Geometric characterizations for variational minimization solutions of the 3-body problem  

作　　者：LONG Yiming and ZHANG Shiqing1. Nankai Institute of Mathematics , Nankai University , Tianjin 300071 , China  2. Department of Applied Mathematics, Chongqing University, Chongqing 400044, China Associate Member of the ICTP. 

出　　处：《Chinese Science Bulletin》1999年第18期1653-1655,共3页

摘　　要：For any given positive masses it is proved that the variational minimization solutions of the 3-body problem in 3 or 2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular restricted 3-body problem in 3 or 2 are also planar equilateral triangle circular solutions.For any given positive masses it is proved that the variational minimization solutions of the 3-body problem in ?3 or ?2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular restricted 3-body problem in ?3 or ?2 are also planar equilateral triangle circular solutions.

关 键 词：3-body problem VARIATIONAL MINIMIZATION equilateral TRIANGLE circular solution. 

分 类 号：P132.2[天文地球—天体力学]