Dynamics of the Chaplygin sleigh on a cylinder |
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Authors: | Ivan A. Bizyaev Alexey V. Borisov Ivan S. Mamaev |
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Affiliation: | 1.Steklov Mathematical Institute,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | 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. |
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