| Existence and uniqueness for a class of double pyramidal central configurations with a concave pentagonal base |
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| 作者姓名： | 刘学飞 |
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| 作者单位： | Department of |
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| 基金项目： | Natural Science Foundation of China (No.19871096) |
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| 摘 要： | ~~bodies involved have masses m1, m2,,m7 respectively (hereinafter, these symbols of masses also denote the relating bodies ) and m5 lies at the geometrical center of the square consisting of positions of masses m1, m2,, m4 , i.e. m1, m2,,m5 form a concave pentagon. The line between m6 and m7 passes through m5 and is perpendicular to the plane containing the concave pentagon. The distance between m5 and m6 is equal to the distance between m5 and m7. Then the position vectors of m1, m2,,m…
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Existence and uniqueness for a class of double pyramidal central configurations with a concave pentagonal base |
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| LIU Xuefei,.Existence and uniqueness for a class of double pyramidal central configurations with a concave pentagonal base[J].Journal of Chongqing University,2003,2(1). |
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| Authors: | LIU Xuefei |
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| Institution: | Department of Mathematics, Chongqing Three Gorges College, Chongqing 404000, P.R. China;College of Mathematics and Sciences, Chongqing University, Chongqing 400044, P.R. China |
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| Abstract: | Based on some necessary conditions for double pyramidal central configurations with a concave pentagonal base, for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configurations with a concave pentagonal base in 7-body problems are proved and the range of the ratio between radius and half-height is obtained, within which the 7 bodies involved form a central configuration or form uniquely a central configuration. |
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| Keywords: | N-body problem existence and uniqueness concave pentagonal base double pyramidal central configuration |
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