Table of Contents Author Guidelines Submit a Manuscript
Advances in Astronomy
Volume 2014, Article ID 287174, 17 pages
http://dx.doi.org/10.1155/2014/287174
Research Article

Existence of Resonance Stability of Triangular Equilibrium Points in Circular Case of the Planar Elliptical Restricted Three-Body Problem under the Oblate and Radiating Primaries around the Binary System

1Department of Mathematics, Bhilai Institute of Technology, Durg, Chhattisgarh 491001, India
2Department of Mathematics, Rungta College of Engineering & Technology, Bhilai, Chhattisgarh 490024, India

Received 31 January 2014; Revised 28 March 2014; Accepted 1 April 2014; Published 15 May 2014

Academic Editor: Wing Huen Ip

Copyright © 2014 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. 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
  2. A. Narayan and C. Ramesh, “Existence and stability of collinear equilibrium points in elliptical restricted three body problem under the effects of radiational and oblateness primaries,” International Journal of Pure and Applied Mathematics, vol. 80, no. 4, pp. 477–494, 2012. View at Google Scholar
  3. 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 Scopus
  4. A. Narayan and C. R. Kumar, “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
  5. 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
  6. D. Selaru and C. Cucu-Dumitrescu, “An analytic asymptotical solution in the three body problem,” Romanian Astronomical Journal, vol. 4, no. 1, pp. 59–67, 1994. View at Google Scholar
  7. E. Balint, “A parametric study of stability and resonance around L4 in the elliptical restricted three body problem,” Celestial Mechanics and Dynamical Astronomy, vol. 104, pp. 145–158, 2009. View at Google Scholar
  8. J. Gyorgrey, “On the non-linear stability of motion's around L5 in the elliptic restricted problem of the three bodies,” Celestial Mechanics and Dynamical Astronomy, vol. 36, no. 3, pp. 281–285, 1985. View at Google Scholar
  9. J. M. A. Danby, “Stability of the triangular points in elliptic restricted problem of three bodies,” The Astronomical Journal, vol. 69, pp. 165–172, 1964. View at Google Scholar
  10. 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
  11. P. P. Halan and N. Rana, “The existence and stability of equilibrium points in the Robe's restricted three body problem,” Celestial Mechanics and Dynamical Astronomy, vol. 79, pp. 145–155, 2001. View at Google Scholar
  12. P. V. subbarao and R. K. Sharma, “A note on the stability of the triangular points of the equilibrium in the restricted three body problem,” Astronomy & Astrophysics, vol. 43, pp. 381–383, 1975. View at Google Scholar
  13. 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 Scopus
  14. S. N. Khasan, “Three dimensional periodic solutions to the radiational Hill problem,” Cosmic Research, vol. 34, no. 5, pp. 299–317, 1990. View at Google Scholar
  15. S. N. Khasan, “Liberation Solutions to the radiational restricted three body problem,” Cosmic Research, vol. 34, no. 2, pp. 146–151, 1996. View at Google Scholar
  16. S. Zsoft and B. Erdi, “Sympletic mapping for the Trojan-type motion in the elliptic restricted three body problem,” Celestial Mechanics and Dynamical Astronomy, vol. 86, pp. 301–319, 2003. View at Google Scholar
  17. T. Schauner, “Die Bevegung in der Nach der Dreieckspu mkte des elliptischen eingeschrinkten Dreikorpen problems,” Celestial Mechanics and Dynamical Astronomy, vol. 3, pp. 189–196, 1971. View at Google Scholar
  18. V. Gyorgrey, “On the non-linear stability of motion's around L{5} in the elliptic restricted problem of the three bodies,” Celestial Mechanics and Dynamical Astronomy, vol. 36, no. 3, pp. 281–285, 1985. View at Google Scholar
  19. V. Kumar and R. K. Choudhry, “Nonlinear stability of the triangular libration points for the photo gravitational elliptic restricted problem of three bodies,” Celestial Mechanics and Dynamical Astronomy, vol. 48, no. 4, pp. 299–317, 1990. View at Publisher · View at Google Scholar · View at Scopus
  20. 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
  21. 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
  22. J. Singh and U. Aishetu, “On the stability of triangular points in the elliptical R3BP under the radiating and oblate primaries,” Astrophys Space Science, vol. 341, no. 2, pp. 349–358, 2012. View at Publisher · View at Google Scholar
  23. C. Pinyol, “Ejection-collision orbits with the more massive primary in the planar elliptic restricted three body problem,” Celestial Mechanics and Dynamical Astronomy, vol. 61, no. 4, pp. 315–331, 1995. View at Publisher · View at Google Scholar · View at Scopus
  24. D. Şelaru and C. Cucu-Dumitrescu, “Infinitesimal orbits around lagrange points in the elliptic, restricted three-body problem,” Celestial Mechanics and Dynamical Astronomy, vol. 61, no. 4, pp. 333–346, 1995. View at Publisher · View at Google Scholar · View at Scopus
  25. L. Floria, “On an analytical solution 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
  26. K. B. Bhatnagar, U. Gupta, and R. Bhardwaj, “Effect of perturbed potentials on the non-linear stability of libration point L4 in the restricted problem,” Celestial Mechanics & Dynamical Astronomy, vol. 59, no. 4, pp. 345–374, 1994. View at Publisher · View at Google Scholar · View at Scopus
  27. A. P. Markeev, Libration Points in Celestial Mechanics and Cosmodynamics, Nauka, Moscow, Russia, 1978.
  28. A. Narayan and A. Shrivastava, “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
  29. A. Narayan and A. Shrivastava, “Pulsating different curves of zero velocity around triangular equilibrium points in elliptical restricted three-body problem,” Journal of Mathematics, vol. 2013, Article ID 936859, 8 pages, 2013. View at Publisher · View at Google Scholar