Dynamics of an isosceles problem generated by a perturbation of Euler's collinear solution

TL;DR

This paper investigates the stability and dynamics of an isosceles three-body configuration resulting from a perturbation of Euler's collinear solution, using Hamiltonian mechanics and stability analysis.

Contribution

It introduces a reduced two-degree-of-freedom model for the perturbed isosceles problem and analyzes its equilibrium points and stability properties.

Findings

Identified a circumference of relative equilibria points.

Reduced the original system to a simpler, periodic system with a single equilibrium.

Discussed linear and parametric stability of the simplified model.

Abstract

This paper presents a study of the isosceles problem resulting by a perturbation of Euler's collinear solution under Newtonian gravitational attraction of three bodies in space. After the Hamiltonian was obtained, a circumference of relative equilibria points was found. The original system was subsequently reduced to another system with two degrees of freedom, periodic in the time, where there is now a single point of equilibrium. Linear and parametric stability were discussed in this simplified model of the three-body problem.