Cosserat media in dynamics
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912123759624192 |
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| author | de Saxcé, Géry |
| author_facet | de Saxcé, Géry |
| contents | Our aim is to develop a general approach for the dynamics of material bodies of dimension d represented by a mater manifold of dimension (d + 1) embedded into the space-time. It can be declined for d = 0 (pointwise object), d = 1 (arch if it is a solid, flow in a pipe or jet if it is a fluid), d = 2 (plate or shell if it is a solid, sheet of fluid), d = 3 (bulky bodies). We call torsor a skew-symmetric bilinear map on the vector space of affine real functions on the affine tangent space to the space-time. We use the affine connections as originally developed by Élie Cartan, that is the connections associated to the affine group. We introduce a general principle of covariant divergence free torsor from which we deduce 10 balance equations. We show the relevance of this general principle by applying it for d from 1 to 4 in the context of the Galilean relativity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cosserat media in dynamics de Saxcé, Géry General Mathematics 22E70 (Primary) 83C10, 74K10, 74K25, 76A20, 76B10 (Secondary) Our aim is to develop a general approach for the dynamics of material bodies of dimension d represented by a mater manifold of dimension (d + 1) embedded into the space-time. It can be declined for d = 0 (pointwise object), d = 1 (arch if it is a solid, flow in a pipe or jet if it is a fluid), d = 2 (plate or shell if it is a solid, sheet of fluid), d = 3 (bulky bodies). We call torsor a skew-symmetric bilinear map on the vector space of affine real functions on the affine tangent space to the space-time. We use the affine connections as originally developed by Élie Cartan, that is the connections associated to the affine group. We introduce a general principle of covariant divergence free torsor from which we deduce 10 balance equations. We show the relevance of this general principle by applying it for d from 1 to 4 in the context of the Galilean relativity. |
| title | Cosserat media in dynamics |
| topic | General Mathematics 22E70 (Primary) 83C10, 74K10, 74K25, 76A20, 76B10 (Secondary) |
| url | https://arxiv.org/abs/2411.11860 |