Equilibrium positions of a weight on a cable fixed to a dumbbell-shaped space station moving along a circular geocentric orbit

Rodnikov, A. V.

doi:10.1134/s0010952506010060

Cited by 8 publications

(5 citation statements)

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“…-chaos and integrability for planar oscillations of a satellite [18,24], and -periodic solutions and bifurcations (see, e.g., [14,15,19,21,23,26,27]). …”

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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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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“…-chaos and integrability for planar oscillations of a satellite [18,24], and -periodic solutions and bifurcations (see, e.g., [14,15,19,21,23,26,27]). …”

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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“…where u 0 (0) = 1 rp , du 0 (0) dτ = 0 and u 0 (τ + 2π, A) = u 0 (τ, A) with a solution (24) u 0g (τ ) = k h 2 (1 + e 0 cos τ ), being (25) r = h 2 /k 1 + e 0 cos τ .…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Rodnikov [24] studied equilibrium positions of a weight on a cable fixed to a dumbbell-shaped space station moving along a circular geocentric orbit. This model is composed by two masses coupled by a weightless rod, while the cable is weightless and non-stretched.…”

Section: Introductionmentioning

confidence: 99%

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

Abouelmagd

Guirao

Vera

2015

Communications in Nonlinear Science and Numerical Simulation

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Abstract. The aim of the present paper is to study the dynamics of a dumbbell satellite moving in a gravity field generated by an oblate body considering the effect of the zonal harmonic parameter. We prove that the pass trajectory of the mass center of the system is periodic and different from the classical one when the effect of the zonal harmonic parameter is non zero. Moreover, we complete the classical theory showing that the equations of motion in the satellite approximation can be reduced to Beletsky's equation when the zonal harmonic parameter is zero. The main tool for proving these results is the Lindstedt-Poincare's technique.

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“…During the last few decades, the dynamics of many different types of dumbbell satellites have attracted wide attention of many researchers. We refer the reader to classical monographs [4,15,16,18,21,[27][28][29] for the existence of periodic oscillations of dumbbell satellite systems, [3,9,19,30] for the stability of periodic oscillations, [1,7,8,10,14,22,25] for the stability of equilibria points, and [23,24,26] for the dynamics and control. For example, Guirao et al [15] gave sufficient conditions for the existence of periodic motions about the dumbbell satellite's center of mass that are asymptotic to translational motion in an absolute coordinate system by the use of the averaging method.…”

Section: Introductionmentioning

confidence: 99%

Periodic solutions for a dumbbell satellite equation

Liang

Liao

2018

Nonlinear Dyn

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In this paper, we study the existence of at least two geometrically distinct periodic solutions for a differential equation which models the 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. And at least one of such two periodic solutions is unstable. The proof is based on the version of the Poincaré-Birkhoff theorem due to Franks. Moreover, we also study the existence and multiplicity of periodic solutions and subharmonic solutions with winding number.

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Equilibrium positions of a weight on a cable fixed to a dumbbell-shaped space station moving along a circular geocentric orbit

Cited by 8 publications

References 0 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

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

Periodic solutions for a dumbbell satellite equation

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