We consider the plane 3 body problem with 2 of the masses small. Periodic solutions with near collisions of small bodies were named by Poincare second species periodic solutions. Such solutions shadow chains of collision orbits of 2 uncoupled Kepler problems. Poincare only sketched the proof of the existence of second species solutions. Rigorous proofs appeared much later and only for the restricted 3 body problem. We develop a variational approach to the existence of second species periodic solutions for the nonrestricted 3 body problem. As an application, we give a rigorous proof of the existence of a class of second species solutions.
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|Titolo:||Variational approach to second species periodic solutions of Poincaré of the 3 body problem|
|Data di pubblicazione:||2013|
|Appartiene alla tipologia:||01a Articolo in rivista|