| Eight-body central configuration for conjugate-nested regular tetrahedrons |
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| 引用本文： | LIU Xue-fei FENG Tian-xiang CHEN Xiao-chun. Eight-body central configuration for conjugate-nested regular tetrahedrons[J]. 重庆大学学报(英文版), 2007, 6(4): 294-298 |
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| 作者姓名： | LIU Xue-fei FENG Tian-xiang CHEN Xiao-chun |
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| 作者单位： | College of |
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| 基金项目： | Funded by Natural Science Foundation of China (No. 10231010)，KJ of Chongqing Educational Committee (No.KJ071105)，and Chongqing Three Gorges University (No. SXXYYB07004). |
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| 摘 要： | The sufficient and necessary conditions, the existence and uniqueness of a new class of central configuration in R3, for the conjugate-nest consisting of two regular tetrahedrons, are proved. If the configuration is a central configuration, then all masses of outside layer are equivalent, and the masses of inside layer are also equivalent. At the same time ρ (the ratio of the sizes) and mass ratio τ=m/?m must be satisfied by some formulas. For any radius ratios ρ∈(0, 0.152 996 918 2) or (0.715 223 148 7, 1.398 165 037), there is only one central configuration. Otherwise, for any given mass ratio τ , there may exist more than one central configuration.
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| 关 键 词： | 数学理论 计算方法 结构特征 四面体 |
| 文章编号： | 1671-8224（2007）04-0294-05 |
| 收稿时间： | 2006-12-25 |
| 修稿时间： | 2007-05-16 |
Eight-body central configuration for conjugate-nested regular tetrahedrons |
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| LIU Xue-fei,FENG Tian-xiang,CHEN Xiao-chun. Eight-body central configuration for conjugate-nested regular tetrahedrons[J]. Journal of Chongqing University(English Edition), 2007, 6(4): 294-298 |
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| Authors: | LIU Xue-fei FENG Tian-xiang CHEN Xiao-chun |
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| Abstract: | The sufficient and necessary conditions, the existence and uniqueness of a new class of central configuration in R3, for the conjugate-nest consisting of two regular tetrahedrons, are proved. If the configuration is a central configuration, then all masses of outside layer are equivalent, and the masses of inside layer are also equivalent. At the same time ρ (the ratio of the sizes) and mass ratio τ=m/m must be satisfied by some formulas. For any radius ratios ρ∈(0, 0.152 996 918 2) or (0.715 223 148 7, 1.398 165 037), there is only one central configuration. Otherwise, for any given mass ratio τ , there may exist more than one central configuration. |
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| Keywords: | eight-body problem conjugate-nested tetrahedrons existence and uniqueness central configuration |
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