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Regular and Chaotic Dynamics

, Volume 24, Issue 2, pp 212–233 | Cite as

Qualitative Analysis of the Nonholonomic Rolling of a Rubber Wheel with Sharp Edges

  • Alexander A. KilinEmail author
  • Elena N. Pivovarova
Article
  • 7 Downloads

Abstract

This paper presents a qualitative analysis of the dynamics in a fixed reference frame of a wheel with sharp edges that rolls on a horizontal plane without slipping at the point of contact and without spinning relative to the vertical. The wheel is a ball that is symmetrically truncated on both sides and has a displaced center of mass. The dynamics of such a system is described by the model of the ball’s motion where the wheel rolls with its spherical part in contact with the supporting plane and the model of the disk’s motion where the contact point lies on the sharp edge of the wheel. A classification is given of possible motions of the wheel depending on whether there are transitions from its spherical part to sharp edges. An analysis is made of the behavior of the point of contact of the wheel with the plane for different values of the system parameters, first integrals and initial conditions. Conditions for boundedness and unboundedness of the wheel’s motion are obtained. Conditions for the fall of the wheel on the plane of sections are presented.

Keywords

integrable system system with discontinuity nonholonomic constraint bifurcation diagram body of revolution sharp edge wheel rubber body model permanent rotations dynamics in a fixed reference frame resonance quadrature unbounded motion 

MSC2010 numbers

70E15 70E18 70E40 37Jxx 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Udmurt State UniversityIzhevskRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyiRussia
  3. 3.Center for Technologies in Robotics and Mechatronics ComponentsInnopolis UniversityInnopolisRussia

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