Numerical Methods for Nonsmooth Dynamical Systems

Applications in Mechanics and Electronics

  • Vincent Acary
  • Bernard Brogliato

Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 35)

Table of contents

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

    1. Front Matter
      Pages 1-1
    2. Vincent Acary, Bernard Brogliato
      Pages 1-54
  3. Formulations of Nonsmooth Dynamical Systems

    1. Front Matter
      Pages 55-55
    2. Vincent Acary, Bernard Brogliato
      Pages 57-105
    3. Vincent Acary, Bernard Brogliato
      Pages 107-163
    4. Vincent Acary, Bernard Brogliato
      Pages 165-176
    5. Vincent Acary, Bernard Brogliato
      Pages 177-188
    6. Vincent Acary, Bernard Brogliato
      Pages 189-195
  4. Time Integration of Nonsmooth Dynamical Systems

    1. Front Matter
      Pages 196-196
    2. Vincent Acary, Bernard Brogliato
      Pages 203-217
    3. Vincent Acary, Bernard Brogliato
      Pages 219-241
    4. Vincent Acary, Bernard Brogliato
      Pages 243-284
    5. Vincent Acary, Bernard Brogliato
      Pages 285-317
    6. Vincent Acary, Bernard Brogliato
      Pages 319-325
  5. Numerical Methods for the One-Step Nonsmooth Problems

    1. Front Matter
      Pages 326-326
    2. Vincent Acary, Bernard Brogliato
      Pages 331-402
    3. Vincent Acary, Bernard Brogliato
      Pages 403-440
  6. The SICONOS Software: Implementation and Examples

    1. Front Matter
      Pages 441-441
    2. Vincent Acary, Bernard Brogliato
      Pages 443-488

About this book

Introduction

This book concerns the numerical simulation of dynamical systems whose trajectories may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, firstly because of the many applications in which nonsmooth models are useful, secondly because they give rise to new problems in various fields of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution variational inequalities, each of these classes being itself split into several subclasses.

With detailed examples of multibody systems with contact, impact and friction and electrical circuits with piecewise linear and ideal components, the book is is mainly intended for researchers in Mechanics and Electrical Engineering, but it will be attractive to researchers from other scientific communities like Systems and Control, Robotics, Physics of Granular Media, Civil Engineering, Virtual Reality, Haptic Systems, Computer Graphics, etc.

Keywords

electrical engineering electronics numerical methods programming robot robotics simulation

Authors and affiliations

  • Vincent Acary
    • 1
  • Bernard Brogliato
    • 1
  1. 1.INRIA, team-project BIPOP InovalléeMontbonnotFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-75392-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-540-75391-9
  • Online ISBN 978-3-540-75392-6
  • Series Print ISSN 1613-7736
  • About this book