Perturbing Masses: A Study of Centered Co-Circular Configurations in Power-Law n-Body Problems

2023/10/31 by Tang, Zhengyang, Zhu, Shuqiang
#70F10 #70F15 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.20313

Abstract

This research investigates centered co-circular central configurations in the general power-law potential n-body problem. Firstly, there are no such configurations when all masses are equal, except for two; secondly, unless all masses are equal, no such configurations exist when masses can be divided into two sets of equal masses. We adapt Wang's criterion and incorporate insights on cyclic quadrilaterals, alongside mathematical induction.

Related

• On the Nonexistence of Centered Co-Circular Central Configurations With Three Unequal masses
• On the centered co-circular central configurations for the n-body problem
• Planar central configurations of some restricted (4 + 1)-body problems
• The central configurations of four masses x, -x, y, -y
• On the uniqueness of the isosceles trapezoidal central configuration in the 4-body problem for power-law potentials