balanced sphere or a body of revolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08072 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Affine generalizations of the nonholonomic problem of a convex body rolling without slipping on the plane Villegas, M. Costa García-Naranjo, L. C. Mathematical Physics Dynamical Systems 37J60, 70F25, 70E18, 70E40 We introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body rolling without slipping on the plane. We investigate dynamical aspects of the system such as existence of first integrals, smooth invariant measure and integrability, giving special attention to the cases in which the convex body is a dynamically balanced sphere or a body of revolution. |
| title | Affine generalizations of the nonholonomic problem of a convex body rolling without slipping on the plane |
| topic | Mathematical Physics Dynamical Systems 37J60, 70F25, 70E18, 70E40 |
| url | https://arxiv.org/abs/2409.08072 |