Stability of Fixed Points and Associated Relative Equilibria of the 3-Body Problem on S~1 and S~2

Diacu Florin; Manuel Sanchez-Cerritos Juan; Zhu Shuqiang

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Stability of Fixed Points and Associated Relative Equilibria of the 3-Body Problem on S~1 and S~2

机译：S〜1和S〜2上三体问题的不动点的稳定性和相关的相对平衡

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摘要

We prove that the fixed points of the curved 3-body problem and their associated relative equilibria are Lyapunov stable if the solutions are restricted to S-1, but unstable if the bodies are considered in S-2.

机译：我们证明，如果解限于S-1，则弯曲的3体问题的不动点及其相关的相对平衡是Lyapunov稳定的，而如果在S-2中考虑该体，则它们是不稳定的。

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来源
《Journal of dynamics and differential equations》 |2018年第1期|209-225|共17页
作者
Diacu Florin; Manuel Sanchez-Cerritos Juan; Zhu Shuqiang;
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作者单位

Pacific Inst Math Sci, Victoria, BC, Canada;

Univ Autonoma Metropolitana Iztapalapa, Dept Matemat, Mexico City, DF, Mexico;

Univ Victoria, Dept Math & Stat, Victoria, BC, Canada;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Celestial mechanics; Curved 3-body problem; Fixed-point solutions; Relative equilibria; Stability;

机译：天体力学;弯曲三体问题;定点解;相对平衡;稳定性;

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1. ALMOST ALL 3-BODY RELATIVE EQUILIBRIA ON S~2 AND H~2 ARE INCLINED [J] . FLORIN DIACU, SHUQIANG ZHU Discrete and continuous dynamical systems . 2020,第4期

机译：在S〜2和H〜2上几乎所有3体相对平衡都是倾斜的
2. All the Lagrangian relative equilibria of the curved 3-body problem have equal masses [J] . Diacu Florin, Popa Sergiu Journal of Mathematical Physics . 2014,第11期

机译：弯曲的三体问题的所有拉格朗日相对平衡具有相等的质量
3. EULERIAN RELATIVE EQUILIBRIA OF THE CURVED 3-BODY PROBLEMS IN S~2 [J] . SHUQIANG ZHU Proceedings of the American Mathematical Society . 2014,第8期

机译：S〜2中弯曲的三体问题的Eulerian相对平衡
4. Artificial 3-Body Equilibria for Hybrid Low-Thrust Propulsion and Stabilisation [C] . Shahid Baig, Colin R. Mclnnes International astronautical congress;IAC 2008 . 2008

机译：混合式低推力推进和稳定的人工3体平衡
5. Bifurcation and stability of relative equilibria with isotropy in Lagrangian systems with symmetry. [D] . Matsui, Eric Tsuyoshi. 2001

机译：具有对称性的拉格朗日系统中具有各向同性的相对平衡的分支和稳定性。
6. General iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractions [O] . Qian-Wen Wang, Jin-Lin Guan, Lu-Chuan Ceng, -1

机译：具有广义混合均衡和伪压缩不动点问题的变分不等式系统的通用迭代方法
7. Almost all 3-body relative equilibria on egin{document}$ mathbb S^2 $end{document} and egin{document}$ mathbb H^2 $end{document} are inclined [O] . Florin Diacu, Shuqiang Zhu 2020

机译：几乎所有3体相对均衡在 begin {document} $ mathbb s ^ 2 $ nod {document} 和<内联公式> begin {document} $ mathbb h ^ 2 $ end {document} 倾斜

Stability of Fixed Points and Associated Relative Equilibria of the 3-Body Problem on S~1 and S~2

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