Dynamics of the Chaplygin Sleigh on a Cylinder

    2016, Volume 21, Number 1, pp.  136-146

    Author(s): 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.

    Keywords: Chaplygin sleigh, invariant measure, nonholonomic mechanics
    Citation: Bizyaev I. A., Borisov A. V., Mamaev I. S., Dynamics of the Chaplygin Sleigh on a Cylinder, Regular and Chaotic Dynamics, 2016, Volume 21, Number 1, pp. 136-146

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