Dynamics of a dumbbell satellite under the zonal harmonic effect of an oblate body

Abouelmagd, Elbaz I.; Guirao, Juan Luis García; Vera, Juan A.

doi:10.1016/j.cnsns.2014.06.033

Cited by 40 publications

(21 citation statements)

References 19 publications

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“…First of all, recall that the planar oscillations for such a system are described through the upcoming secondorder differential equation, first appeared in [1]:…”

Section: Introductionmentioning

confidence: 99%

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On the dynamics of planar oscillations for a dumbbell satellite in $$\varvec{J_{2}}$$ J 2 problem

2015

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In the present paper, we study regular and chaotic dynamics from planar oscillations of a dumbbell satellite under the influence of the gravity field generated by an oblate body, considering the effect of the zonal harmonic parameter J 2 . We theoretically show the existence of chaotic oscillations provided that the eccentricity becomes arbitrarily small, and the parameter J 2 is of the same order of magnitude as the eccentricity. This is carried out by applying the so-called Melnikov method. Finally, for arbitrarily chosen values for the parameters involved in such a problem, we study the transition from regular to chaotic oscillations for a dumbbell satellite via the analysis of chaotic maps and Poincaré surfaces of section, respectively.

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“…First of all, recall that the planar oscillations for such a system are described through the upcoming secondorder differential equation, first appeared in [1]:…”

Section: Introductionmentioning

confidence: 99%

“…To deal with, both Lagrangian and Hamiltonian formulations for such dynamics become the main tools considered in the formulation of that problem [1].…”

Section: Introductionmentioning

confidence: 99%

On the dynamics of planar oscillations for a dumbbell satellite in $$\varvec{J_{2}}$$ J 2 problem

2015

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“…They show the existence of chaotic orbits in their system via the Melnikov method, and study the transition between regular to chaotic orbits numerically through the use of Poincaré maps. The model studied was originally derived in Abouelmagd et al (2015), and while interesting, is fairly restrictive on the geometry and mass distribution in the rigid body, while further assuming that the satellite body is of much smaller mass to the oblate body it orbits.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Dynamics in the Planar Gravitational Many-Body Problem with Rigid Body Rotations

Kwiecinski

Kovács

Krause

et al. 2018

Int. J. Bifurcation Chaos

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The discovery of Pluto's small moons in the last decade brought attention to the dynamics of the dwarf planet's satellites. With such systems in mind, we study a planar N -body system in which all the bodies are point masses, except for a single rigid body. We then present a reduced model consisting of a planar N -body problem with the rigid body treated as a 1D continuum (i.e. the body is treated as a rod with an arbitrary mass distribution). Such a model provides a good approximation to highly asymmetric geometries, such as the recently observed interstellar asteroid 'Oumuamua, but is also amenable to analysis. We analytically demonstrate the existence of homoclinic chaos in the case where one of the orbits is nearly circular by way of the Melnikov method, and give numerical evidence for chaos when the orbits are more complicated. We show that the extent of chaos in parameter space is strongly tied to the deviations from a purely circular orbit. These results suggest that chaos is ubiquitous in many-body problems when one or more of the rigid bodies exhibits non-spherical and highly asymmetric geometries. The excitation of chaotic rotations does not appear to require tidal dissipation, obliquity variation, or orbital resonance. Such dynamics give a possible explanation for routes to chaotic dynamics observed in N -body systems such as the Pluto system where some of the bodies are highly non-spherical.

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“…In particular, when g = 0, y 3,4 = 0, the center of mass coincides with the origin of the coordinate system and the Ox−axis remains the axis of symmetry. Therefore, we obtain a symmetric configuration where two equal masses m 3,4 are placed opposite to each other and are symmetrical about the Ox-axis. In the present scenario, it is assumed that (m 2 ≥ m 1 ), whereas (m 1 ≥ m 2 ) is the mirror configuration.…”

Section: Properties Of the Dynamical Systemmentioning

confidence: 99%

On the Newton–Raphson basins of convergence associated with the libration points in the axisymmetric restricted five-body problem: The concave configuration

Suraj

Sachan

Zotos

et al. 2019

International Journal of Non-Linear Mechanics

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The axisymmetric five-body problem with the concave configuration has been studied numerically to reveal the basins of convergence, by exploring the Newton-Raphson iterative scheme, corresponding to the coplanar libration points (which act as attractors). In addition, four primaries are set in axisymmetric central configurations introduced byÉrdi and Czirják [13] and the motion is governed by mutual gravitational attraction only. The evolution of the positions of libration points is illustrated, as a function of the value of angle parameters. A systematic and rigorous investigation is performed in an effort to unveil how the angle parameters affect the topology of the basins of convergence. In addition, the relation of the domain of basins of convergence with required number of iterations and the corresponding probability distributions are illustrated.

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Dynamics of a dumbbell satellite under the zonal harmonic effect of an oblate body

Cited by 40 publications

References 19 publications

On the dynamics of planar oscillations for a dumbbell satellite in $$\varvec{J_{2}}$$ J 2 problem

On the dynamics of planar oscillations for a dumbbell satellite in $$\varvec{J_{2}}$$ J 2 problem

Chaotic Dynamics in the Planar Gravitational Many-Body Problem with Rigid Body Rotations

On the Newton–Raphson basins of convergence associated with the libration points in the axisymmetric restricted five-body problem: The concave configuration

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