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Libration points in the restricted three-body problem: Euler angles, existence and stability

  • * Corresponding author: Elbaz I. Abouelmagd

    * Corresponding author: Elbaz I. Abouelmagd
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  • The objective of the present paper is to study in an analytical way the existence and the stability of the libration points, in the restricted three-body problem, when the primaries are triaxial rigid bodies in the case of the Euler angles of the rotational motion are equal to $ θ_i = π/2, \, ψ_i = 0, \,\varphi_i = π/2 $, $ i = 1, 2 $. We prove that the locations and the stability of the triangular points change according to the effect of the triaxiality of the primaries. Moreover, the solution of long and short periodic orbits for stable motion is presented.

    Mathematics Subject Classification: Primary: 2010; Secondary: 37N05, 70F15.

    Citation:

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      E. I. Abouelmagd , M. E. Awad , E. M. A. Elzayat  and  I. A. Abbas , Reduction the secular solution to periodic solution in the generalized restricted three-body problem, Astrophys. Space Sci., 350 (2014) , 495-505. 
      E. I. Abouelmagd  and  S. M. El-Shaboury , Periodic orbits under combined effects of oblateness and radiation in the restricted problem of three bodies, Astrophys. Space Sci., 341 (2012) , 331-341. 
      E. I. Abouelmagd , Existence and stability of triangular points in the restricted three-body problem with numerical applications, Astrophys. Space Sci., 342 (2012) , 45-53. 
      E. I. Abouelmagd  and  M. A. Sharaf , The motion around the libration points in the restricted three-body problem with the effect of radiation and oblateness, Astrophys. Space Sci., 344 (2013) , 321-332. 
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      E. I. Abouelmagd, A. Mostafa and J. L. G. Guirao, A first order automated Lie transform International Journal of Bifurcation and Chaos, 25 (2015), 1540026, 10pp. doi: 10.1142/S021812741540026X.
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