ON the stability of triangular Lagrangian points in the spatial restricted three-body problem
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914094190166016 |
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| author | Sosnitskii, Stepan P. |
| author_facet | Sosnitskii, Stepan P. |
| contents | In the present paper, which is a development of an earlier study by the author \cite{Sosnitskii08}, we consider the stability of triangular libration points in the spatial circular restricted three-body problem and improve the result of author's work \cite{Sosnitskii08}. Unlike \cite{Sosnitskii08}, where the instability of libration points was established on the base of reduced approximate equations, we succeeded in this paper to use a new approach that made it possible to prove the instability of triangular libration points on the base of a closed complete system of equations. The relationship between the Lyapunov stability and Birkhoff stability (formal stability) is also discussed |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_13388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | ON the stability of triangular Lagrangian points in the spatial restricted three-body problem Sosnitskii, Stepan P. Solar and Stellar Astrophysics In the present paper, which is a development of an earlier study by the author \cite{Sosnitskii08}, we consider the stability of triangular libration points in the spatial circular restricted three-body problem and improve the result of author's work \cite{Sosnitskii08}. Unlike \cite{Sosnitskii08}, where the instability of libration points was established on the base of reduced approximate equations, we succeeded in this paper to use a new approach that made it possible to prove the instability of triangular libration points on the base of a closed complete system of equations. The relationship between the Lyapunov stability and Birkhoff stability (formal stability) is also discussed |
| title | ON the stability of triangular Lagrangian points in the spatial restricted three-body problem |
| topic | Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2510.13388 |