Regularisation of isolated codimension-2 discontinuity sets
Dynamical Systems
2021-05-28 v2
Abstract
Work on standard piecewise-smooth (PWS) dynamical systems, with codimension-1 discontinuity sets, relies on the Filippov framework, which does not always readily generalise to systems with higher codimension discontinuities. These higher order degeneracies occur in applications, with spatial Coulomb friction being the prominent example. In this work, we consider PWS systems with isolated codimension-2 discontinuity sets using regularization and blowup to study the dynamics. We present a general framework and give specific results for the local dynamics in a class of problems, and generalising Filippov sliding, crossing and sliding vector fields.
Cite
@article{arxiv.2105.12622,
title = {Regularisation of isolated codimension-2 discontinuity sets},
author = {Noah Cheesman and Kristian Uldall Kristiansen and S. J. Hogan},
journal= {arXiv preprint arXiv:2105.12622},
year = {2021}
}
Comments
32 pages, 24 Figures, preprint