Home > Articles > Published articles > On co-orbital quasi-periodic motion in the three-body problem |
Date: | 2019 |
Abstract: | Within the framework of the planar three-body problem we establish the existence of quasi-periodic motions and KAM 4-tori related to the co-orbital motion of two small moons about a large planet where the moons move in nearly circular orbits with almost equal radii. The approach is based on a combination of normal form and symplectic reduction theories and the application of a KAM theorem for high-order degenerate systems. To accomplish our results we need to expand the Hamiltonian of the three-body problem as a perturbation of two uncoupled Kepler problems. This approximation is valid in the region of phase space where co-orbital solutions occur. |
Grants: | Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 Ministerio de Economía y Competitividad MTM2014-59433-C2-1-P Ministerio de Economía y Competitividad MTM2017-88137-C2-1-P |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Three-body problem ; Symplectic scaling ; Co-orbital regime ; 1:1 mean-motion resonance ; Normalization and reduction ; KAM theory for multiscale systems ; Quasi-periodic motion and invariant 4-tori |
Published in: | SIAM Journal on Applied Dynamical Systems, Vol. 18, Issue 1 (2019) , p. 334-353, ISSN 1536-0040 |
Postprint 18 p, 1.8 MB |