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Variational approach to second species periodic solutions of Poincar'e of the 3 body problem | | Sergey Bolotin
; Piero Negrini
; | | Date: |
12 Apr 2011 | | Abstract: | We consider the plane 3 body problem with 2 of the masses small. Periodic
solutions with near collisions of small bodies were named by Poincar’e second
species periodic solutions. Such solutions shadow chains of collision orbits of
2 uncoupled Kepler problems. Poincar’e 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. | | Source: | arXiv, 1104.2288 | | Services: | Forum | Review | PDF | Favorites | |
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