Canards in Stiction: On Solutions of a Friction Oscillator by Regularization

We study the solutions of a friction oscillator subject to stiction. The vector field of this discontinuous model does not follow the Filippov convention, and the concept of Filippov solution cannot be used. Furthermore, some Caratheodory solutions are unphysical. Therefore, we introduce the concept of stiction solutions: these are the Caratheodory solutions that are physically relevant, i.e., the ones that follow the stiction law. However, we find that some of the stiction solutions are forward nonunique in subregions of the slip onset. We call these solutions singular, in contrast to the regular stiction solutions that are forward unique. In order to further the understanding of the nonunique dynamics, we introduce a regularization of the model. This gives a singularly perturbed problem that captures the main features of the original discontinuous problem. We identify a repelling slow manifold that separates the forward slipping from the forward sticking solutions, leading to a high sensitivity to the i...

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