Regular and Chaotic Dynamics

, Volume 24, Issue 2, pp 145–170 | Cite as

On the Normal Force and Static Friction Acting on a Rolling Ball Actuated by Internal Point Masses

  • Vakhtang PutkaradzeEmail author
  • Stuart M. Rogers


The goal of this paper is to investigate the normal and tangential forces acting at the point of contact between a horizontal surface and a rolling ball actuated by internal point masses moving in the ball’s frame of reference. The normal force and static friction are derived from the equations of motion for a rolling ball actuated by internal point masses that move inside the ball’s frame of reference, and, as a special case, a rolling disk actuated by internal point masses. The masses may move along one-dimensional trajectories fixed in the ball’s and disk’s frame. The dynamics of a ball and disk actuated by masses moving along one-dimensional trajectories are simulated numerically and the minimum coefficients of static friction required to prevent slippage are computed.


nonholonomic mechanics holonomic mechanics rolling balls rolling disks 

MSC2010 numbers

37J60 70E18 70E60 


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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Department of Mathematical and Statistical Sciences, Faculty of ScienceUniversity of AlbertaEdmontonCanada
  2. 2.Institute for Mathematics and its Applications, College of Science and EngineeringUniversity of MinnesotaMinneapolisUSA

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