On co-orbital quasi-periodic motion in the three-body problem
Fecha
2019Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
Impacto
|
10.1137/18M1190859
Resumen
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 hig ...
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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. [--]
Materias
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
Editor
Society for Industrial and Applied Mathematics (SIAM)
Publicado en
SIAM Journal on Applied Dynamical Systems 2019, Vol. 18, No. 1 : pp. 334-353
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
Versión del editor
Entidades Financiadoras
J. M. Cors was partially supported by grants MTM2016-77278-P (FEDER) and AGAUR
grant 2017 SGR 1617. J. F. Palacián and P. Yanguas have been partially supported by grants
MTM 2014-59433-C2-1-P and MTM 2017-88137-C2-1-P.