ON the stability of triangular Lagrangian points in the spatial restricted three-body problem
Solar and Stellar Astrophysics
2025-10-16 v1
Abstract
In the present paper, which is a development of an earlier study by the author \cite{Sosnitskii08}, we consider the stability of triangular libration points in the spatial circular restricted three-body problem and improve the result of author's work \cite{Sosnitskii08}. Unlike \cite{Sosnitskii08}, where the instability of libration points was established on the base of reduced approximate equations, we succeeded in this paper to use a new approach that made it possible to prove the instability of triangular libration points on the base of a closed complete system of equations. The relationship between the Lyapunov stability and Birkhoff stability (formal stability) is also discussed
Keywords
Cite
@article{arxiv.2510.13388,
title = {ON the stability of triangular Lagrangian points in the spatial restricted three-body problem},
author = {Stepan P. Sosnitskii},
journal= {arXiv preprint arXiv:2510.13388},
year = {2025}
}