Relative equilibria in quasi-homogeneous three body problems

TL;DR

This paper investigates the families of relative equilibria in the planar three body problem with quasi-homogeneous potentials, revealing how the number of solutions depends on masses and system size.

Contribution

It introduces a study of relative equilibria for three bodies under quasi-homogeneous potentials, extending classical results to more general interaction functions.

Findings

Number of relative equilibria varies with masses and system size

Families of solutions characterized for quasi-homogeneous potentials

Dependence on moment of inertia analyzed

Abstract

In this paper we find the families of relative equilibria for the three body problem in the plane, when the interaction between the bodies is given by a quasi-homogeneous potential, which is the sum of two homogeneous functions. The number of the relative equilibria depends of the values of the masses and of the size of the system, measured by the moment of inertia.