Regularization of Isolated Codimension-2 Discontinuity Sets

Noah Cheesman; Kristian Uldall Kristiansen; S J Hogan

doi:10.1137/21M142157X

Regularization of Isolated Codimension-2 Discontinuity Sets

Noah Cheesman, Kristian Uldall Kristiansen, S J Hogan

Research output: Contribution to journal › Article (Academic Journal) › peer-review

7 Citations (Scopus)

Abstract

Work on standard piecewise-smooth (PWS) dynamical systems, with codimension-1 discontinuity sets, relies on the Filippov framework, which does not always readily generalize 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 generalizing Filippov sliding, crossing, and sliding vector fields.

Original language	English
Pages (from-to)	2630–2670
Number of pages	41
Journal	SIAM Journal on Applied Dynamical Systems
Volume	20
Issue number	4
DOIs	https://doi.org/10.1137/21M142157X
Publication status	Published - 20 Dec 2021

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Engineering Mathematics Research Group

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10.1137/21M142157XLicence: Unspecified

https://arxiv.org/abs/2105.12622

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Applications of geometric singular perturbation theory to mechanics: the Painlevé paradox in 3D and related problems
Cheesman, N. (Author), Hogan, J. (Supervisor) & Kristiansen, K. U. (Supervisor), 21 Jun 2022
Student thesis: Doctoral Thesis › Doctor of Philosophy (PhD)

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title = "Regularization of Isolated Codimension-2 Discontinuity Sets",

abstract = "Work on standard piecewise-smooth (PWS) dynamical systems, with codimension-1 discontinuity sets, relies on the Filippov framework, which does not always readily generalize 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 generalizing Filippov sliding, crossing, and sliding vector fields.",

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AU - Kristiansen, Kristian Uldall

AU - Hogan, S J

PY - 2021/12/20

Y1 - 2021/12/20

N2 - Work on standard piecewise-smooth (PWS) dynamical systems, with codimension-1 discontinuity sets, relies on the Filippov framework, which does not always readily generalize 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 generalizing Filippov sliding, crossing, and sliding vector fields.

AB - Work on standard piecewise-smooth (PWS) dynamical systems, with codimension-1 discontinuity sets, relies on the Filippov framework, which does not always readily generalize 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 generalizing Filippov sliding, crossing, and sliding vector fields.

U2 - 10.1137/21M142157X

DO - 10.1137/21M142157X

M3 - Article (Academic Journal)

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JO - SIAM Journal on Applied Dynamical Systems

JF - SIAM Journal on Applied Dynamical Systems

IS - 4

ER -

Regularization of Isolated Codimension-2 Discontinuity Sets

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Applications of geometric singular perturbation theory to mechanics: the Painlevé paradox in 3D and related problems

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