Linear stability of the elliptic relative equilibria for the restricted 4-body problem: the Euler case

2022/05/21 by Bowen Liu, Qinglong Zhou, Liu, Bowen +1
Engineering · Physics and Astronomy · #34C25 #70F10 #70H14 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nuclear physics research studies #Spacecraft Dynamics and Control #Stellar, planetary, and galactic studies

paper · pdf · doi:10.48550/arxiv.2205.10514

openalex publication_date 2022/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the elliptic relative equilibria of the restricted 4-body problems, where the three primaries form an Euler collinear configuration and the four bodies span R². We obtain the symplectic reduction to the general restricted N-body problem. By analyzing the relationship between this restricted 4-body problems and the elliptic Lagrangian solutions, we obtain the linear stability of the restricted 4-body problem by the ω-Maslov index. Via numerical computations, we also obtain conditions of the stability on the mass parameters for the symmetric cases.

Related

• Linear stability of the elliptic relative equilibria for the restricted N-body problem: two special cases
• The symplectic reduction of the linearized Hamiltonian systems at elliptic relative equilibria of four-body problem
• Quantitative Linear Stability Analysis of Elliptic Relative Equilibria in the Planar N-Body Problem
• Stability of the triangular points in the elliptic restricted problem of three bodies
• The number of relative equilibria in the PCR4PB