ALMOST ALL 3-BODY RELATIVE EQUILIBRIA ON S~2 AND H~2 ARE INCLINED

FLORIN DIACU; SHUQIANG ZHU

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ALMOST ALL 3-BODY RELATIVE EQUILIBRIA ON S~2 AND H~2 ARE INCLINED

机译：在S〜2和H〜2上几乎所有3体相对平衡都是倾斜的

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We answer here a question posed by F. Diacu in 2012 that asked whether there exist relative equilibria on S~2 and H~2 that move in a plane non-perpendicular to the rotation axis. For 3-body non-geodesic ordinary central configurations on S~2 and H~2, we find all relative equilibria that move in a plane perpendicular to the rotation axis. We also show that the set of shapes of 3-body non-geodesic ordinary central configurations on S~2 and H~2 is a 3-dimensional manifold. Then we conclude that almost all 3-body relative equilibria move in planes non-perpendicular to the rotation axis.

机译：在这里，我们在这里回答了F. Diacu在2012年提出的问题，询问是否存在于S〜2和H〜2上的相对平衡，这些情况在旋转轴上的平面中移动。对于S〜2和H〜2上的3体非测地普通中央配置，我们发现所有相对平衡的相对平衡，在垂直于旋转轴的平面中移动。我们还表明，S〜2和H〜2上的3体非测地普通中央配置的形状为三维歧管。然后，我们得出结论，几乎所有3体相对平衡的平面在非垂直于旋转轴上移动。

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来源
《Discrete and continuous dynamical systems》 |2020年第4期|1131-1143|共13页
作者
FLORIN DIACU; SHUQIANG ZHU;
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作者单位

Yale-NUS College National University of Singapore Republic of Singapore;

School of Mathematical Sciences University of Science and Technology of China Hefei China;

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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; relative equilibria; central configurations; three-body problem;

机译：天体力学;弯曲的3体问题;相对均衡;中央配置;三体问题;

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专利

1. Stability of Fixed Points and Associated Relative Equilibria of the 3-Body Problem on S~1 and S~2 [J] . Diacu Florin, Manuel Sanchez-Cerritos Juan, Zhu Shuqiang Journal of dynamics and differential equations . 2018,第1期

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
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. Charting the state space of plane Couette flow: Equilibria, relative equilibria, and heteroclinic connections. [D] . Halcrow, Jonathan J. 2008

机译：绘制平面Couette流的状态空间图：平衡，相对平衡和异斜面连接。
6. Cuticular Permeability Percent Body Water Loss and Relative Humidity Equilibria Comparisons of Four Termite Species [O] . John Zukowski, Nan-Yao Su 2019

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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

ALMOST ALL 3-BODY RELATIVE EQUILIBRIA ON S~2 AND H~2 ARE INCLINED

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