On co-orbital quasi-periodic motion in the three-body problem

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 combin...

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Detalles Bibliográficos
Autores: Cors Iglesias, Josep Maria|||0000-0002-9803-8490, Palacián, Jesus F., Yanguas, Patricia
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:236671
Acceso en línea:https://ddd.uab.cat/record/236671
https://dx.doi.org/urn:doi:10.1137/18M1190859
Access Level:acceso abierto
Palabra clave: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
Descripción
Sumario: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.