Projects per year
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 behaviour 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.
Original language  English 

Article number  022914 
Number of pages  11 
Journal  Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 
Volume  90 
Issue number  2 
DOIs  
Publication status  Published  26 Aug 2014 
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Projects
 1 Finished

When Worlds Collide: the asymptotics of interacting systems (Career Acceleration Fellowship)
1/08/12 → 1/08/16
Project: Research
Profiles

Dr Robert Szalai
 Department of Engineering Mathematics  Senior Lecturer in Engineering Mathematics
 Dynamics and Control
 Applied Nonlinear Mathematics
Person: Academic , Member