Perturbed Hill's problem with variable mass

Bouaziz, Ferdaous; Ansari, Abdullah A.

doi:10.1002/asna.202113870

Cited by 19 publications

(9 citation statements)

References 32 publications

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“…Therefore it is sufficient to show the stability of L 1 and L 3 . Following the procedure given by [15], we can write the characteristic polynomial of the Eq. (2.6) in the planar case as:…”

Section: Stability Statesmentioning

confidence: 99%

Hill restricted four-body problem with variable mass

Ansari¹

2022

GJOM

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The presentation of the paper consists the extended version of the Hill restricted three-body problem i.e. the Hill restricted four-body problem where the mass of the fourth smallest body is supposed to variable with time and also suppose that the other three massive bodies are remain fixed at the apices of an equilateral triangle. After shifting the origin and using the various transformations, we determine the equations of motion and quasi-Jacobi integral for this model. The properties like the equilibrium points and stability are performed analytically.

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“…Therefore it is sufficient to show the stability of L 1 and L 3 . Following the procedure given by [15], we can write the characteristic polynomial of the Eq. (2.6) in the planar case as:…”

Section: Stability Statesmentioning

confidence: 99%

Hill restricted four-body problem with variable mass

Ansari¹

2022

GJOM

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“…Utilizing the method adopted by [29], we shall examine numerically the stability states for the equilibrium points. Since L 1, 2 and L 3, 4 are symmetrical about η-axis as well as L 5 and L 6 are symmetrical about ξ-axis.…”

Section: Stability Statesmentioning

confidence: 99%

Effects of Mass Variation in the Collinear Perturbed Moulton-Copenhagen Configuration

Ansari

Yadav²

2022

Int. J. Anal. Appl.

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The main idea of this paper is to investigate the motion properties of the smallest body under the gravitational forces of the three collinear spherical primaries. Here we place the three primaries on the same line where the masses of two primary bodies are taken equal and third primary body is having the solar radiation effect. The effects of Coriolis and centrifugal forces on the system is considered. Therefore this system is recognized as collinear perturbed Moulton-Copenhagen configuration. After determining the equations of motion and quasi-Jacobi integral, we numerically illustrate the locations of equilibrium points (in-plane and out-of-plane), regions of motion, Poincaré surfaces of section, basins of attraction and periodic orbits. And then the examination of stability for the equilibrium points lie either in-plane or out-of-plane are examined.

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“…The locations of equilibrium points were evaluated both analytically and numerically, as well as the stability of these points. In [17], Bouaziz and Ansari studied numerically some dynamical properties of motion of infinitesimal body having a variable mass in the Hill problem. They obtained that there is an effective and perceptible variation of basins of attraction.…”

Section: Introductionmentioning

confidence: 99%

Oblateness and mass variation effects on the Hill R4BP Abdullah

Ansari

Sahdev

Alebraheem

et al. 2023

Preprint

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The oblateness and mass variation effects are studied in the circular Hill restricted 4-body problem (R4BP). Here we assume two bodies as oblate in shape and third one as spherical in shape, these three bodies are at the vertices of a triangle. The 4th infinitesimal body varies its mass and moving under the perturbed gravitational forces in the plane of primaries. With these perturbations, we evaluate the equations of motion and quasi-jacobian integral using specific scales and transformations. Finally, the numerical presentations are given such as stationary points, regions of motion, surfaces of section, periodic orbits and basins of convergence. 2010 MSC: 00-01, 99-00

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Perturbed Hill's problem with variable mass

Cited by 19 publications

References 32 publications

Hill restricted four-body problem with variable mass

Hill restricted four-body problem with variable mass

Effects of Mass Variation in the Collinear Perturbed Moulton-Copenhagen Configuration

Oblateness and mass variation effects on the Hill R4BP Abdullah

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