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.
Variational approach to second species periodic solutions of Poincaré of the 3 body problem / Sergey, Bolotin; Negrini, Piero. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 33:3(2013), pp. 1009-1032. [10.3934/dcds.2013.33.1009]
Variational approach to second species periodic solutions of Poincaré of the 3 body problem
NEGRINI, Piero
2013
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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.