Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 479093, 15 pages
http://dx.doi.org/10.1155/2012/479093
Research Article

Matched Asymptotic Expansions to the Circular Sitnikov Problem with Long Period

1High Temperatures Department, Instituto de Innovación en Minería y Metalurgia, Ahumada 341, 8320181 Santiago, Chile
2Department of Physics, Universidad Gabriela Mistral, Avenida Ricardo Lyon 1177, Santiago, Chile

Received 3 August 2012; Revised 22 November 2012; Accepted 23 November 2012

Academic Editor: Roberto Barrio

Copyright © 2012 Marco Rosales-Vera. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. Sitnikov, “Existence of oscillating motions for the three-body problem,” Doklady Akademii Nauk, vol. 133, no. 2, pp. 303–306, 1960. View at Google Scholar
  2. W. D. MacMillan, “An integrable case in the restricted problem of three bodies,” Astronomical Journal, vol. 27, no. 625-626, pp. 11–13, 1911. View at Google Scholar
  3. J. Moser, Stable and Random Motions in Dynamical Systems, Princeton University Press, Princeton, NJ, USA, 1973.
  4. E. Perdios and V. V. Markellos, “Stability and bifurcations of Sitnikov motions,” Celestial Mechanics and Dynamical Astronomy, vol. 42, no. 1–4, pp. 187–200, 1987. View at Publisher · View at Google Scholar
  5. R. Dvorak, “Numerical results to the Sitnikov-problem,” Celestial Mechanics and Dynamical Astronomy, vol. 56, pp. 71–80, 1993. View at Google Scholar
  6. J. Hagel, “A new analytic approach to the Sitnikov problem,” Celestial Mechanics and Dynamical Astronomy, vol. 53, no. 3, pp. 267–292, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. J. Liu and Y. S. Sun, “On the Sitnikov problem,” Celestial Mechanics and Dynamical Astronomy, vol. 49, no. 3, pp. 285–302, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. K. Wodnar, Predictability, Stability, and Chaos in N-Body Dynamical Systems, Plenum Press, New York, NY, USA, 1991, Edited by: A. E. Roy.
  9. E. Belbruno, J. Llibre, and M. Ollé, “On the families of periodic orbits which bifurcate from the circular Sitnikov motions,” Celestial Mechanics and Dynamical Astronomy, vol. 60, no. 1, pp. 99–129, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. S. B. Faruque, “Solution of the Sitnikov problem,” Celestial Mechanics and Dynamical Astronomy, vol. 87, no. 4, pp. 353–369, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. R. Dvorak, “The Sitnikov problem—a complete picture of phase space,” Publications of the Astronomy Department of the Eötvös University, vol. 19, pp. 129–140, 2007. View at Google Scholar
  12. T. Kovács and B. Érdi, “The structure of the extended phase space of the Sitnikov problem,” Astronomische Nachrichten, vol. 328, pp. 801–804, 2007. View at Google Scholar
  13. R. Dvorak and Y. S. Sun, “The phase space structure of the extended Sitnikov-problem,” Celestial Mechanics and Dynamical Astronomy, vol. 67, no. 1, pp. 87–106, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. P. Soulis, T. Bountis, and R. Dvorak, “Stability of motion in the Sitnikov 3-body problem,” Celestial Mechanics and Dynamical Astronomy, vol. 99, no. 2, pp. 129–148, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. J. Hagel, “An analytical approach to small amplitude solutions of the extended nearly circular Sitnikov problem,” Celestial Mechanics and Dynamical Astronomy, vol. 103, no. 3, pp. 251–266, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. T. Bountis and K. E. Papadakis, “The stability of vertical motion in the N-body circular Sitnikov problem,” Celestial Mechanics and Dynamical Astronomy, vol. 104, no. 1-2, pp. 205–225, 2009. View at Publisher · View at Google Scholar
  17. V. V. Sidorenko, “On the circular Sitnikov problem: the alternation of stability and instability in the family of vertical motions,” Celestial Mechanics and Dynamical Astronomy, vol. 109, no. 4, pp. 367–384, 2011. View at Publisher · View at Google Scholar
  18. S. Di Ruzza and C. Lhotka, “High order normal form construction near the elliptic orbit of the Sitnikov problem,” Celestial Mechanics and Dynamical Astronomy, vol. 111, no. 4, pp. 449–464, 2011. View at Publisher · View at Google Scholar