On co-orbital quasi-periodic motion in the three-body problem
Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
Palacián, Jesus F. (Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas)
Yanguas, Patricia (Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas)

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

DOI: 10.1137/18M1190859

Postprint 18 p, 1.8 MB

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