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Dynamics of the Chaplygin sleigh on a cylinder

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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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  1. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    Ivan A. Bizyaev, Alexey V. Borisov & Ivan S. Mamaev

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  1. Ivan A. Bizyaev
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  2. Alexey V. Borisov
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  3. Ivan S. Mamaev
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Correspondence to Ivan A. Bizyaev.

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Bizyaev, I.A., Borisov, A.V. & Mamaev, I.S. Dynamics of the Chaplygin sleigh on a cylinder. Regul. Chaot. Dyn. 21, 136–146 (2016). https://doi.org/10.1134/S1560354716010081

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  • DOI: https://doi.org/10.1134/S1560354716010081

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