3n体三重嵌套正多边形中心构型问题

Central configurations for planar 3n-body problem: triple nested regular polygons

摘要:

本文运用Dziobek方程组研究了9体和12体三重嵌套正多边形中心构型问题. 对于9体问题, 本文发现了三类新的三重嵌套正三角形中心构型. 对于12体问题,本文也发现了几类不同的三重嵌套正多边形中心构型.

Abstract:

We study the existence of some families of triple nested planar central configurations for the n-body problem with n=9, 12. For 9-body problem we show that there exist three families of triple nested triangular central configurations. For 12-body problem we show that there exist different families of triple nested regular polygonal central configurations in different cases.