On the Chaotic Instability of a Nonsliding Liquid-Filled Top with a Small Spheroidal Base via Melnikov-Holmes-Marsden Integrals |
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| Authors: | J L Kuang P A Meehan A Y T Leung |
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| Institution: | (1) Faculty of Science and Engineering, City University of Hong Kong, Hong Kong, P. R. China;(2) Department of Mechanical Engineering, University of Queensland, Brisbane, Qld, 4072, Australia;(3) Faculty of Science and Engineering, City University of Hong Kong, Hong Kong, P. R. China |
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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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| Keywords: | liquid-filled top Melnikov-Holmes-Marsden (MHM) integrals chaos heteroclinic orbits stable and unstable manifolds Poincare map |
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