From the Lagrange Triangle to the Figure Eight Choreography: Proof of Marchal's Conjecture
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866918419716112384 |
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| author | Calleja, Renato García-Azpeitia, Carlos Hénot, Olivier Lessard, Jean-Philippe James, Jason D. Mireles |
| author_facet | Calleja, Renato García-Azpeitia, Carlos Hénot, Olivier Lessard, Jean-Philippe James, Jason D. Mireles |
| contents | For the three body problem with equal masses, we prove that the most symmetric continuation class of Lagrange's equilateral triangle solution, also referred to as the $P_{12}$ family of Marchal, contains the remarkable figure eight choreography discovered by Moore in 1993, and proven to exist by Chenciner and Montgomery in 2000. This settles a conjecture of Marchal which dates back to the 1999 conference on Celestial Mechanics in Evanston Illinois, celebrating Donald Saari's 60th birthday. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17564 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From the Lagrange Triangle to the Figure Eight Choreography: Proof of Marchal's Conjecture Calleja, Renato García-Azpeitia, Carlos Hénot, Olivier Lessard, Jean-Philippe James, Jason D. Mireles Dynamical Systems For the three body problem with equal masses, we prove that the most symmetric continuation class of Lagrange's equilateral triangle solution, also referred to as the $P_{12}$ family of Marchal, contains the remarkable figure eight choreography discovered by Moore in 1993, and proven to exist by Chenciner and Montgomery in 2000. This settles a conjecture of Marchal which dates back to the 1999 conference on Celestial Mechanics in Evanston Illinois, celebrating Donald Saari's 60th birthday. |
| title | From the Lagrange Triangle to the Figure Eight Choreography: Proof of Marchal's Conjecture |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2406.17564 |