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

  • Ivan A. Bizyaev
  • Alexey V. BorisovEmail author
  • Ivan S. Mamaev
Original paper
  • 49 Downloads

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.

Keywords

Chaplygin sleigh Unbalanced rotor Nonholonomic mechanics Strange attractor Regular and chaotic trajectories Invariant measure Integrable systems system of two bodies 

Notes

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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  2. 2.Center for Technologies in Robotics and Mechatronics ComponentsInnopolis UniversityInnopolisRussia
  3. 3.Udmurt State UniversityIzhevskRussia
  4. 4.Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN)MoscowRussia

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