Collinear equilibrium points of Hill’s problem with radiation and oblateness and their fractal basins of attraction

Douskos, Christos

doi:10.1007/s10509-009-0213-5

Cited by 86 publications

(46 citation statements)

References 15 publications

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“…Plotting the starting points leading to convergence to each complex root of the equation creates an image of the basins of attraction of each root. Douskos (2010) presented such basins for the collinear equilibrium points of a variant of Hill's problem with radiation and oblateness. We note here that |z| has been written in (22) and (23) of that paper instead of the correct √ z 2 .…”

Section: The New Equilibrium Points On the Z-axismentioning

confidence: 99%

On Sitnikov-like motions generating new kinds of 3D periodic orbits in the R3BP with prolate primaries

Douskos

Kalantonis

Markellos

et al. 2011

Astrophys Space Sci

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The existence of new equilibrium points is established in the restricted three-body problem with equal prolate primaries. These are located on the Z-axis above and below the inner Eulerian equilibrium point L 1 and give rise to a new type of straight-line periodic oscillations, different from the well known Sitnikov motions. Using the stability properties of these oscillations, bifurcation points are found at which new types of families of 3D periodic orbits branch out of the Z-axis consisting of orbits located entirely above or below the orbital plane of the primaries. Several of the bifurcating families are continued numerically and typical member orbits are illustrated.

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Section: The New Equilibrium Points On the Z-axismentioning

confidence: 99%

On Sitnikov-like motions generating new kinds of 3D periodic orbits in the R3BP with prolate primaries

Douskos

Kalantonis

Markellos

et al. 2011

Astrophys Space Sci

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“…We call the set of the initial points that lead to the discrete equilibrium points or the dynamically equivalent points, "basins of attraction" (or "basins of convergence", or "attracting domains"). These regions have been studied in the past in some problems of Celestial Dynamics, such as the restricted three-body problem [3], the ring problem of (N + 1)-bodies [4][5][6][7][8], and the Hill's problem with radiation and oblateness [9]. The technique to find these regions is based on a double scanning process of the Oxy plane.…”

Section: Basins Of Attractionmentioning

confidence: 99%

Basins of Attraction in the Copenhagen Problem Where the Primaries Are Magnetic Dipoles

Kalvouridis¹,

Gousidou-Koutita²

2012

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We deal with the Copenhagen problem where the two big bodies of equal masses are also magnetic dipoles and we study some aspects of the dynamics of a charged particle which moves in the electromagnetic field produced by the primaries. We investigate the equilibrium positions of the particle and their parametric variations, as well as the basins of attraction for various numerical methods and various values of the parameter λ.

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“…In this topic, many scientists have studied and determined the basins of attraction. Among them, we can cite for example the works of Douskos [22], Kumari et al in [31], de Assis and Terra in [21], Matthies et al in [35], Paricio in [26], Asique et al in [12], Zotos in [62][63][64][65], etc.…”

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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Collinear equilibrium points of Hill’s problem with radiation and oblateness and their fractal basins of attraction

Cited by 86 publications

References 15 publications

On Sitnikov-like motions generating new kinds of 3D periodic orbits in the R3BP with prolate primaries

On Sitnikov-like motions generating new kinds of 3D periodic orbits in the R3BP with prolate primaries

Basins of Attraction in the Copenhagen Problem Where the Primaries Are Magnetic Dipoles

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

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