March  2010, 3(1): 129-140. doi: 10.3934/dcdss.2010.3.129

Two rolling disks or spheres


Applied Mathematics and Mathematical Physics, Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan, Canada, Canada

Received  July 2008 Revised  July 2009 Published  December 2009

The mechanical system of two disks, moving freely in the plane, while in contact and rolling against each other without slipping, may be written as a Lagrangian system with three degrees of freedom and one holonomic rolling constraint. We derive simple geometric criteria for the rotational relative equilibria and their stability. Extending to three dimensions, we derive the kinematics of the analogous system where two spheres replace two disks, and we verify that the rolling disk system occurs as a holonomic subsystem of the rolling sphere system.
Citation: George W. Patrick, Tyler Helmuth. Two rolling disks or spheres. Discrete and Continuous Dynamical Systems - S, 2010, 3 (1) : 129-140. doi: 10.3934/dcdss.2010.3.129

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