Partially rigid motions in the planar three-body problem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915346792841216 |
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| author | Moeckel, Richard |
| author_facet | Moeckel, Richard |
| contents | A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid motions, where some but not all of the distances are constant. For the planar three-body problem with equal masses, we show that partially rigid motions are impossible -- if even one of the three mutual distances is constant, the motion must be a relative equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13570 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partially rigid motions in the planar three-body problem Moeckel, Richard Dynamical Systems 37N05, 70F10, 70F15, 70F16, 70G60 A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid motions, where some but not all of the distances are constant. For the planar three-body problem with equal masses, we show that partially rigid motions are impossible -- if even one of the three mutual distances is constant, the motion must be a relative equilibrium. |
| title | Partially rigid motions in the planar three-body problem |
| topic | Dynamical Systems 37N05, 70F10, 70F15, 70F16, 70G60 |
| url | https://arxiv.org/abs/2506.13570 |