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 comb...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/132984 |
| Acceso en línea: | https://hdl.handle.net/2117/132984 https://dx.doi.org/10.1137/18M1190859 |
| Access Level: | acceso abierto |
| Palabra clave: | Three-body problem Celestial mechanics 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 Problema dels tres cossos Mecànica celest Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics Classificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamics Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::37 Dynamical systems and ergodic theory::37N Applications Àrees temàtiques de la UPC::Matemàtiques i estadística |
| 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. |
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