Existence of a lower bound for the distance between point masses of relative equilibria in ${\mathbb{S}}^{k-1}$, $k\ge 3$

Abstract

We prove that if for the curved $n$-body problem in ${\mathbb{S}}^{k-1}$, $k\ge 3$, 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.

References in corpus (1)

• On the stability of tetrahedral relative equilibria in the positively curved 4-body problem