Nonlinear Dynamics

, Volume 10, Issue 3, pp 287–305 | Cite as

The dynamies of rolling disks and sliding disks

  • O. M. O'Reilly


The dynamics of disks which move with one point in contact with a fixed horizontal surface are investigated. Two cases are considered: one where the disk rolls without slipping and a second where the disk slides. A two-parameter family of integrable second order differential equations is established for both of these systems by exploiting classical integrability results. Using these families of dynamical systems, complete descriptions of the bifurcations and stability of the steady motions of the disks are presented. One of these families is also used to establish the existence of motions which result in the rolling disk colliding with the horizontal surface. These motions occur for arbitrarily large angular velocities and in the absence of dissipation. The paper closes with some comments on non-integrability.

Key words

Bifurcations steady motions constrained dynamical systems integrability 


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • O. M. O'Reilly
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of California at BerkeleyBerkeleyU.S.A.

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