Symplectic coordinates on S2 × S2 for perturbed Keplerian problems: Application to the dynamics of a generalised Størmer problem

  1. Iñarrea, M. 1
  2. Lanchares, V. 1
  3. Palacián, J.F. 2
  4. Pascual, A.I. 1
  5. Salas, J.P. 1
  6. Yanguas, P. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad Pública de Navarra
    info

    Universidad Pública de Navarra

    Pamplona, España

    ROR https://ror.org/02z0cah89

Revista:
Journal of Differential Equations

ISSN: 0022-0396

Any de publicació: 2011

Volum: 250

Número: 3

Pàgines: 1386-1407

Tipus: Article

DOI: 10.1016/J.JDE.2010.09.027 SCOPUS: 2-s2.0-78349305994 WoS: WOS:000285214000007 GOOGLE SCHOLAR

Altres publicacions en: Journal of Differential Equations

Repositori institucional: lock_openAccés obert Editor

Projectes relacionats

FORMAS NORMALES EN SISTEMAS DINÁMICOS HAMILTONIANOS: ASPECTOS TEÓRICOS Y APLICACIONES.

2009/00017/001

Resum

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.