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Numerical Methods for Nonsmooth Dynamical Systems

Applications in Mechanics and Electronics

  • Book
  • © 2008

Overview

Authors:
  1. Vincent Acary

    1. INRIA, team-project BIPOP Inovallée, Montbonnot, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Bernard Brogliato

    1. INRIA, team-project BIPOP Inovallée, Montbonnot, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Provides a complete exposition of the algorithms, with numerous examples and benchmarks, and an emphasis on the implementation of the schemes with different complementarity problems solvers
  • A sort of advanced users' manual, that PhD students or senior researchers who want to get acquainted with this field and make numerical simulations on their computer, can use as a source of information

Part of the book series: Lecture Notes in Applied and Computational Mechanics (LNACM)

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-XX
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  2. Nonsmooth Dynamical Systems: Motivating Examples and Basic Concepts

    1. Front Matter

      Pages 1-1
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    2. Nonsmooth Dynamical Systems: Motivating Examples and Basic Concepts

      • Vincent Acary, Bernard Brogliato
      Pages 1-54

  3. Formulations of Nonsmooth Dynamical Systems

    1. Front Matter

      Pages 55-55
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    2. Nonsmooth Dynamical Systems: A Short Zoology

      • Vincent Acary, Bernard Brogliato
      Pages 57-105

    3. Mechanical Systems with Unilateral Constraints and Friction

      • Vincent Acary, Bernard Brogliato
      Pages 107-163

    4. Complementarity Systems

      • Vincent Acary, Bernard Brogliato
      Pages 165-176

    5. Higher Order Constrained Dynamical Systems

      • Vincent Acary, Bernard Brogliato
      Pages 177-188

    6. Specific Features of Nonsmooth Dynamical Systems

      • Vincent Acary, Bernard Brogliato
      Pages 189-195

  4. Time Integration of Nonsmooth Dynamical Systems

    1. Front Matter

      Pages 196-196
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    2. Event-Driven Schemes for Inclusions with AC Solutions

      • Vincent Acary, Bernard Brogliato
      Pages 203-217

    3. Event-Driven Schemes for Lagrangian Systems

      • Vincent Acary, Bernard Brogliato
      Pages 219-241

    4. Time-Stepping Schemes for Systems with AC Solutions

      • Vincent Acary, Bernard Brogliato
      Pages 243-284

    5. Time-Stepping Schemes for Mechanical Systems

      • Vincent Acary, Bernard Brogliato
      Pages 285-317

    6. Time-Stepping Scheme for the HOSP

      • Vincent Acary, Bernard Brogliato
      Pages 319-325

  5. Numerical Methods for the One-Step Nonsmooth Problems

    1. Front Matter

      Pages 326-326
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    2. Basics on Mathematical Programming Theory

      • Vincent Acary, Bernard Brogliato
      Pages 331-402

    3. Numerical Methods for the Frictional Contact Problem

      • Vincent Acary, Bernard Brogliato
      Pages 403-440

  6. The SICONOS Software: Implementation and Examples

    1. Front Matter

      Pages 441-441
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    2. The SICONOS Platform

      • Vincent Acary, Bernard Brogliato
      Pages 443-488
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Keywords

About this book

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.

Reviews

From the reviews:

"This monograph is a valuable and concise contribution to the numerics of nonsmooth ODEs … . It is clearly designed for engineering applications in computational mechanics, and the main concern is the discussion of the construction of algorithms and their properties … . written in a formal mathematical style with precise definitions, followed by results stated as Lemma, Proposition, or Theorem (and references to the literature for the proofs). This makes the overall work accessible for both, researchers in mechanics and in mathematics." (Christian Wieners, Zentralblatt für Angewandte Mathemtik und Mechanik, Vol. 88 (7), 2008)

“The present book is a research monograph with numerous information and references to original publications which gives to the book an encyclopaedic nature. … parallel presentation of nonsmooth models in mechanics and electronics indicates that the mentioned effects will also be of interest for people working in mechatronics, microelectromechanics and multiphysics. The book is intended for graduate students and scientists doing research and development in mechanics and electrical engineering, designers of modern electromechanical devices, as well as to researchers from other scientific communities … .” (Georgios E. Stavroulakis, Zentralblatt MATH, Vol. 1173, 2009)

Authors and Affiliations

  • INRIA, team-project BIPOP Inovallée, Montbonnot, France

    Vincent Acary, Bernard Brogliato

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