Existence of a lower bound for the distance between point masses of relative equilibria in \mathbbS^k-1, k≥ 3

2014/01/23 by Pieter Tibboel, Tibboel, Pieter
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Cosmology and Gravitation Theories #Dynamical Systems (math.DS) #FOS: Mathematics #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.1401.5884

openalex publication_date 2014/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if for the curved n-body problem in \mathbbS^k-1, k≥ 3, the masses are given, the minimum distance between the point masses of a specific type of relative equilibrium solution that is a generalisation of positive elliptic relative equilibria and positive elliptic-elliptic relative equilibria has a universal lower bound that is not equal to zero.

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