Maslov-type indices and linear stability of elliptic Euler solutions of the three-body problem

TL;DR

This paper applies Maslov-type index theory and linear operator analysis to study the linear stability of elliptic Euler solutions in the three-body problem, providing new insights into their stability properties.

Contribution

It introduces a novel application of Maslov-type -index theory combined with linear operator methods to analyze stability in the three-body problem.

Findings

Computed -indices for elliptic Euler solutions.

Identified stability properties of these solutions.

Provided theoretical framework for stability analysis.

Abstract

In this paper, we use the central configuration coordinate decomposition to study the linearized Hamiltonian system near the elliptic Euler solutions. Then using the Maslov-type \omega-index theory of symplectic paths and the theory of linear operators we compute the \omega-indices and obtain certain properties of linear stability of the Euler elliptic solutions of the classical three-body problem.