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On the Chaotic Instability of a Nonsliding Liquid-Filled Top with a Small Spheroidal Base via Melnikov-Holmes-Marsden Integrals

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Abstract

Chaotic orientations of a top containing a fluid filled cavity are investigated analytically and numerically under small perturbations. The top spins and rolls in nonsliding contact with a rough horizontal plane and the fluid in the ellipsoidal shaped cavity is considered to be ideal and describable by finite degrees of freedom. A Hamiltonian structure is established to facilitate the application of Melnikov-Holmes-Marsden (MHM) integrals. In particular, chaotic motion of the liquid-filled top is identified to be arisen from the transversal intersections between the stable and unstable manifolds of an approximated, disturbed flow of the liquid-filled top via the MHM integrals. The developed analytical criteria are crosschecked with numerical simulations via the 4th Runge-Kutta algorithms with adaptive time steps.

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Authors and Affiliations

  1. Faculty of Science and Engineering, City University of Hong Kong, Hong Kong, P. R. China

    J. L. Kuang

  2. Department of Mechanical Engineering, University of Queensland, Brisbane, Qld, 4072, Australia

    P. A. Meehan

  3. Faculty of Science and Engineering, City University of Hong Kong, Hong Kong, P. R. China

    A. Y. T. Leung

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  1. J. L. Kuang
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  2. P. A. Meehan
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  3. A. Y. T. Leung
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Correspondence to J. L. Kuang.

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Kuang, J.L., Meehan, P.A. & Leung, A.Y.T. On the Chaotic Instability of a Nonsliding Liquid-Filled Top with a Small Spheroidal Base via Melnikov-Holmes-Marsden Integrals. Nonlinear Dyn 46, 113–147 (2006). https://doi.org/10.1007/s11071-006-9019-y

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  • DOI: https://doi.org/10.1007/s11071-006-9019-y

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