Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction

by Monteiro Marques

Overview

The book is devoted to evolution problems which arise in the dynamics of mechanical systems involving unilateral constraints, possibly in the presence of dry friction. Collisions may be the result. In such a context, the velocity function cannot be expected to be absolutely continuous, so the traditional theory of differential equations or inclusions does not apply. Some effective numerical techniques have been proposed, but existence results were missing until now. This book starts filling that gap. At first, some typical mathematical tools are introduced, such as compactness results in the space of vector functions of bounded variation in time and approximation in the sense of graphs. The sweeping process by a moving convex set in a Hilbert space plays a central role. The latest existence results concerning this process are presented in chapter 2. In chapters 3 and 4, the study of the mechanical problems is undertaken. Connected areas of research are briefly reviewed in chapter 5. Proofs are constructive whenever possible and convergence of algorithms is often considered. The book presupposes only a moderate background in functional analysis.

Product Details

ISBN-13:	9783034876162
Publisher:	Birkhäuser Basel
Publication date:	05/03/2013
Series:	Progress in Nonlinear Differential Equations and Their Applications , #9
Edition description:	Softcover reprint of the original 1st ed. 1993
Pages:	182
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

0 Preliminaries.- 1 Regularization and Graph Approximation of a Discontinuous Evolution.- 2 Sweeping Processes by Convex Sets with Nonempty Interior.- 3 Inelastic Shocks with or without Friction: Existence Results.- 4 Externally Induced Dissipative Collisions.- 5 Further Applications and Related Topics.- Index of Notation.