具广义力势n体问题的中心构形(Ⅱ)——2≤n≤4情形下中心构形的个数与形状

CENTRAL CONFIGURATIONS OF N-BODY PROBLEM WITH GENERAL ATTRACTION (Ⅱ)——THE NUMBERS AND THE SHAPES OF THE CENTRAL CONFIGURATIONS WHEN 2≤N≤4

本文是文[1]的继续,用理论分析及数值探索的方法,详细地研究了n(=2,3,4)体中心构形的个数与形状及其对广义力势参数k的依赖关系,得到了一些有价值的结果.

This paper is a sequel of [1], in which central configurations of n-body (n=2,3,4) are studied. Some theoretical results about one-dimension central configurations show that Moulton's theorem does not apply to the situation when k (parameter in the general force function) is less than zero. Also given are the theoretical resuits concerning the qualitative properties of the shapes of 4-body two-dimension central configurations. By means of classification, these properties are expressed succinctly. Furthermore, numerical explorations are invoked for illustrating how the numbers and the shapes of central configurations of n-body (n=3,4) depend on the parameter k.