Equivalence of Rigid Motions and Relative Equilibria in the N-Body Problem on the Two-Sphere
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929756650340352 |
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| author | Fujiwara, Toshiaki Pérez-Chavela, Ernesto Zhu, Shuqiang |
| author_facet | Fujiwara, Toshiaki Pérez-Chavela, Ernesto Zhu, Shuqiang |
| contents | We investigate the relationship between rigid motions and relative equilibria in the N-body problem on the two-dimensional sphere, S2. We prove that any rigid motion of the N-body system on S2 must be a relative equilibrium. Our approach extends the classical study of rigid body dynamics by Euler and utilizes a rotating frame attached to the particles to derive the corresponding equations of motion. We further show that our results can be extended to the N-body gravitational system in R3. The results are oriented to a broader understanding of the dynamics of N-body systems on curved surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16545 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivalence of Rigid Motions and Relative Equilibria in the N-Body Problem on the Two-Sphere Fujiwara, Toshiaki Pérez-Chavela, Ernesto Zhu, Shuqiang Dynamical Systems 70F10 We investigate the relationship between rigid motions and relative equilibria in the N-body problem on the two-dimensional sphere, S2. We prove that any rigid motion of the N-body system on S2 must be a relative equilibrium. Our approach extends the classical study of rigid body dynamics by Euler and utilizes a rotating frame attached to the particles to derive the corresponding equations of motion. We further show that our results can be extended to the N-body gravitational system in R3. The results are oriented to a broader understanding of the dynamics of N-body systems on curved surfaces. |
| title | Equivalence of Rigid Motions and Relative Equilibria in the N-Body Problem on the Two-Sphere |
| topic | Dynamical Systems 70F10 |
| url | https://arxiv.org/abs/2409.16545 |