Table of Contents Author Guidelines Submit a Manuscript
Journal of Mathematics
Volume 2013, Article ID 936859, 8 pages
http://dx.doi.org/10.1155/2013/936859
Research Article

Pulsating Different Curves of Zero Velocity around Triangular Equilibrium Points in Elliptical Restricted Three-Body Problem

1Department of Mathematics, Bhilai Institute of Technology, Durg 491001, India
2Department of Mathematics, Rungta College of Engineering and Technology, Bhilai 490020, India

Received 30 December 2012; Revised 15 February 2013; Accepted 16 February 2013

Academic Editor: Baoding Liu

Copyright © 2013 A. Narayan and Amit Shrivastava. 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. J. M. A. Danby, “Stability of the triangular points in the elliptic restricted problem of three bodies,” The Astronomical Journal, vol. 69, pp. 165–172, 1964. View at Publisher · View at Google Scholar · View at MathSciNet
  2. M. K. Ammar, “The effect of solar radiation pressure on the Lagrangian points in the elliptic restricted three-body problem,” Astrophysics and Space Science, vol. 313, no. 4, pp. 393–408, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. A. Bennett, “Characteristic exponents of the five equilibrium solutions in the elliptically restricted problem,” Icarus, vol. 4, no. 2, pp. 177–187, 1965. View at Google Scholar · View at Scopus
  4. V. V. Markellos, E. Perdios, and P. Labropoulou, “Linear stability of the triangular equilibrium points in the photogravitational elliptic restricted problem, I,” Astrophysics and Space Science, vol. 194, no. 2, pp. 207–213, 1992. View at Publisher · View at Google Scholar · View at Scopus
  5. R. Meire, “The stability of the triangular points in the elliptic restricted problem,” Celestial Mechanics, vol. 23, no. 1, pp. 89–95, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. E. Rabe, “Two new classes of periodic Trojan liberation in the elliptical restricted problem and there stabilities,” in Periodic Orbits, Stability and Resonance, G. E. O. Giacaglia, Ed., pp. 33–44, Reidel Publication Company, Dordrecht, The Netherlands, 1970. View at Google Scholar
  7. E. Rabe, “Elliptical restricted problem : fourth-order stability analysis of the triangular points,” in Recent Advances in Dynamical Astronomy, E. D. Toply and V. Szebehely, Eds., pp. 155–160, D. Reidel Publication Company, Dordrecht, The Netherlands, 1973. View at Google Scholar
  8. G. E. Roberts, “Linear stability of the elliptic Lagrangian triangle solutions in the three-body problem,” Journal of Differential Equations, vol. 182, no. 1, pp. 191–218, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. S. Zimovshchikov and V. N. Tkhai, “Instability of libration points and resonance phenomena in the photogravitational elliptic restricted three-body problem,” Solar System Research, vol. 38, no. 2, pp. 155–163, 2004. View at Publisher · View at Google Scholar · View at Scopus
  10. B. Érdi, E. Forgács-Dajka, I. Nagy, and R. Rajnai, “A parametric study of stability and resonances around L4 in the elliptic restricted three-body problem,” Celestial Mechanics & Dynamical Astronomy, vol. 104, no. 1-2, pp. 145–158, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Gyorgrey, “On the non-linear stability of motion's around L5 in the elliptic restricted problem of the three bodies,” Celestial Mechanics, vol. 36, no. 3, pp. 281–285, 1985. View at Google Scholar
  12. V. Kumar and R. K. Choudhry, “Nonlinear stability of the triangular libration points for the photogravitational elliptic restricted problem of three bodies,” Celestial Mechanics & Dynamical Astronomy, vol. 48, no. 4, pp. 299–317, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  13. S. N. Khasan, “Three dimensional periodic solutions to the photogravitational Hill problem,” Cosmic Research, vol. 34, no. 5, pp. 299–317, 1990. View at Google Scholar
  14. S. N. Khasan, “Liberation solutions to the photogravitational restricted three-body problem,” Cosmic Research, vol. 34, no. 2, pp. 146–151, 1996. View at Google Scholar
  15. C. Pinyol, “Ejection-collision orbits with the more massive primary in the planar elliptic restricted three-body problem,” Celestial Mechanics & Dynamical Astronomy, vol. 61, no. 4, pp. 315–331, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. L. Floria, “On an analytical solutions in the planar elliptic restricted three body problem,” Monografías del Seminario Matemático García de Galdeano, vol. 31, pp. 135–144, 2004. View at Google Scholar
  17. P. P. Hallan and N. Rana, “The existence and stability of equilibrium points in the Robe's restricted three-body problem,” Celestial Mechanics & Dynamical Astronomy, vol. 79, no. 2, pp. 145–155, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. W. H. Jefferys, “A new class of periodic solutions of the three dimensional restricted problem,” The Astronomical Journal, vol. 71, no. 2, pp. 99–102, 1966. View at Publisher · View at Google Scholar · View at MathSciNet
  19. W. H. Jefferys, “Doubly symmetric periodic orbits in the three-dimensional restricted problem,” The Astronomical Journal, vol. 70, no. 6, pp. 393–394, 1965. View at Publisher · View at Google Scholar · View at MathSciNet
  20. A. P. Markeev, “On one special case of parametric resonance in problems of celestial mechanics,” Astronomy Letters, vol. 31, no. 5, pp. 350–356, 2005. View at Publisher · View at Google Scholar · View at Scopus
  21. A. P. Markeev, Libration Points in Celestial Mechanics and Cosmodynamics, Nauka, Moscow, Russia, 1978.
  22. D. Selaru and C. Cucu-Dumitreacu, “An analysis asymptotical solution in the three body problem,” Romanian Astron. Journal, vol. 4, no. 1, pp. 59–67, 1994. View at Google Scholar
  23. D. Şelaru and C. Cucu-Dumitrescu, “Infinitesimal orbits around Lagrange points in the elliptic, restricted three-body problem,” Celestial Mechanics & Dynamical Astronomy, vol. 61, no. 4, pp. 333–346, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. T. Schauner, “Die Bevegung in der Nach der Dreieckspu mkte des elliptischen eingeschrinkten Dreikorpen problems,” Celestial Mechanics, vol. 3, no. 2, pp. 189–196, 1971. View at Publisher · View at Google Scholar
  25. Z. Sándor and B. Érdi, “Symplectic mapping for Trojan-type motion in the elliptic restricted three-body problem,” Celestial Mechanics & Dynamical Astronomy, vol. 86, no. 4, pp. 301–319, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. Z. Sàndor, R. Balla, F. Téger et al., “Short time lyapunov, indicator in the restricted three-body problem,” Celestial Mechanics and Dynamical Astronomy, vol. 79, no. 1, pp. 29–40, 2001. View at Publisher · View at Google Scholar
  27. A. Narayan and C. Ramesh Kumar, “Effects of photogravitational and oblantensss on the triangular Lagrangian points in the elliptical restricted three body problem,” International Journal of Pure and Applied Mathematics, vol. 68, no. 2, pp. 201–224, 2011. View at Google Scholar · View at MathSciNet
  28. A. Narayan and C. Ramesh, “Stability of triangular equilibrium points in elliptical restricted three body problem under the effects of photogravitational and oblateness of primaries,” International Journal of Pure and Applied Mathematics, vol. 70, no. 5, pp. 735–754, 2011. View at Google Scholar · View at Scopus
  29. A. Narayan and C. Ramesh, “Existence and stability of collinear equilibrium points in elliptical restricted three body problem under the effects of photogravitational and oblateness primaries,” International Journal of Pure and Applied Mathematics, vol. 80, no. 4, pp. 477–494, 2012. View at Google Scholar
  30. S. Jagdish and U. Aishetu, “On the stability of triangular points in the elliptical R3BP under the radiating and oblate primaries,” Astrophysics and Space Science, vol. 341, no. 2, pp. 349–358, 2012. View at Publisher · View at Google Scholar
  31. A. Narayan and S. Amit, “Effects of oblateness and radiation of primaries on the equilibrium points in the ellipted restricted three body problem,” International Journal of Mathematical Science, vol. 32, no. 10, pp. 330–345, 2012. View at Google Scholar