On the periodic orbits of the circular double Sitnikov problem
arXiv:0903.2126 · doi:10.1016/j.crma.2009.01.011
Abstract
We introduce a restricted four body problem in a 2+2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the planewhere the primaries evolve, so 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.
4 pages. Accepted in C. R. Acad. Sci. de Paris, Serie I. This is not the final version