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...
| Autores: | , , |
|---|---|
| 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 |
| 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. |
|---|