Overview
- 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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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.
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Table of contents (14 chapters)
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Front Matter
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Nonsmooth Dynamical Systems: Motivating Examples and Basic Concepts
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Front Matter
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Formulations of Nonsmooth Dynamical Systems
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Front Matter
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Time Integration of Nonsmooth Dynamical Systems
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Front Matter
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Numerical Methods for the One-Step Nonsmooth Problems
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Front Matter
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The SICONOS Software: Implementation and Examples
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Front Matter
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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
Bibliographic Information
Book Title: Numerical Methods for Nonsmooth Dynamical Systems
Book Subtitle: Applications in Mechanics and Electronics
Authors: Vincent Acary, Bernard Brogliato
Series Title: Lecture Notes in Applied and Computational Mechanics
DOI: https://doi.org/10.1007/978-3-540-75392-6
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Hardcover ISBN: 978-3-540-75391-9Published: 19 February 2008
Softcover ISBN: 978-3-642-09464-4Published: 22 November 2010
eBook ISBN: 978-3-540-75392-6Published: 30 January 2008
Series ISSN: 1613-7736
Series E-ISSN: 1860-0816
Edition Number: 1
Number of Pages: XXI, 525
Topics: Mechanical Engineering, Theoretical and Applied Mechanics, Vibration, Dynamical Systems, Control, Computational Intelligence