Table of Contents Author Guidelines Submit a Manuscript
Advances in Astronomy
Volume 2016, Article ID 9897681, 11 pages
http://dx.doi.org/10.1155/2016/9897681
Research Article

Planar Central Configurations of Symmetric Five-Body Problems with Two Pairs of Equal Masses

1Department of Mathematics, University of Ha’il, P.O. Box 2440, Ha’il 81451, Saudi Arabia
2Abu Dhabi Men’s College, Higher Colleges of Technology, P.O. Box 25035, Abu Dhabi, UAE
3Applied Mathematics and Sciences, Khalifa University of Science Technology and Research, P.O. Box 127788, Abu Dhabi, UAE

Received 2 November 2015; Revised 11 January 2016; Accepted 18 January 2016

Academic Editor: Elmetwally Elabbasy

Copyright © 2016 Muhammad Shoaib et al. 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. M. Gidea and J. Llibre, “Symmetric planar central configurations of five bodies: euler plus two,” Celestial Mechanics and Dynamical Astronomy, vol. 106, no. 1, pp. 89–107, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. C. Deng and S. Zhang, “Planar symmetric concave central configurations in Newtonian four-body problems,” Journal of Geometry and Physics, vol. 83, pp. 43–52, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. W. D. MacMillan and W. Bartky, “Permanent configurations in the problem of four bodies,” Transactions of the American Mathematical Society, vol. 34, no. 4, pp. 838–875, 1932. View at Publisher · View at Google Scholar · View at MathSciNet
  4. J. Llibre and L. F. Mello, “New central configurations for the planar 5-body problem,” Celestial Mechanics & Dynamical Astronomy, vol. 100, no. 2, pp. 141–149, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. C. Simo, “Relative equilibrium solutions in the four-body problem,” Celestial Mechanics, vol. 18, no. 2, pp. 165–184, 1978. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. T.-L. Lee and M. Santoprete, “Central configurations of the five-body problem with equal masses,” Celestial Mechanics and Dynamical Astronomy, vol. 104, no. 4, pp. 369–381, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. M. Shoaib, A. Sivasankaran, and A. Kashif, “Central configurations in the collinear 5-body problem,” Turkish Journal of Mathematics, vol. 38, no. 3, pp. 576–585, 2014. View at Publisher · View at Google Scholar · View at Scopus
  8. X. Su and C. Deng, “Two classes of stacked central configurations for the spatial 2n+1-body problem: nested regular polyhedra plus one,” Journal of Geometry and Physics, vol. 76, pp. 1–9, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. T. Ouyang and Z. Xie, “Collinear central configuration in four-body problem,” Celestial Mechanics and Dynamical Astronomy, vol. 93, no. 1, pp. 147–166, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. S. Smale, “Mathematical problems for the next century,” The Mathematical Intelligencer, vol. 20, no. 2, pp. 7–15, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. Hampton and R. Moeckel, “Finiteness of relative equilibria of the four-body problem,” Inventiones Mathematicae, vol. 163, no. 2, pp. 289–312, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. A. Albouy and V. Kaloshin, “Finiteness of central configurations of five bodies in the plane,” Annals of Mathematics, vol. 176, no. 1, pp. 535–588, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. M. Hampton and A. Jensen, “Finiteness of spatial central configurations in the five-body problem,” Celestial Mechanics and Dynamical Astronomy, vol. 109, no. 4, pp. 321–332, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. A. Albouy and R. Moeckel, “The inverse problem for collinear central configurations,” Celestial Mechanics and Dynamical Astronomy, vol. 77, no. 2, pp. 77–91, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  15. Z. Xie, “Inverse problem of central configurations and singular curve in the collinear 4-body problem,” Celestial Mechanics and Dynamical Astronomy, vol. 107, no. 3, pp. 353–376, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. M. Hampton, “Stacked central configurations: new examples in the planar five-body problem,” Nonlinearity, vol. 18, no. 5, pp. 2299–2304, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. M. Shoaib, I. Faye, and A. Sivasankaran, “Some special solutions of the rhomboidal five-body problem,” in Proceedings of the International Conference on Fundamental and Applied Sciences (ICFAS '12), vol. 1482 of AIP Conference Proceedings, pp. 496–501, AIP Publishing, Kuala Lumpur, Malaysia, June 2012. View at Publisher · View at Google Scholar
  18. Z. Xie, “Isosceles trapezoid central configurations of the Newtonian four-body problem,” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 142, no. 3, pp. 665–672, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. M. Shoaib, “Regions of central configurations in a symmetric 4 + 1-body problem,” Advances in Astronomy, vol. 2015, Article ID 284189, 1 pages, 2015. View at Publisher · View at Google Scholar