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Regular version of the site

Article

Dynamics of the Chaplygin Sleigh on a Cylinder

Regular and Chaotic Dynamics. 2016. Vol. 21. No. 1. P. 136-146.
Bizyaev I. A., Borisov A. V., Mamaev I. S.

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.