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

Stepan P. Sosnitskii

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

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

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
Paper Structure (5 sections, 78 equations)

This paper contains 5 sections, 78 equations.

Table of Contents

  1. Introduction
  2. Equations of Motion for the Circular Restricted Three-Body Problem
  3. Equations of Perturbed Motion in a Neighborhood of Libration Points
  4. On the Instability of Libration Points
  5. Conclusion