Fundamental matrix solutions of piecewise smooth differential systems
type: Item
instance of: scholarly article
title: Fundamental matrix solutions of piecewise smooth differential systems
zbMATH Open document ID: 1215.65121
author: Luca Dieci
author: Luciano Lopez
published in: Mathematics and Computers in Simulation
publication date: 2011-03-22T00:00:00Z
review text: This paper is concerned with the study of some properties of the matrix solutions of variational equations around continuous solutions of piecewise smooth differential systems. The systems under consideration are termed as Filippov type systems in which the vector field has a finite number of switching surfaces \( \Sigma_j\), \(j=1, \dots ,k\) of discontinuity so that any trajectory that reaches a switching surface \( \Sigma_j\) may be continued either by a transversal intersection or else be continued sliding along \( \Sigma_j\). In the first part of the paper a brief review of Filippov's theory on non smooth differential systems is given. After that a detailed study of the properties of the fundamental matrix solution around a given Filippov solution is carried out both in cross and slide motion on a surface \( \Sigma_j\). Then the theory is extended to the case of two surfaces. The paper ends by illustrating the theory with an example due to \textit{U. Galvanetto} [Journal of Sound and Vibration 248, 653--669 (2001)] which consist of a system of two blocks on a moving belt connected by a spring and subject to a dry friction force, by computing the eigenvalues of the fundamental matrix around a periodic solution.
reviewed by: Manuel Calvo
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 74M10
zbMATH DE Number: 5869213
zbMATH Keywords: piecewise smooth differential systems
zbMATH Keywords: variational equations around Filippov solutions
zbMATH Keywords: properties of fundamental matrix solutions
zbMATH Keywords: numerical examples
zbMATH Keywords: friction
MaRDI profile type: Publication
full work available at URL: j.matcom.2010.10.012
OpenAlex ID: W2066213568
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DOI: 10.1016/J.MATCOM.2010.10.012
description: scientific article; zbMATH DE number 5869213