| Existence and uniqueness for a class of nine-bodies central configurations |
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| 作者姓名： | LIU Xue-fei DU Xianglin FENG Tian-xiang |
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| 作者单位： | College of Mathematics and Computer Science, Chongqing Three Gorges University, Chongqing 404000, P.R. China |
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| 摘 要： | On some necessary conditions for double pyramidal central configurations with concave heptagon for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configurations with concave heptagon base for nine-body problems is proved in this paper, and the range of the ratio cr of the circularity radius of the heptagon to the half-height of the double pyramidal central configuration involved in this class configurations is obtained, which is in the interval （√3/3,1.099 600 679）, and the configuration involved in the bodies with any σ∈ （√3/3, 1.099 600 679） can form a central configuration which is a uniquely central configuration is proved.
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| 关 键 词： | 九体问题 存在性 唯一性 双锥形中心结构 n体问题 |
| 文章编号： | 1671-8224（2006）01-0053-04 |
| 收稿时间： | 2005-04-30 |
| 修稿时间： | 2005-11-10 |
Existence and uniqueness for a class of nine-bodies central configurations |
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| LIU Xue-fei DU Xianglin FENG Tian-xiang.Existence and uniqueness for a class of nine-bodies central configurations[J].Journal of Chongqing University,2006,5(1):53-56. |
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| Authors: | LIU;Xue-fei;DU;Xianglin;FENG;Tian-xiang |
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| Abstract: | On some necessary conditions for double pyramidal central configurations with concave heptagon for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configurations with concave heptagon base for nine-body problems is proved in this paper, and the range of the ratio of the circularity radius of the heptagon to the half-height of the double pyramidal central configuration involved in this class configurations is obtained, which is in the interval(√3/3,1.099 600 679), and the configuration involved in the bodies with anyσ∈(√3/3,1.099 600 679) can form a central configuration which is a uniquely central configuration is proved. |
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| Keywords: | nine-body problem existence and uniqueness concave heptagon base double pyramidal central configuration |
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