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Dynamics of a Chaplygin sleigh with an unbalanced rotor: regular and chaotic motions

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Abstract

This paper addresses the problem of the motion of a sleigh with a free rotor. It is shown that this system exhibits chaotic and regular motions. The case in which the system is balanced relative to the knife edge is of particular interest because it has an additional integral. In this case, the problem reduces to investigating a vector field on a torus and to classifying singular points on it.

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Funding

The work of I. A. Bizyaev (Section 2) was supported by the RNF under Grant No. 18-71-00110. The work of I. S. Mamaev (Section 3) was supported by the RFBR Grant No. 18-29-10051_mk and was carried out at MIPT under project 5-100 for state support for leading universities of the Russian Federation. The work of A. V. Borisov (Section 1) was carried out within the framework of the state assignment of the Ministry of Education and Science of Russia (1.2404.2017/4.6) and was supported by the RFBR Grant No. 18-08- 00999_a.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudny, Russia, 141700

    Ivan A. Bizyaev & Ivan S. Mamaev

  2. Center for Technologies in Robotics and Mechatronics Components, Innopolis University, ul. Universitetskaya 1, Innopolis, Russia, 420500

    Ivan A. Bizyaev & Ivan S. Mamaev

  3. Udmurt State University, ul. Universitetskaya 1, Izhevsk, Russia, 426034

    Alexey V. Borisov

  4. Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), per. M. Kharitonyevsky 4, Moscow, Russia, 101990

    Alexey V. Borisov

Authors
  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 Alexey V. Borisov.

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Bizyaev, I.A., Borisov, A.V. & Mamaev, I.S. Dynamics of a Chaplygin sleigh with an unbalanced rotor: regular and chaotic motions. Nonlinear Dyn 98, 2277–2291 (2019). https://doi.org/10.1007/s11071-019-05325-7

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  • DOI: https://doi.org/10.1007/s11071-019-05325-7

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