On the chaotic instability of a nonsliding liquid-filled top with a small spheroidal base via Melnikov-Holmes-Marsden integrals

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

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

Detail(s)

Original languageEnglish
Pages (from-to)113-147
Journal / PublicationNonlinear Dynamics
Volume46
Issue number1-2
Publication statusPublished - Oct 2006

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. © Springer 2006.

Research Area(s)

  • Chaos, Heteroclinic orbits, Liquid-filled top, Melnikov-Holmes-Marsden (MHM) integrals, Poincare map, Stable and unstable manifolds

Citation Format(s)

On the chaotic instability of a nonsliding liquid-filled top with a small spheroidal base via Melnikov-Holmes-Marsden integrals. / Kuang, J. L.; Meehan, P. A.; Leung, A. Y T.
In: Nonlinear Dynamics, Vol. 46, No. 1-2, 10.2006, p. 113-147.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review