Effect of Oblateness, Radiation and a Circular Cluster of Material Points on the Stability of Equilibrium Points in the Restricted Four-Body Problem

Falaye, Babatunde J.

doi:10.1007/s00601-014-0922-3

Cited by 8 publications

(4 citation statements)

References 7 publications

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“…Recently, the oblateness coefficient [2], radiation pressure force [3], PoyntingRobertson drag [4], and other perturbing effects have been taken into consideration during the mathematical modeling for the RFBP. However, mathematically, based on the equation of motion, we still can classify these models into two types, the autonomous type and the non-autonomous type.…”

Section: Introductionmentioning

confidence: 99%

Parametric stability analysis for planar bicircular restricted four-body problem

Qian

Yang

et al. 2018

Astrodyn

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Section: Introductionmentioning

confidence: 99%

Parametric stability analysis for planar bicircular restricted four-body problem

Qian

Yang

et al. 2018

Astrodyn

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“…And in the third and last case, he has taken two of the primaries as oblate body and all the three primaries are source of radiation pressure. Falaye [16] investigated the stability of the equilibrium points in the restricted four-body problem under the effects of oblateness and solar radiation pressure and found that these equilibrium points are unstable. Arribas et al [22] investigated the equilibria of the symmetric collinear restricted four-body problem where primaries are placed in a collinear central configuration with both masses and radiation pressure of the peripheral bodies are equal.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the effect of albedo and oblateness on the circular restricted four variable bodies problem

Ansari

2017

Applied Mathematics and Nonlinear Sciences

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The present paper investigates the motion of the variable infinitesimal body in circular restricted four variable bodies problem. We have constructed the equations of motion of the infinitesimal variable mass under the effect of source of radiation pressure due to which albedo effects are produced by another two primaries and one primary is considered as an oblate body which is placed at the triangular equilibrium point of the classical restricted three-body problem and also the variation of Jacobi Integral constant has been determined. We have studied numerically the equilibrium points, Poincaré surface of sections and basins of attraction in five cases (i. Third primary is placed at one of the triangular equilibrium points of the classical restricted three-body problem, ii. Variation of masses, iii. Solar radiation pressure, iv. Albedo effect, v. Oblateness effect.) by using Mathematica software. Finally, we have examined the stability of the equilibrium points and found that all the equilibrium points are unstable.

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“…They showed that the presence of oblateness coefficient and various values of Jacobi constant expanded the stability regions of the equilibrium points. Falaye in [23] investigated the stability of equilibrium points in the circular restricted four-body problem with the effect of oblateness, radiation, and a circular cluster of material points. After considering two equal masses, he obtained that all the equilibrium points are unstable.…”

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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Effect of Oblateness, Radiation and a Circular Cluster of Material Points on the Stability of Equilibrium Points in the Restricted Four-Body Problem

Cited by 8 publications

References 7 publications

Parametric stability analysis for planar bicircular restricted four-body problem

Parametric stability analysis for planar bicircular restricted four-body problem

Investigation of the effect of albedo and oblateness on the circular restricted four variable bodies problem

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

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