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

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Abstract

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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Acknowledgments

The first author specially acknowledges the valuable support provided by Centro Universitario de la Defensa en la Academia General del Aire de San Javier (Murcia, Spain). Both the second and the third authors acknowledge the support of MICINN/FEDER, Grant No. MTM2011-22587, and Fundación Séneca de la Región de Murcia, Grant No. 19219/PI/14.

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Authors and Affiliations

  1. University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, 30720, Santiago de la Ribera, Murcia, Spain

    M. Fernández-Martínez & J. A. Vera

  2. Department of Mathematics, University of Castilla-La Mancha, 16071, Cuenca, Spain

    Miguel A. López

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  1. M. Fernández-Martínez
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  2. Miguel A. López
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  3. J. A. Vera
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Correspondence to M. Fernández-Martínez.

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All the authors of this paper do declare that there are no conflicts of interest associated with this publication.

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Fernández-Martínez, M., López, M.A. & Vera, J.A. On the dynamics of planar oscillations for a dumbbell satellite in \(\varvec{J_{2}}\) problem. Nonlinear Dyn 84, 143–151 (2016). https://doi.org/10.1007/s11071-015-2308-6

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  • DOI: https://doi.org/10.1007/s11071-015-2308-6

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