Polygonal rotopulsators of the curved $n$-body problem

Abstract

We revisit polygonal positive elliptic rotopulsator solutions and polygonal negative elliptic rotopulsator solutions of the $n$-body problem in ${\mathbb{H}}^3$ and ${\mathbb{S}}^3$ and prove existence of these solutions, prove that the masses of these rotopulsators have to be equal if the rotopulsators are of nonconstant size and show that the number of negative elliptic relative equilibria of this type is finite, as is the number of positive elliptic relative equilibria if an upper bound on the size of the relative equilibrium is imposed. Additionally, we prove that a class of negative hyperbolic rotopulsators is in fact a subclass of the class of polygonal negative elliptic rotopulsators.

arXiv commentarXiv admin note: text overlap with arXiv:1608.07931

References in corpus (3)

• The classical N-body problem in the context of curved space
• All the Lagrangian relative equilibria of the curved 3-body problem have equal masses
• Existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi-homogeneous $n$-body problems and the curved $n$-body problem