Periodic orbits under combined effects of oblateness and radiation in the restricted problem of three bodies

Abouelmagd, Elbaz I.; Elshaboury, S. M.

doi:10.1007/s10509-012-1093-7

Cited by 80 publications

(38 citation statements)

References 11 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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“…The existence and stability of the libration points in the restricted problem, when the three bodies are oblate and the primaries are radiating, were studied in [10]. They also provided the periodic orbits around the triangular points.…”

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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“…They also illustrated the periodic orbits, the Poincare surface of section and their stability under the effect of radiation pressure. Abouelmagd in [3][4][5][6] explored the restricted three-body problem with different perturbations. Papadakis in [40,41] studied the 3D symmetric periodic orbits of the circular restricted four-body problem, through their bifurcation from the plane orbits.…”

Section: Introductionmentioning

confidence: 99%

The effect of perturbations on the circular restricted four-body problem with variable masses

Ansari¹,

Alhussain²,

Kellil³

2017

J. Math. Computer Sci.

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This paper presents a new investigation of the circular restricted four body problem under the effect of any variation in coriolis and centrifugal forces. Here, masses of all the bodies vary with time. This has been done by considering one of the primaries as oblate body and all the primaries are placed at the vertices of a triangle. Due to the oblateness, the triangular configuration becomes an isosceles triangular configuration which was an equilateral triangle in the classical case. After evaluating the equations of motion, we have determined the equilibrium points, the surfaces of the motion, the time series and the basins of attraction of the infinitesimal body. We note that, when we increase both the coriolis and centrifugal forces, the curves, surfaces of motion, and the basins of attraction are shrinking except when we fix the centrifugal force and increase the value of coriolis force, the curves are expanding and the equilibrium points are away from the origin. The behavior of the surfaces of motion and the basins of attraction in the last case (fixing the centrifugal force and increasing the value of coriolis force) will be studied next. In all the present study, we found that all the equilibrium points are unstable.

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Periodic orbits under combined effects of oblateness and radiation in the restricted problem of three bodies

Cited by 80 publications

References 11 publications

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

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

Periodic orbits around the collinear libration points

The effect of perturbations on the circular restricted four-body problem with variable masses

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