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

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. (c) 2006 Elsevier Ltd. All rights reserved.

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

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.

Plaid motion rivalry: Correlates with binocular rivalry and positive mood state

Recently Hupe and Rubin (2003, Vision Research 43 531 - 548) re-introduced the plaid as a form of perceptual rivalry by using two sets of drifting gratings behind a circular aperture to produce quasi-regular perceptual alternations between a coherent moving plaid of diamond-shaped intersections and the two sets of component 'sliding' gratings. We call this phenomenon plaid motion rivalry (PMR), and have compared its temporal dynamics with those of binocular rivalry in a sample of subjects covering a wide range of perceptual alternation rates. In support of the proposal that all rivalries may be mediated by a common switching mechanism, we found a high correlation between alternation rates induced by PMR and binocular rivalry. In keeping with a link discovered between the phase of rivalry and mood, we also found a link between PMR and an individual's mood state that is consistent with suggestions that each opposing phase of rivalry is associated with one or the other hemisphere, with the 'diamonds' phase of PMR linked with the 'positive' left hemisphere.