Effect of Perturbations in the Coriolis and Centrifugal Forces on the Stability of Equilibrium Points in the Restricted Four-Body Problem

Singh, Jagadish; Vincent, Aguda Ekele

doi:10.1007/s00601-015-1019-3

Cited by 32 publications

(10 citation statements)

References 16 publications

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“…If we take α = 0, the above equations reduce to the equations presented by Singh & Vincent (). For α ≠ 0, the positions of the libration points are same as that of Mittal et al () if we take σ 2 = 1.…”

Section: Libration Pointsmentioning

confidence: 98%

The effect of small perturbations in the Coriolis and centrifugal forces on the existence of libration points in the restricted four‐body problem with variable mass

et al. 2018

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This paper shows the effect of small perturbations in the Coriolis and centrifugal forces in the restricted four‐body problem (R4BP) with variable mass. The existence, location, and stability of the libration points are investigated numerically and graphically under these perturbations. In the present problem, a fourth body with infinitesimal mass is moving under the Newtonian gravitational attraction of three primaries which are moving in a circular orbit around their common center of mass fixed at the origin of the coordinate system. Moreover, according to the solution of Lagrange, the primaries are fixed at the vertices of an equilateral triangle. The fourth body does not affect the motion of three primaries. Furthermore, the fourth body's mass varies according to Jeans' law. The equations of motion of the test particle, i.e., fourth body moving under the gravitational influence of the primaries, are derived. Throughout the paper, we consider the case where the primary body placed along the x‐axis is dominant while the other two small primaries are equal. Further, it is shown that there exist either 8 or 10 libration points out of which 2 or 4 are collinear with the dominating primary and the rest are non‐collinear for fixed values of the parameters. The linear stability of all the libration points under consideration is investigated, and these libration points are found to be unstable. The allowed regions of motion are determined by using the zero‐velocity surface, and the positions of the libration points on the orbital plane are presented. Moreover, by using the Newton–Raphson iterative scheme, we unveiled the effects of the Coriolis and centrifugal forces on the topology of the basins of convergence associated with the libration points.

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Section: Libration Pointsmentioning

confidence: 98%

The effect of small perturbations in the Coriolis and centrifugal forces on the existence of libration points in the restricted four‐body problem with variable mass

et al. 2018

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“…The collinear libration points are always unstable whereas the noncollinear libration points are stable for all mass ratios in the range of linear stability except the three mass ratios. Moreover, many authors have also extended their study to unveil the effect of small perturbations in the Coriolis and centrifugal forces in the frame of the restricted four-body problem as well as in their photogravitational version, where they have discussed the existence and stability of libration points, regions of possible motions, and the basins of convergence connected to the libration points of the system (e.g., [5], [14], [15], [21], [26] ).…”

Section: Introductionmentioning

confidence: 99%

On the perturbed photogravitational restricted five-body problem: the analysis of fractal basins of convergence

Suraj

Aggarwal

Mittal

et al. 2019

Astrophys Space Sci

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In the framework of photogravitational version of the restricted five-body problem, the existence and stability of the in-plane equilibrium points, the possible regions for motion are explored and analysed numerically, under the combined effect of small perturbations in the Coriolis and centrifugal forces. Moreover, the multivariate version of the Newton-Raphson iterative scheme is applied in an attempt to unveil the topology of the basins of convergence linked with the libration points as function of radiation parameters, and the parameters corresponding to Coriolis and centrifugal forces.

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“…Furthermore, the existence and stability of equilibrium points in the restricted four-body problem are studied and presented in a series of research articles: Kumari & Kushvah (2013), Asique et al (2016), Asique et al (2017), Papadouris & Papadakis (2013), and Singh & Vincent (2016). The effect of small perturbations in the Coriolis and centrifugal forces on the stability of libration points in the restricted four-body problem is studied by Singh & Vincent (2015b). They have shown that the perturbations in these forces have a substantial impact on the regions of possible motion of the fourth body.…”

Section: Introductionmentioning

confidence: 99%

Divulging the effect of small perturbations in the Coriolis and centrifugal forces in the photogravitational version of autonomous restricted four‐body problem with oblate primary

et al. 2019

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In the present problem, we have studied the effect of small perturbations in the Coriolis and centrifugal forces on the locations and stability of libration points by taking the smaller primary as radiating oblate spheroid in the restricted four‐body problem. We have supposed that all the primaries are set in an equilateral triangle configuration, moving in circular orbit around their common center of mass. We have observed that the oblateness and radiation of the third primary, and the effect of the small perturbation in centrifugal force have substantial influences on the locations of libration points but the effect of the small perturbation in the Coriolis force has no impact on their locations. However, the stability of the libration points is highly influenced by the effect of the small perturbation in the Coriolis force. Furthermore, it is obtained that the effect of the small perturbation in the centrifugal force has a substantial influence on the regions of possible motion. In addition, we have also discussed how the oblateness and radiation pressure of the third primary, and the small perturbations in the Coriolis and centrifugal forces influence geometry of the basins of convergence by using multivariate version of the Newton–Raphson iterative scheme.

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Effect of Perturbations in the Coriolis and Centrifugal Forces on the Stability of Equilibrium Points in the Restricted Four-Body Problem

Cited by 32 publications

References 16 publications

The effect of small perturbations in the Coriolis and centrifugal forces on the existence of libration points in the restricted four‐body problem with variable mass

The effect of small perturbations in the Coriolis and centrifugal forces on the existence of libration points in the restricted four‐body problem with variable mass

On the perturbed photogravitational restricted five-body problem: the analysis of fractal basins of convergence

Divulging the effect of small perturbations in the Coriolis and centrifugal forces in the photogravitational version of autonomous restricted four‐body problem with oblate primary

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