Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction

Description

This book is devoted to the sndy of some clifferentia.l inclusions motivated by Mechanics and of existcnce rcsults for the dynamics of systems with inelastic shocks, with or without friction. This ensures a certain unity of subject, techniques and applications, at the price of not including some earlier works [Mon 1-4] . In the introductory Chapter 0, sevcral essentia.l mathematical tools (either recent or recently rediscoven d) are presented. l\1ainly they concern functions of bouncled variation defincd in real interva.ls ( deriva.tion of Stieltjcs measures, compactness results. convergencrc in tlw sense of graphs) a.ncl geometrical inequa.lities. In Chapters 1 and 2, Ivforea.u' s swecpiug process is considcred; this is a first-order differential inclusion (1) where the right-ha.nd siele is tla: ' outw Front Matter....Pages i-x Preliminaries....Pages 1-26 Regularization and Graph Approximation of a Discontinuous Evolution....Pages 27-44 Sweeping Processes by Convex Sets with Nonempty Interior....Pages 45-71 Inelastic Shocks with or without Friction: Existence Results....Pages 72-111 Externally Induced Dissipative Collisions....Pages 112-131 Further Applications and Related Topics....Pages 132-165 Back Matter....Pages 167-182