On the Periodic Solutions Emerging from the Equilibria of the Hill Lunar Problem with Oblateness

• de Bustos, M Teresa ^[1] ; López, Miguel A ^[2] ; Martínez, Raquel ^[2] ; Vera, Juan A ^[3]
  1. [1] Universidad de Salamanca

     Universidad de Salamanca

     Salamanca, España

     
  2. [2] Universidad de Castilla-La Mancha

     Universidad de Castilla-La Mancha

     Ciudad Real, España

     
  3. [3] Universidad Politécnica de Cartagena

     Universidad Politécnica de Cartagena

     Cartagena, España

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 2, 2018, págs. 331-344
• Idioma: inglés
• DOI: 10.1007/s12346-017-0233-4
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• Resumen

  • In this paper, using the averaging theory of first order, we obtain sufficient conditions for computing periodic solutions in the 3D Hill problem with oblateness.

• Referencias bibliográficas
  • 1. Abouelmagd, E.I., Guirao, J.L.G.: On the perturbed restricted three-body problem. Appl. Math. Nonlinear Sci. 1(1), 123–144 (2016)
  • 2. Buica, A., Francoise, J.P., Llibre, J.: Periodic solutions of nonlinear periodic differential systems with a small parameter. Commun. Pure...
  • 3. Buica, A., García, I.: Periodic solutions of some perturbed symmetric Euler top. Topol. Methods Nonlinear Anal. 36, 91–100 (2010)
  • 4. de Bustos, M.T., Guirao, J.L.G., Vera, J.A., Vigo-Aguilar, J.: Periodic orbits and C1-integrability in the planar Stark–Zeeman problem....
  • 5. de Bustos, M.T., Guirao, J.L.G., Vera, J.A.: The spatial Hill Lunar problem: periodic solutions emerging from equilibria. Dyn. Syst., 1–14....
  • 6. Llibre, J., Rodrigues, A.: On the periodic orbits of Hamiltonian systems. J. Math. Phys. 51, 042704 (2010)
  • 7. Malkin, I.G.: Some problems of the theory of nonlinear oscillations. In: Gosudarstv. Izdat. Tehn.–Teor. Lit., Moscow (1956) (Russian)
  • 8. Markakis, M.P., Perdiou, A.E., Douskos, C.N.: The photogravitational Hill problem with oblateness: equilibrium points and Lyapunov families....
  • 9. Markellos, V.V., Roy, A.E., Perdios, E.A., Douskos, C.N.: A Hill problem with oblate primaries and effect of oblateness on Hill stability...
  • 10. Markellos, V.V., Roy, A.E., Velgakis, M.J., Kanavos, S.S.: A photogravitational Hill problem and radiation effects on Hill stability of...
  • 11. Papadakis, K.E.: The planar Hill problem with oblate primary. Astrophys. Space Sci. 293(3), 271–287 (2004)
  • 12. Papadakis, K.E.: The planar photogravitational Hill problem. Int. J. Bifurc. Chaos Appl. Sci. Eng. 16, 1809–1821 (2006)
  • 13. Perdiou, A.E., Markellos, V.V., Douskos, C.N.: The Hill problem with oblate secondary: numerical exploration. Earth Moon Planets 97, 127–145...
  • 14. Perdiou, A.E., Perdios, E.A., Kalantonis, V.S.: Periodic orbits of the Hill problem with radiation and oblateness. Astrophys. Space Sci....
  • 15. Pérez-Chavela, E., Tamayo, C.: Relative equilibria in the 4-vortex problem bifurcating from an equilateral triangle configuration. Appl....
  • 16. Roseau, M.: Vibrations non linéaires et théorie de la stabilité. In: Springer Tracts in Natural Philosophy, vol. 8. Springer, Berlin,...