TOPOLOGY OF CONFIGURATION SPACE FOR A THREE-BODY PROBLEM  

作　　者：古志鸣[1] 

机构地区：[1]南京航空航天大学理学院

出　　处：《Transactions of Nanjing University of Aeronautics and Astronautics》1998年第2期84-87,共4页南京航空航天大学学报（英文版）

摘　　要：A mechanics system consisting of three mass points on sphere S 2 is considered. The configuration space of the system is a fibre bundle over S 2 . It is proved that first Chern class of the bundle is -2 c 1(γ) where γ is the canonical line bundle over the complex projective space CP 1=S 2 , which shows the bundle is non trivial. The information about the first Chern class makes the cohomology groups and homotopy groups of the configuration space worked out. In addition the effects of these topolo gical properties of the configuration space on the behavior in large scale of the system, as the number of equilibrium positions, periodic orbits and reduced phase space, are discussed.考虑了限制在球面Ｓ２上运动的三个质点的力学系统，该系统的构型空间是Ｓ２上的一个纤维丛。本文证明了这个丛的第１陈省身示性类等于－２ｃ１（γ），其中γ是复射影空间ＣＰ１＝Ｓ２上的典范线丛。这个结果蕴涵该构型空间是Ｓ２上的非平凡丛。由此又算出了它的上同调群与同伦群。此外还讨论了上述拓扑性质对于诸如平衡位置的数目，周期轨道及约化相空间等涉及系统大范围性状的影响。

关 键 词：N  body problem CONFIGURATION Chern characteristic class cohomology groups homotopy groups 

分 类 号：O189[理学—数学]