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
-
1
Universidad de La Rioja
info
-
2
Universidad Pública de Navarra
info
ISSN: 0022-0396
Argitalpen urtea: 2011
Alea: 250
Zenbakia: 3
Orrialdeak: 1386-1407
Mota: Artikulua
Beste argitalpen batzuk: Journal of Differential Equations
Lotura duten proiektuak
Laburpena
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.