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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.17899 |
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| _version_ | 1866916227141599232 |
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| author | Muscas, Anna-Monika Pasca, Daniel Stoica, Cristina |
| author_facet | Muscas, Anna-Monika Pasca, Daniel Stoica, Cristina |
| contents | We study the linear stability of regular $n$-gon rotating equilibria in the $n$-body problem with logarithm interaction. In the presence of a central mass $M$, linear stability is insured if $M$ is bounded below and above by constants depending on the number and mass of the (equal) outer $n$ bodies. Moreover, we provide explicit equations of these bounds. In the absence of a central mass we find that the regular $n$-gon is linearly stable for $n =2,3,\ldots 6$ only. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17899 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of the regular $n$-gon rotating equilibria with logarithm interaction Muscas, Anna-Monika Pasca, Daniel Stoica, Cristina Dynamical Systems Astrophysics of Galaxies 70F10, 70F15 We study the linear stability of regular $n$-gon rotating equilibria in the $n$-body problem with logarithm interaction. In the presence of a central mass $M$, linear stability is insured if $M$ is bounded below and above by constants depending on the number and mass of the (equal) outer $n$ bodies. Moreover, we provide explicit equations of these bounds. In the absence of a central mass we find that the regular $n$-gon is linearly stable for $n =2,3,\ldots 6$ only. |
| title | Stability of the regular $n$-gon rotating equilibria with logarithm interaction |
| topic | Dynamical Systems Astrophysics of Galaxies 70F10, 70F15 |
| url | https://arxiv.org/abs/2404.17899 |