Combined effects of perturbations, radiation and oblateness on the periodic orbits in the restricted three-body problem

Abdulraheem, Abdulrazaq; Singh, Jagadish

doi:10.1007/s10509-008-9841-4

Cited by 65 publications

(33 citation statements)

References 5 publications

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“…We choose the unit of time such as to make the gravitation constant equal to unity. Let the coordinates of the infinitesimal mass be (x, y) and those of masses m 1 , m 2 and m 3 are: is the oblateness coefficient of m 2 with R e and R p , as the equatorial and polar radii, respectively, and R is the separation between the primaries. In general, we have 0 < A 2 << 1.…”

Section: Equations Of Motionmentioning

confidence: 99%

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Combined Effects of Radiation and Oblateness on the Existence and Stability of Equilibrium Points in the Perturbed Restricted Four-Body Problem

Singh

2017

J Astrophys Aerospace Technol

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Section: Equations Of Motionmentioning

confidence: 99%

“…In recent time, many researchers have taken into account the effects of radiation and oblateness in their study of restricted threebody problem [2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Combined Effects of Radiation and Oblateness on the Existence and Stability of Equilibrium Points in the Perturbed Restricted Four-Body Problem

Singh

2017

J Astrophys Aerospace Technol

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“…and λ 1,2,3,4 are given by (24). If at time t = 0, initial conditions are X = X 0 , Y = Y 0 ,Ẋ =Ẋ 0 anḋ Y =Ẏ 0 then four arbitrary constant P j and hence, constants Q j are determined from the solution of the four simultaneous linear equations…”

Section: Stability Analysismentioning

confidence: 99%

“…which are sufficiently oblate. In literature, a number of researchers as [20], [21], [22], [23], [24], [25], [13], [26], [14] etc. have studied different aspects of restricted three body problem (RTBP), by taking one or both primary as source of radiation or oblate spheroid or both and have discussed their effects on the motion of infinitesimal mass.…”

Section: Introductionmentioning

confidence: 99%

The Linear Stability of Collinear Equilibrium Points and Resonances

Kishor¹,

Kushvah²

2017

AdAp

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The stability properties, dynamical processes and factors affecting these are very important aspects to describing the behaviour of a dynamical system because these play a significant role in the study of their past evolution. The present article discuss about the existence of collinear equilibrium points, their computation and stability analysis in the Chermnykh-Like problem under the influence of perturbations in the form of radiation pressure, oblateness and a disc. In the presence of the disc, there exists a new collinear equilibrium point in addition to the three points of the classical problem. We examine the linear stability of the collinear equilibrium points with respect to disc's outer radius b instead of mass parameter µ and it is found that all the collinear equilibrium points are unstable except L3 which is stable for b ∈ (1.3312, 1.5275) provided that remaining parameters are fixed. Further, we obtain stability regions and perturbed mass ratio in the case of three main resonances for L3 under appropriate approximations. We analyze the effect of the perturbations numerically and it is observed that they significantly affect the motion of infinitesimal mass. The results are limited up to the regular symmetric disc and the radiation effect of the bigger primary but further it can be extended for more generalized cases.

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“…They have discussed also the spectral stability and their bifurcations with all the possible configurations. AbdulRaheem et al in [1,2] studied the stability and periodic orbits of equilibrium points in the restricted three-body problem under the effect of radiation, oblateness, and perturbing forces. They observed that the perturbing forces affect the stability, period, orientation, and the eccentricities of the long and short periodic 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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Combined effects of perturbations, radiation and oblateness on the periodic orbits in the restricted three-body problem

Cited by 65 publications

References 5 publications

Combined Effects of Radiation and Oblateness on the Existence and Stability of Equilibrium Points in the Perturbed Restricted Four-Body Problem

Combined Effects of Radiation and Oblateness on the Existence and Stability of Equilibrium Points in the Perturbed Restricted Four-Body Problem

The Linear Stability of Collinear Equilibrium Points and Resonances

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

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