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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2001.03702 |
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| _version_ | 1866910591498584064 |
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| author | Barrera, Carlos Bengochea, Abimael García-Azpeitia, Carlos |
| author_facet | Barrera, Carlos Bengochea, Abimael García-Azpeitia, Carlos |
| contents | The time-dependent restricted $(n+1)$-body problem concerns the study of a massless body (satellite) under the influence of the gravitational field generated by $n$ primary bodies following a periodic solution of the $n$-body problem. We prove that the satellite has periodic solutions close to the large-amplitude circular orbits of the Kepler problem (comet solutions), and in the case that the primaries are in a relative equilibrium, close to small-amplitude circular orbits near a primary body (moon solutions). The comet and moon solutions are constructed with the application of a Lyapunov-Schmidt reduction to the action functional. In addition, using reversibility technics, we compute numerically the comet and moon solutions for the case of four primaries following the super-eight choreography. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_03702 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Comet and moon solutions in the time-dependent restricted $(n+1)$-body problem Barrera, Carlos Bengochea, Abimael García-Azpeitia, Carlos Dynamical Systems The time-dependent restricted $(n+1)$-body problem concerns the study of a massless body (satellite) under the influence of the gravitational field generated by $n$ primary bodies following a periodic solution of the $n$-body problem. We prove that the satellite has periodic solutions close to the large-amplitude circular orbits of the Kepler problem (comet solutions), and in the case that the primaries are in a relative equilibrium, close to small-amplitude circular orbits near a primary body (moon solutions). The comet and moon solutions are constructed with the application of a Lyapunov-Schmidt reduction to the action functional. In addition, using reversibility technics, we compute numerically the comet and moon solutions for the case of four primaries following the super-eight choreography. |
| title | Comet and moon solutions in the time-dependent restricted $(n+1)$-body problem |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2001.03702 |