ON the stability of triangular Lagrangian points in the spatial restricted three-body problem

2025/10/15 by S. P. Sosnitskii, Sosnitskii, Stepan P.
Engineering · Physics and Astronomy · #Astro and Planetary Science #FOS: Physical sciences #Solar and Stellar Astrophysics (astro-ph.SR) #Space Satellite Systems and Control #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.2510.13388

openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

In the present paper, which is a development of an earlier study by the author \citeSosnitskii08, we consider the stability of triangular libration points in the spatial circular restricted three-body problem and improve the result of author's work \citeSosnitskii08. Unlike \citeSosnitskii08, 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

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