Regular and chaotic attractors in the nonholonomic model of Chapygin’s ball

Alexey V. Borisov ; Alexey O. Kazakov ; Igor R. Sataev

Russian journal of nonlinear dynamics, Tome 10 (2014) no. 3, pp. 361-380.

Résumé

We study both analytically and numerically the dynamics of an inhomogeneous ball on a rough horizontal plane under the infuence of gravity. A nonholonomic constraint of zero velocity at the point of contact of the ball with the plane is imposed. In the case of an arbitrary displacement of the center of mass of the ball, the system is nonintegrable without the property of phase volume conservation. We show that at certain parameter values the unbalanced ball exhibits the effect of reversal (the direction of the ball rotation reverses). Charts of dynamical regimes on the parameter plane are presented. The system under consideration exhibits diverse chaotic dynamics, in particular, the figure-eight chaotic attractor, which is a special type of pseudohyperbolic chaos.

Détail

Keywords: Chaplygin’s top, rolling without slipping, reversibility, involution, integrability, reverse, chart of dynamical regimes, strange attractor.

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