Partially rigid motions in the planar three-body problem

2025/06/16 by Richard Moeckel, Moeckel, Richard
Engineering · Physics and Astronomy · #37N05 #70F10 #70F15 #70F16 #70G60 #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Space Satellite Systems and Control #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.2506.13570

openalex publication_date 2025/06/16 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid motions, where some but not all of the distances are constant. For the planar three-body problem with equal masses, we show that partially rigid motions are impossible -- if even one of the three mutual distances is constant, the motion must be a relative equilibrium.

Citations

• Partially rigid motions in the n-body problem
• The Lagrange reduction of the N-body problem, a survey

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