平面2N体问题的正N边形中心构型

REGULAR N-SIDED POLYGONAL CENTRAL CONFIGURATION FOR PLANE 2N-BODY PROBLEM

在对N体问题中心构型的研究中,正多边形解是研究对象之一.其特点是,N个等质量的质点,位于一个正N边形的顶点上.有没有2 N个质点,构成一个正N边形解呢?即N个等质量的质点,位于一个正N边形的顶点上,另外N个等质量的质点,位于该正N边形的边的中点.本文研究了这种解的存在条件,并给出了具体的解.

One solution for central configuration of N-body problem is regular N-sided polygon.Regular N-sided polygon solution has the characteristic that N equal mass particles lie on the vertices of a regular N-sided polygon.This paper investigates whether a regular N-sided polygon solution exists for the 2N particles problem,or whether N equal mass particles lies on the vertices of a regular N-sided polygon,and whether another N equal mass particles lies on the midpoints of the sides.The conditions giving the solution were discussed and the solution was shown.