On the periodic orbits of the circular double Sitnikov problem

Details On the periodic orbits of the circular double Sitnikov problem On the periodic orbits of the circular double Sitnikov problem

2009-03-12

arxiv.org/abs/0903.2126v1

C. R. Acad. Sci. de Paris, Serie I, Vol 347, Issue 5, (2009) pp 333-336

Physics

Mathematical Physics

4 pages. Accepted in C. R. Acad. Sci. de Paris, Serie I. This is not the final version

Scientific paper

10.1016/j.crma.2009.01.011

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.

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