Non-deterministic dynamics of a mechanical system

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)
401 Downloads (Pure)


A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. 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 non-deterministic 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 languageEnglish
Article number022914
Number of pages11
JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
Issue number2
Publication statusPublished - 26 Aug 2014

Structured keywords

  • Engineering Mathematics Research Group


Dive into the research topics of 'Non-deterministic dynamics of a mechanical system'. Together they form a unique fingerprint.

Cite this