2021/05/26 by Noah Cheesman, Cheesman, Noah, Kristian Uldall Kristiansen +3
Engineering · Mathematics · #34E15 #37N15 #74H35 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #Elasticity and Wave Propagation #FOS: Mathematics #Stability and Control of Uncertain Systems
paper · doi:10.48550/arxiv.2105.12622
openalex publication_date 2021/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.