Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and

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Numerical Methods for Nonsmooth Dynamical Systems by Vincent Acary, Bernard Brogliato

This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. 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.

FORMAT
Hardcover LANGUAGE
English CONDITION
Brand New Publisher Description

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.

Back Cover

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.

Table of Contents

Nonsmooth Dynamical Systems: Motivating Examples and Basic Concepts.- Nonsmooth Dynamical Systems: Motivating Examples and Basic Concepts.- Formulations of Nonsmooth Dynamical Systems.- Nonsmooth Dynamical Systems: A Short Zoology.- Mechanical Systems with Unilateral Constraints and Friction.- Complementarity Systems.- Higher Order Constrained Dynamical Systems.- Specific Features of Nonsmooth Dynamical Systems.- Time Integration of Nonsmooth Dynamical Systems.- Event-Driven Schemes for Inclusions with AC Solutions.- Event-Driven Schemes for Lagrangian Systems.- Time-Stepping Schemes for Systems with AC Solutions.- Time-Stepping Schemes for Mechanical Systems.- Time-Stepping Scheme for the HOSP.- Numerical Methods for the One-Step Nonsmooth Problems.- Basics on Mathematical Programming Theory.- Numerical Methods for the Frictional Contact Problem.- The SICONOS Software: Implementation and Examples.- The SICONOS Platform.

Review

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)

Long Description

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.

Review Quote

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)

Feature

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

Details ISBN3540753915 Author Bernard Brogliato Short Title NUMERICAL METHODS FOR NONSMOOT Pages 525 Series Lecture Notes in Applied and Computational Mechanics Language English ISBN-10 3540753915 ISBN-13 9783540753919 Media Book Format Hardcover Series Number 35 Year 2008 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Subtitle Applications in Mechanics and Electronics Place of Publication Berlin Country of Publication Germany DEWEY 515.39 Edition 2008th DOI 10.1007/978-3-540-75392-6 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 2008 ed. Publication Date 2008-02-19 Audience Undergraduate Illustrations XXI, 525 p. Country of Origin DE Product Class Description Mechanical Engineering Alternative 9783540753926
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