五体问题的中心构型及其相对平衡解

胡盛清, 王硕

数学学报 ›› 2014, Vol. 57 ›› Issue (6) : 1199-1202.

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数学学报 ›› 2014, Vol. 57 ›› Issue (6) : 1199-1202. DOI: 10.12386/A2014sxxb0110
论文

五体问题的中心构型及其相对平衡解

    胡盛清1, 王硕2
作者信息 +

5-body Central Configuration and Its Relative Equilibrium Solution

    Sheng Qing HU1, Shuo WANG2
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文章历史 +

摘要

N体问题的中心构型非常重要,但它们的分类很复杂.本文讨论了一类菱形五体问题的中心构型及其相对平衡解,证明了菱形五体问题的相对平衡解的存在唯一性.

Abstract

The central configurations of the N-body problems are important and their classifications are very complex.We discuss the central configuration of a rhombus 5- body problem and its relative equilibrium solution, and we prove the existence and uniqueness of the rhombus 5-body problem's relative equilibrium solution.

关键词

五体问题 / 中心构型 / 相对平衡解 / 存在性 / 唯一性

Key words

5-body problem / central configuration / relative equilibrium solution / existence / uniqueness

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导出引用
胡盛清, 王硕. 五体问题的中心构型及其相对平衡解. 数学学报, 2014, 57(6): 1199-1202 https://doi.org/10.12386/A2014sxxb0110
Sheng Qing HU, Shuo WANG. 5-body Central Configuration and Its Relative Equilibrium Solution. Acta Mathematica Sinica, Chinese Series, 2014, 57(6): 1199-1202 https://doi.org/10.12386/A2014sxxb0110

参考文献

[1] Abraham R., Marsden J., Foundations of Mechanics, 2nd ed., Benjamin/Cumming, London, 1978.

[2] Hampton M., Moeckel R., Finiteness of relative equilibria of the the four-body problem, Invent.Math., 2006. 163: 289-312.

[3] Long Y.M., Admissible shape of 4-body non-collinear relative equilibria, Advanced Nonlinear Studies, 2003. 1: 495-509.

[4] Meyer K., Hall G., Introduction to Hamiltonian Systems and the N-body Problems, Springer, Berlin, 1992.

[5] Stein E.M., Shakarchi R., Complex Analysis, Princeton University Press, Princeton, 2003.

[6] Zhang S.Q, Zhou Q., Periodic solutions for planar 2N-body problems, Proc.Amer.Math.Soc., 2003, 131. 2161-2170.
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