Symplectic coordinates on S2 × S2 for perturbed Keplerian problems: Application to the dynamics of a generalised Størmer problem
- Iñarrea, M. 1
- Lanchares, V. 1
- Palacián, J.F. 2
- Pascual, A.I. 1
- Salas, J.P. 1
- Yanguas, P. 2
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1
Universidad de La Rioja
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2
Universidad Pública de Navarra
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ISSN: 0022-0396
Année de publication: 2011
Volumen: 250
Número: 3
Pages: 1386-1407
Type: Article
D'autres publications dans: Journal of Differential Equations
Projets liés
Résumé
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.