Energy levels of periodic solutions of the circular 2+2 Sitnikov problem

TL;DR

This paper investigates the energy levels and periodic solutions of the circular double Sitnikov problem, extending solutions beyond collisions using symplectic regularization and analyzing the structure of energy surfaces.

Contribution

It introduces a symplectic regularization for the circular double Sitnikov problem and studies the structure of energy surfaces containing periodic orbits.

Findings

Almost all solutions are collision orbits.

Energy surfaces contain foliations of periodic orbits.

Regularization extends solutions beyond collisions.

Abstract

We study a 2+2 body problem introduced in a previous paper as the circular double Sitnikov problem. Since the secondary bodies are moving on the same perpendicular line where evolve the primaries, almost every solution is a collision orbit. We extend the solutions beyond collisions with a symplectic regularization and study the set of energy surfaces that contain periodic orbits and their foliations .