Dynamics of the Chaplygin sleigh on a cylinder

I. A. Bizyaev ; A. V. Borisov ; I. S. Mamaev

Russian journal of nonlinear dynamics, Tome 12 (2016) no. 4, pp. 675-687.

Résumé

This paper is concerned with the motion of the Chaplygin sleigh on the surface of a circular cylinder. In the case of inertial motion, the problem reduces to the study of the dynamical system on a (two-dimensional) torus and to the classification of singular points. Particular cases in which the system admits an invariant measure are found. In the case of a balanced and dynamically symmetric Chaplygin sleigh moving in a gravitational field it is shown that on the average the system has no drift along the vertical.

Détail

Keywords: Chaplygin sleigh, invariant measure, nonholonomic mechanics.

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