Chaotic Motion of an Ellipsoidal Satellite. I.

Khan, Ayub; Sharma, Richa; Saha, L. M.

doi:10.1086/300532

Cited by 16 publications

(6 citation statements)

References 14 publications

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“…Beletskii, Pivovarov & Starostin (1996) considered a number of models, including the gravitational, magnetic and tidal moments as well as rotation in gravitational field of two centers. A model with a tidal torque was examined analytically using Melnikov's integrals and assymptotic methods (Khan, Sharma & Saha 1998). The stability of resonances with application to the Solar System satellites was inferred based on a series expansion of the terms in the equation of rotational motion (Celletti & Chierchia 1998.…”

Section: Introductionmentioning

confidence: 99%

Influence of a second satellite on the rotational dynamics of an oblate moon

Tarnopolski¹

2016

Celest Mech Dyn Astr

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The gravitational influence of a second satellite on the rotation of an oblate moon is numerically examined. A simplified model, assuming the axis of rotation perpendicular to the (Keplerian) orbit plane, is derived. The differences between the two models, i.e. in the absence and presence of the second satellite, are investigated via bifurcation diagrams and by evolving compact sets of initial conditions in the phase space. It turns out that the presence of another satellite causes some trajectories, that were regular in its absence, to become chaotic. Moreover, the highly structured picture revealed by the bifurcation diagrams in dependence on the eccentricity of the oblate body's orbit is destroyed when the gravitational influence is included, and the periodicities and critical curves are destroyed as well. For demonstrative purposes, focus is laid on parameters of the Saturn-Titan-Hyperion system, and on oblate satellites on low-eccentric orbits, i.e. e ≈ 0.005.

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Section: Introductionmentioning

confidence: 99%

Influence of a second satellite on the rotational dynamics of an oblate moon

Tarnopolski¹

2016

Celest Mech Dyn Astr

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“…We neglect the tidal torque in the derivation of Eqs. (1) and (2), which can be estimated as shown below [7], [12]:…”

Section: Revolving Scheme For Solving Cascades Of Abel Equations For mentioning

confidence: 99%

Revolving scheme for solving a cascade of Abel equations in dynamics of planar satellite rotation

Ershkov

2017

Theoretical and Applied Mechanics Letters

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The main objective for this research was the analytical exploration of the dynamics of planar satellite rotation during the motion of an elliptical orbit around a planet.First, we revisit the results of J. Wisdom et al. (1984), in which, by the elegant change of variables (considering the true anomaly f as the independent variable), the governing equation of satellite rotation takes the form of an Abel ODE of the second kind, a sort of generalization of the Riccati ODE. We note that due to the special character of solutions of a Riccati-type ODE, there exists the possibility of sudden jumping in the magnitude of the solution at some moment of time.In the physical sense, this jumping of the Riccati-type solutions of the governing ODE could be associated with the effect of sudden acceleration/deceleration in the satellite rotation around the chosen principle axis at a definite moment of parametric time. This means that there exists not only a chaotic satellite rotation regime (as per the results of J. Wisdom et al. (1984)), but a kind of gradient catastrophe (Arnold 1992) could occur during the satellite rotation process. We especially note that if a gradient catastrophe could occur, this does not mean that it must occur: such a possibility depends on the initial conditions.In addition, we obtained asymptotical solutions that manifest a quasi-periodic character even with the strong simplifying assumptions e → 0, p = 1, which reduce the governing equation of J. Wisdom et al. (1984) to a kind of Beletskii's equation.

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“…Eq. ( 1)], l = a(1 − e 2 ) (Khan et al 1998), one can transform Eq. ( 3) so that f is the independent variable [the famous Beletskii (1966)…”

Section: Equations Of Motionmentioning

confidence: 99%

Rotation of an oblate satellite: Chaos control

Tarnopolski

2017

A&A

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Aims. This paper investigates the chaotic rotation of an oblate satellite in the context of chaos control. Methods. A model of planar oscillations, described with the Beletskii equation, was investigated. The Hamiltonian formalism was utilized to employ a control method for suppressing chaos.Results. An additive control term, which is an order of magnitude smaller than the potential, is constructed. This allows not only for significantly diminished diffusion of the trajectory in the phase space, but turns the purely chaotic motion into strictly periodic motion.

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Chaotic Motion of an Ellipsoidal Satellite. I.

Cited by 16 publications

References 14 publications

Influence of a second satellite on the rotational dynamics of an oblate moon

Influence of a second satellite on the rotational dynamics of an oblate moon

Revolving scheme for solving a cascade of Abel equations in dynamics of planar satellite rotation

Rotation of an oblate satellite: Chaos control

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