Reduction the secular solution to periodic solution in the generalized restricted three-body problem

Abouelmagd, Elbaz I.; Awad, Mona; Elzayat, E. M. A.; Abbas, Ibrahim A.

doi:10.1007/s10509-013-1756-z

Cited by 49 publications

(24 citation statements)

References 19 publications

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“…For instance, the existence of libration points, their stability and the periodic orbits in the proximity of these points under the oblateness, triaxialty of the primaries or the effect of photogravitational force or combination of them are studied by Sharma [3], Singh and Ishwar [4], Sharma et al [5,6], Singh and Mohammed [7], Abouelmagd and El-Shaboury [8], Abouelmagd [9], Abouelmagd [10,11], Abouelmagd et al [12], Abouelmagd and Sharaf [13], Abouelmagd et al [14,15], Abouelmagd et al [1,16,17,18], Abouelmagd and Mostafa [19], Abouelmagd et al [20], Abouelmagd and Guirao [21].…”

Section: Introductionmentioning

confidence: 99%

On the libration collinear points in the restricted three – body problem

et al. 2017

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Abstract:In the restricted problem of three bodies when the primaries are triaxial rigid bodies, the necessary and sufficient conditions to find the locations of the three libration collinear points are stated. In addition, the Linear stability of these points is studied for the case of the Euler angles of rotational motion being θ i = 0, ψ i + φ i = π/2, i = 1, 2 accordingly. We underline that the model studied in this paper has special importance in space dynamics when the third body moves in gravitational fields of planetary systems and particularly in a Jupiter model or a problem including an irregular asteroid.

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Section: Introductionmentioning

confidence: 99%

On the libration collinear points in the restricted three – body problem

et al. 2017

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“…Abouelmagd and his research group. See for example, but not limited to, [5,6,7,9,11,12]. Furthermore, there are also some studies focus on this problem under the effect of the aforementioned perturbed forces,that must be taken into a consideration of the reader, see [1,19,23,26].…”

Section: Introductionmentioning

confidence: 99%

Periodic orbits around the collinear libration points

Abouelmagd¹,

Alzahrani²,

Hobiny³

et al. 2016

J. Nonlinear Sci. Appl.

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The locations for the collinear libration points in the framework of the restricted three-body problem are determined when the bigger primary is a triaxial rigid body. The analysis of the periodic motion around these points is performed and given up to second order in the case that the initial state of the motion gives rise to periodic orbits. Moreover, some numerical results for the locations of collinear points are provided and the graphical investigations for the periodic motion are plotted, as well. It is worth mentioning that the collinear libration points and associated periodic orbits are considered the optimal placement to transfer a spacecraft to the nominal periodic orbits or to an associated stable manifold.

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“…The problem is generalized in the sense that the bigger primary is a source of radiation and the smaller one is an oblate spheroid. Moreover, Abouelmagd et al (2014a) found the secular solution around the triangular equilibrium points and reduce it to a periodic solution in the frame work of the generalized restricted three-body problem, in sense that both primaries are oblate and radiating as well as the gravitational potential from a belt. They also showed that the linearized equation of motion of the infinitesimal body around the triangular equilibrium points has a secular solution when the value of the masses ratio is equal to the critical mass value.…”

Section: Introductionmentioning

confidence: 99%