publication . Article . 2016

Existence and Stability of the Libration Points in the Circular Restricted Three Body Problem with Variable Masses

Abdullah, A; Alam, Mehtab;
Open Access English
  • Published: 21 Oct 2016 Journal: International Annals of Science (issn: 2456-7132, eissn: 2456-7132, Copyright policy)
  • Publisher: AIJR Publisher
Abstract
We have investigated the existence and stability of the libration points in the circular restricted three body problem with the variation of all the masses (primaries and infinitesimal body) with time. We have used the Meshcherskii transformation for finding the autonomized equations of motion and found at most nine libration points. We have drawn the zero velocity curves and Poincare surface of sections for the different values of parameter k. Finally, we have checked the stability and found that all the libration points are unstable.
Subjects
arXiv: Astrophysics::Earth and Planetary Astrophysics
free text keywords: Variable mass, Autonomized system, Zero velocity curves, Libration points, Poincare surface of sections, Stability
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17 references, page 1 of 2

[1] [2] [3] [4] [5] [6] [7] J. H. Jeans," Astronomy and Cosmogony," Cambridge University Press, Cambridge, 1928.

Meshcherskii, I.V.: Studies on the Mechanics of Bodies of Variable Mass. GITTL, Moscow, 1949.

I. V. Meshcherskii, "Works on the Mechanics of Bodies of Variable Mass," GITTL, Moscow, 1952.

V. Szebehely, "Theory of Orbits," Academic Press, New York, 1967.

K. B. Bhatnagar, "Periodic orbits of collision in the restricted problem of three bodies in a Three-dimensional coordinate system," Indian Journal of Pure and Applied Mathematics, India, vol 3, no 1, pp 101 -117, 1972.

J. F. L. Simmons, et.al., "The restricted three body problem with radiation pressure,"Celestial Mechanics, 35, 145, 1985.

J. Singh, "Effect of perturbations on the location of equilibrium points in the restricted problem of three bodies with variable mass," Celest. Mech, vol 32, no 4, pp 297-305, 1984.

[8] J. Singh, B. Ishwar, "Effect of perturbations on the stability of triangular points in the restricted problem of three bodies with variable mass," Celest. Mech. Vol 35, pp 201-207, 1985.

[9] J. Singh, "Photogravitational restricted three body problems with variable mass," Indian J. of Pure and Applied Math, vol 32, no 2, pp 335-341, 2003.

[10] J. Singh, "Stability of photogravitational restricted three body problem with variable mass," Astrophysics and Space Sci. vol 326, no 2, pp 305-314, 2010.

[11] M. J. Zhang, C. Y. Zhao, Y. Q. Xiong, "On the triangular libration points in photo-gravitational restricted three body problem with variable mass," Astrophysics Space Sci. vol 337, pp 107-113, 2012.

[12] E. I. Abouelmagd, A. Mostafa, "Out of plane equilibrium points locations and the forbidden movement regions in the restricted three-body problem with variable mass," Astrophysics Space Sci. 357, 58, 2015. [OpenAIRE]

[13] E. I. Abouelmagd, et.al., "The effect of oblateness in the perturbed restricted three body problem," Meccanica, vol 48, pp 2479-2490, 2013. [OpenAIRE]

[14] K. Shalini, et.al., "Existence and Stability of the libration point L4 in the R3BP, when the smaller primary is a heterogeneous axis symmetric body with N layers," J. Appl. Environ. Biol. Sci., vol 6, no 1, pp 249-257, 2016.

[15] Abdullah, "Stability of the equilibrium points in the circular restricted four body problem with oblate primary and variable mass," International Journal of Advanced Astronomy, vol 4, no 1, pp 14-19, 2016.

17 references, page 1 of 2
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