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Chaotic motion of an asymmetric gyrostat in the magnetic field of the earth

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Summary

The attitude motion of an asymmetric magnetic gyrostat satellite in a circular orbit subjected to both gravitational and magnetic forces of the earth is investigated by using the version of Melnikov's method developed for a two-degree of freedom Hamiltonian system withS 1 symmetry. For this purpose Deptrit's canonical variables are introduced to establish the Hamiltonian structure for this problem. It is found that the motion is chaotic in the sense of Smale's horseshoe under certain conditions. The effects of the magnetic moment of the gyrostat and the speed of the rotor in the gyrostat on the global motion are also studied by numerical computation. It is shown that as the magnetic moment of the gyrostat increases, the chaotic area in the Poincaré map will enlarge; as the rotor speed increases, a chaotic motion will turn into a regular motion.

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Author notes

  1. G. Cheng & Y. Z. Liu

    Present address: Department of Engineering Mechanics, Shanghai Jiao Tong University, 200030, Shanghai, P. R. China

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    1. G. Cheng
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    2. Y. Z. Liu
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    Cheng, G., Liu, Y.Z. Chaotic motion of an asymmetric gyrostat in the magnetic field of the earth. Acta Mechanica 141, 125–134 (2000). https://doi.org/10.1007/BF01268672

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    • DOI: https://doi.org/10.1007/BF01268672

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