Regular and Chaotic Dynamics

, Volume 23, Issue 7–8, pp 983–994 | Cite as

Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control

  • Ivan A. BizyaevEmail author
  • Alexey V. Borisov
  • Ivan S. Mamaev


In this paper we consider the problem of the motion of the Roller Racer.We assume that the angle ϕ(t) between the platforms is a prescribed function of time. We prove that in this case the acceleration of the Roller Racer is unbounded. In this case, as the Roller Racer accelerates, the increase in the constraint reaction forces is also unbounded. Physically this means that, from a certain instant onward, the conditions of the rolling motion of the wheels without slipping are violated. Thus, we consider a model in which, in addition to the nonholonomic constraints, viscous friction force acts at the points of contact of the wheels. For this case we prove that there is no constant acceleration and all trajectories of the reduced system asymptotically tend to a periodic solution.


Roller Racer speed-up nonholonomic mechanics Rayleigh dissipation function viscous friction integrability by quadratures control constraint reaction force 

MSC2010 numbers

37J60 37C10 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • Ivan A. Bizyaev
    • 1
    • 2
    Email author
  • Alexey V. Borisov
    • 1
  • Ivan S. Mamaev
    • 3
  1. 1.Udmurt State UniversityIzhevskRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyiRussia
  3. 3.M. T. Kalashnikov Izhevsk State Technical UniversityIzhevskRussia

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