This book concerns the numerical simulation of dynamical systems whose
trajec- ries may not be differentiable everywhere. They are named
nonsmooth dynamical systems. They make an important class of systems,
rst because of the many app- cations in which nonsmooth models are
useful, secondly because they give rise to new problems in various elds
of science. Usually nonsmooth dynamical systems are represented as
differential inclusions, complementarity systems, evolution va- ational
inequalities, each of these classes itself being split into several
subclasses. The book is divided into four parts, the rst three parts
being sketched in Fig. 0. 1. The aim of the rst part is to present the
main tools from mechanics and applied mathematics which are necessary to
understand how nonsmooth dynamical systems may be numerically simulated
in a reliable way. Many examples illustrate the th- retical results, and
an emphasis is put on mechanical systems, as well as on electrical
circuits (the so-called Filippov's systems are also examined in some
detail, due to their importance in control applications). The second and
third parts are dedicated to a detailed presentation of the numerical
schemes. A fourth part is devoted to the presentation of the software
platform Siconos. This book is not a textbook on - merical analysis of
nonsmooth systems, in the sense that despite the main results of
numerical analysis (convergence, order of consistency, etc. ) being
presented, their proofs are not provided.
