Abstract
A mechanical system is presented exhibiting a nondeterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become nonunique. A Coulomb friction force applies linear and angular forces to a wheel mounted on a turntable. In certain configurations, the friction force is not uniquely determined. When the dynamics evolves past the singularity and the mechanism slips, the future state becomes uncertain up to a set of possible values. For certain parameters, the system repeatedly returns to the singularity, giving recurrent yet unpredictable behavior that constitutes nondeterministic chaotic dynamics. The robustness of the phenomenon is such that we expect it to persist with more sophisticated friction models, manifesting as extreme sensitivity to initial conditions, and complex global dynamics attributable to a local loss of determinism in the limit of discontinuous friction.
1 More- Received 1 February 2014
DOI:https://doi.org/10.1103/PhysRevE.90.022914
©2014 American Physical Society