Scenarios of transition to chaos in the nonholonomic model of a Chaplygin top

I. R. Sataev ; A. O. Kazakov

Russian journal of nonlinear dynamics, Tome 12 (2016) no. 2, pp. 235-250.

Résumé

We study the dynamics in the Suslov problem which describes the motion of a heavy rigid body with a fixed point subject to a nonholonomic constraint, which is expressed by the condition that the projection of angular velocity onto the body-fixed axis is equal to zero. Depending on the system parameters, we find cases of regular (in particular, integrable) motions and, using a new method for constructing charts of Lyapunov exponents, detect different types of chaotic behavior such as conservative chaos, strange attractors and mixed dynamics, which are typical of reversible systems. In the paper we also examine the phenomenon of reversal, which was observed previously in the motion of Celtic stones.

Détail

Keywords: nonholonomic model, Chaplygin top, Afraimovich – Shilnikov torus-breakdown, cascade of period-doubling bifurcations, scenario of period doublings of tori, figure-eight attractor.

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