两对相邻等质量的四体共圆中心构型

Abstract

Cors和Roberts在2012年的文章[1]中证明了：在四体共圆中心构型中，若两对相邻质点的质量相等，则该共圆中心构型一定是等腰梯形。但是证明方法很复杂，本文采用有向面积方法并结合相对距离坐标给出了一个简洁证明。 In 2012, Cors and Roberts [1] showed that the four-body co-circular central configuration is an isosceles trapezoid when two pairs of adjacent masses are equal. However, their proof is very complicated. In this paper, we give a simpler proof by using the method of oriented areas and mutual coordinates.