Periodic oscillations in the restricted Hip-Hop 2N+1 body problem

TL;DR

This paper proves the existence of specific periodic solutions in a restricted celestial mechanics problem involving 2N primaries moving in a Hip-Hop pattern and a massless body constrained on a line, expanding understanding of such dynamical systems.

Contribution

It introduces new periodic solutions in the restricted (2N+1)-body problem with primaries on a Hip-Hop orbit and a massless body on a perpendicular line, a novel configuration in celestial mechanics.

Findings

Existence of periodic solutions proven for the specified configuration.

The primaries follow a Hip-Hop periodic orbit.

The massless body moves on a line through the center of mass, perpendicular to the primaries' base.

Abstract

We prove the existence of periodic solutions of the restricted $(2N+1)$-body problem when the $2N$-primaries move on a periodic Hip-Hop solution and the massless body moves on the line that contains the center of mass and is perpendicular to the base of the antiprism formed by the $2N$-primaries.