Singularities that induce a breakdown of determinism in mechanics

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We will show that determinism can break down at certain singularities that arise in the mechan- ics of semi-rigid bodies. An example system consists of a wheel slipping and rolling along a surface, such that dry friction applies a torque to the wheel via a standard nonlinear tyre-like interaction. In a certain configuration the force on the wheel and its ensuing motion acquire many possible values. The subsequent motion is there- fore infinitely sensitive to perturbation, constituting a point of non-determinism in an otherwise deterministic system. Moreover the device returns to the singularity repeatedly, so that it suffers repeated bursts of unpredictability, constituting an extreme non-deterministic form of chaos. A non-deterministic chaotic attractor was found for a range of parameters and tyre/friction models in (2013). Here, we explore the building blocks of this dynamics by stripping the model down to its key elements. We investigate the non-deterministic phenomenon when subjected to relaxations of the model that allow for smoothing, noise, and hysteresis. This is part of a wider theory currently emerging in the study of dynamical systems that undergo sharp switches in behaviour, whereby singularities can violate traditional rules of smooth dynamical systems.
Original languageEnglish
Title of host publicationProc. 5th International Conference on Structural Dynamics SEMS, Cape Town
Publication statusPublished - 2013


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