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, Rus. J. Nonlin. Dyn.,
2016, Vol. 12, No. 4,
pp. 675–687
DOI:10.20537/nd1604010