Symplectic coordinates on S2 × S2 for perturbed Keplerian problems: Application to the dynamics of a generalised Størmer problem
In order to analyse the dynamics of a given Hamiltonian system in the space defined as the Cartesian product of two spheres, we propose to combine Delaunay coordinates with Poincaré-like coordinates. The coordinates are of local character and have to be selected accordingly with the type of motions...
| Autores: | , , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universidad de La Rioja (UR) |
| Repositorio: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc697db750603269e81c1d |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc697db750603269e81c1d |
| Access Level: | acceso abierto |
| Palabra clave: | Delaunay coordinates KAM tori Periodic solutions Perturbed Keplerian problems Poincaré-like coordinates Product of two 2-spheres Størmer problem Symplectic reduction |
| Sumario: | In order to analyse the dynamics of a given Hamiltonian system in the space defined as the Cartesian product of two spheres, we propose to combine Delaunay coordinates with Poincaré-like coordinates. The coordinates are of local character and have to be selected accordingly with the type of motions one has to take into consideration, so we distinguish the following types: (i) rectilinear motions; (ii) circular and equatorial motions; (iii) circular non-equatorial motions; (iv) non-circular equatorial motions; and (v) non-circular and non-equatorial motions. We apply the theory to study the dynamics of the reduced flow of a generalised Størmer problem that is modelled as a perturbation of the Kepler problem. After using averaging and reduction theories, the corresponding flow is analysed on the manifold S2×S2, calculating the occurring equilibria and their stability. Finally, the flow of the original problem is reconstructed, concluding the existence of some families of periodic solutions and KAM tori. © 2010 Elsevier Inc. |
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