title: Nondeterministic dynamics of a mechanical system.
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.
authors.affiliation: Engineering Mathematics, University of Bristol, United Kingdom.
authors.forename: Robert
authors.initials: R
authors.lastname: Szalai
authors.affiliation: Engineering Mathematics, University of Bristol, United Kingdom.
authors.forename: Mike R
authors.initials: MR
authors.lastname: Jeffrey
mesh_terms: D003198:Computer Simulation; D017276:Friction; D008962:Models, Theoretical; D017711:Nonlinear Dynamics