一类10-体中心构型的存在唯一性(英文)  

Existence and uniqueness for a class of ten-bodies central configurations

作　　者：刘学飞[1] 

机构地区：[1]重庆三峡学院数学系,重庆万州404000

出　　处：《重庆三峡学院学报》2008年第3期57-60,共4页Journal of Chongqing Three Gorges University

基　　金：Funded by NSF (Natural Science Foundation) of Chongqing Educational Committee(KJ071105)

摘　　要：在张-周等学者[1]相关工作的基础上,讨论了有关双金字塔中心构型的某些必要条件,证明了一类以八边形为基底10-体双金字塔构型在任意给定质量比的前提下构成中心构型的存在唯一性;同时给出了该类构型能够构成中心构型的径高比(基底外接圆半径与半高的比)的取值范围为(^(1/2)3/3,0.8440155430).On Based on the work of Zhang-Zhou and the definition of central configurations and double pyramidal central configurations among Newton n-body problems, some necessary conditions for double pyramidal central configurations are discussed, and for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configurations with octagon base in 10-body problems is proved in this paper. Further more, the range of the ratio between radius and half-height about configurations is obtained, which being in interval （√3/3,0.8440155430）, and for any number V∈ （√3/ 3, 0.84401554 30） the configuration with ratio V can form a central configuration and form a uniquely central configuration.

关 键 词：N-体问题 10-体问题 存在唯一性 八边形基底 双金字塔中心构型 

分 类 号：O175.7[理学—数学]