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On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral

J. L. Kuang, P. A. Meehan, A. Y T Leung

    Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

    Abstract

    The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations. © 2006 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    Pages (from-to)475-490
    JournalInternational Journal of Non-Linear Mechanics
    Volume41
    Issue number4
    DOIs
    Publication statusPublished - May 2006

    Research Keywords

    • Chaotic oscillations
    • First integrals
    • Homoclinic/heteroclinic orbits
    • Liquid-filled gyrostats
    • The Melnikov-Holmes-Marsden integral

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