Non Smooth Dynamical Systems

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Numerical Methods for Nonsmooth Dynamical Systems

Vincent Acary,Bernard Brogliato
Numerical Methods for Nonsmooth Dynamical Systems Book PDF

Author : Vincent Acary,Bernard Brogliato
Publisher : Springer Science & Business Media
Page : 529 pages
File Size : 48,5 Mb
Release : 2008-01-30
Category : Technology & Engineering
ISBN : 9783540753926

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

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.

Non-Smooth Dynamical Systems

Markus Kunze
Non Smooth Dynamical Systems Book PDF

Author : Markus Kunze
Publisher : Springer
Page : 244 pages
File Size : 42,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662206102

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Non-Smooth Dynamical Systems by Markus Kunze Pdf

The book provides a self-contained introduction to the mathematical theory of non-smooth dynamical problems, as they frequently arise from mechanical systems with friction and/or impacts. It is aimed at applied mathematicians, engineers, and applied scientists in general who wish to learn the subject.

Dynamics and Bifurcations of Non-Smooth Mechanical Systems

Remco I. Leine,Henk Nijmeijer
Dynamics and Bifurcations of Non Smooth Mechanical Systems Book PDF

Author : Remco I. Leine,Henk Nijmeijer
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 49,8 Mb
Release : 2013-03-19
Category : Mathematics
ISBN : 9783540443988

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Dynamics and Bifurcations of Non-Smooth Mechanical Systems by Remco I. Leine,Henk Nijmeijer Pdf

This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Non-Smooth Dynamical Systems

Markus Kunze
Non Smooth Dynamical Systems Book PDF

Author : Markus Kunze
Publisher : Springer
Page : 234 pages
File Size : 54,6 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540444411

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Non-Smooth Dynamical Systems by Markus Kunze Pdf

The book provides a self-contained introduction to the mathematical theory of non-smooth dynamical problems, as they frequently arise from mechanical systems with friction and/or impacts. It is aimed at applied mathematicians, engineers, and applied scientists in general who wish to learn the subject.

Nonsmooth Mechanics

Bernard Brogliato
Nonsmooth Mechanics Book PDF

Author : Bernard Brogliato
Publisher : Springer
Page : 628 pages
File Size : 49,8 Mb
Release : 2016-02-29
Category : Technology & Engineering
ISBN : 9783319286648

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Nonsmooth Mechanics by Bernard Brogliato Pdf

Now in its third edition, this standard reference is a comprehensive treatment of nonsmooth mechanical systems refocused to give more prominence to issues connected with control and modelling. It covers Lagrangian and Newton–Euler systems, detailing mathematical tools such as convex analysis and complementarity theory. The ways in which nonsmooth mechanics influence and are influenced by well-posedness analysis, numerical analysis and simulation, modelling and control are explained. Contact/impact laws, stability theory and trajectory-tracking control are given detailed exposition connected by a mathematical framework formed from complementarity systems and measure-differential inclusions. Links are established with electrical circuits with set-valued nonsmooth elements as well as with other nonsmooth dynamical systems like impulsive and piecewise linear systems. Nonsmooth Mechanics (third edition) retains the topical structure familiar from its predecessors but has been substantially rewritten, edited and updated to account for the significant body of results that have emerged in the twenty-first century—including developments in: the existence and uniqueness of solutions; impact models; extension of the Lagrange–Dirichlet theorem and trajectory tracking; and well-posedness of contact complementarity problems with and without friction. Many figures (both new and redrawn to improve the clarity of the presentation) and examples are used to illustrate the theoretical developments. Material introducing the mathematics of nonsmooth mechanics has been improved to reflect the broad range of applications interest that has developed since publication of the second edition. The detail of some mathematical essentials is provided in four appendices. With its improved bibliography of over 1,300 references and wide-ranging coverage, Nonsmooth Mechanics (third edition) is sure to be an invaluable resource for researchers and postgraduates studying the control of mechanical systems, robotics, granular matter and relevant fields of applied mathematics. “The book’s two best features, in my view are its detailed survey of the literature... and its detailed presentation of many examples illustrating both the techniques and their limitations... For readers interested in the field, this book will serve as an excellent introductory survey.” Andrew Lewis in Automatica “It is written with clarity, contains the latest research results in the area of impact problems for rigid bodies and is recommended for both applied mathematicians and engineers.” Panagiotis D. Panagiotopoulos in Mathematical Reviews “The presentation is excellent in combining rigorous mathematics with a great number of examples... allowing the reader to understand the basic concepts.” Hans Troger in Mathematical Abstracts “/i>

Piecewise-smooth Dynamical Systems

Mario Bernardo,Chris Budd,Alan Richard Champneys,Piotr Kowalczyk
Piecewise smooth Dynamical Systems Book PDF

Author : Mario Bernardo,Chris Budd,Alan Richard Champneys,Piotr Kowalczyk
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 41,6 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9781846287084

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Piecewise-smooth Dynamical Systems by Mario Bernardo,Chris Budd,Alan Richard Champneys,Piotr Kowalczyk Pdf

This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.

Smooth Dynamical Systems

Michael Charles Irwin
Smooth Dynamical Systems Book PDF

Author : Michael Charles Irwin
Publisher : World Scientific
Page : 280 pages
File Size : 43,7 Mb
Release : 2001
Category : Mathematics
ISBN : 9812810129

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Smooth Dynamical Systems by Michael Charles Irwin Pdf

This is a reprint of M C Irwin''s beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area. Request Inspection Copy. Contents: Some Simple Examples; Equivalent Systems; Integration of Vector Fields; Linear Systems, Linearization, Stable Manifolds; Stable Systems; Appendices. Readership: Graduate students in mathematics.

Adaptive Control of Nonsmooth Dynamic Systems

Gang Tao,Frank L. Lewis
Adaptive Control of Nonsmooth Dynamic Systems Book PDF

Author : Gang Tao,Frank L. Lewis
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 48,5 Mb
Release : 2013-04-17
Category : Technology & Engineering
ISBN : 9781447136873

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Adaptive Control of Nonsmooth Dynamic Systems by Gang Tao,Frank L. Lewis Pdf

Many of the non-smooth, non-linear phenomena covered in this well-balanced book are of vital importance in almost any field of engineering. Contributors from all over the world ensure that no one area’s slant on the subjects predominates.

Modeling with Nonsmooth Dynamics

Mike R. Jeffrey
Modeling with Nonsmooth Dynamics Book PDF

Author : Mike R. Jeffrey
Publisher : Springer Nature
Page : 104 pages
File Size : 47,6 Mb
Release : 2020-02-22
Category : Mathematics
ISBN : 9783030359874

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Modeling with Nonsmooth Dynamics by Mike R. Jeffrey Pdf

This volume looks at the study of dynamical systems with discontinuities. Discontinuities arise when systems are subject to switches, decisions, or other abrupt changes in their underlying properties that require a ‘non-smooth’ definition. A review of current ideas and introduction to key methods is given, with a view to opening discussion of a major open problem in our fundamental understanding of what nonsmooth models are. What does a nonsmooth model represent: an approximation, a toy model, a sophisticated qualitative capturing of empirical law, or a mere abstraction? Tackling this question means confronting rarely discussed indeterminacies and ambiguities in how we define, simulate, and solve nonsmooth models. The author illustrates these with simple examples based on genetic regulation and investment games, and proposes precise mathematical tools to tackle them. The volume is aimed at students and researchers who have some experience of dynamical systems, whether as a modelling tool or studying theoretically. Pointing to a range of theoretical and applied literature, the author introduces the key ideas needed to tackle nonsmooth models, but also shows the gaps in understanding that all researchers should be bearing in mind. Mike Jeffrey is a researcher and lecturer at the University of Bristol with a background in mathematical physics, specializing in dynamics, singularities, and asymptotics.

A Variational Approach to Nonsmooth Dynamics

Samir Adly
A Variational Approach to Nonsmooth Dynamics Book PDF

Author : Samir Adly
Publisher : Springer
Page : 159 pages
File Size : 48,9 Mb
Release : 2018-02-19
Category : Mathematics
ISBN : 9783319686585

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A Variational Approach to Nonsmooth Dynamics by Samir Adly Pdf

This brief examines mathematical models in nonsmooth mechanics and nonregular electrical circuits, including evolution variational inequalities, complementarity systems, differential inclusions, second-order dynamics, Lur'e systems and Moreau's sweeping process. The field of nonsmooth dynamics is of great interest to mathematicians, mechanicians, automatic controllers and engineers. The present volume acknowledges this transversality and provides a multidisciplinary view as it outlines fundamental results in nonsmooth dynamics and explains how to use them to study various problems in engineering. In particular, the author explores the question of how to redefine the notion of dynamical systems in light of modern variational and nonsmooth analysis. With the aim of bridging between the communities of applied mathematicians, engineers and researchers in control theory and nonlinear systems, this brief outlines both relevant mathematical proofs and models in unilateral mechanics and electronics.

Dynamics and Bifurcations of Non-Smooth Mechanical Systems

Remco Leine,Henk Nijmeijer
Dynamics and Bifurcations of Non Smooth Mechanical Systems Book PDF

Author : Remco Leine,Henk Nijmeijer
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 41,5 Mb
Release : 2006-06-13
Category : Mathematics
ISBN : 3540219870

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Dynamics and Bifurcations of Non-Smooth Mechanical Systems by Remco Leine,Henk Nijmeijer Pdf

This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Bifurcations and Chaos in Piecewise-smooth Dynamical Systems

Zhanybai T. Zhusubaliyev,Erik Mosekilde
Bifurcations and Chaos in Piecewise smooth Dynamical Systems Book PDF

Author : Zhanybai T. Zhusubaliyev,Erik Mosekilde
Publisher : World Scientific
Page : 380 pages
File Size : 46,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9812564438

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Bifurcations and Chaos in Piecewise-smooth Dynamical Systems by Zhanybai T. Zhusubaliyev,Erik Mosekilde Pdf

Technical problems often lead to differential equations withpiecewise-smooth right-hand sides. Problems in mechanicalengineering, for instance, violate the requirements of smoothness ifthey involve collisions, finite clearances, or stickOCoslipphenomena."

Non-Smooth Deterministic or Stochastic Discrete Dynamical Systems

Jerome Bastien,Frederic Bernardin,Claude-Henri Lamarque
Non Smooth Deterministic or Stochastic Discrete Dynamical Systems Book PDF

Author : Jerome Bastien,Frederic Bernardin,Claude-Henri Lamarque
Publisher : John Wiley & Sons
Page : 514 pages
File Size : 48,9 Mb
Release : 2013-03-18
Category : Mathematics
ISBN : 9781118604083

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Non-Smooth Deterministic or Stochastic Discrete Dynamical Systems by Jerome Bastien,Frederic Bernardin,Claude-Henri Lamarque Pdf

This book contains theoretical and application-oriented methods to treat models of dynamical systems involving non-smooth nonlinearities. The theoretical approach that has been retained and underlined in this work is associated with differential inclusions of mainly finite dimensional dynamical systems and the introduction of maximal monotone operators (graphs) in order to describe models of impact or friction. The authors of this book master the mathematical, numerical and modeling tools in a particular way so that they can propose all aspects of the approach, in both a deterministic and stochastic context, in order to describe real stresses exerted on physical systems. Such tools are very powerful for providing reference numerical approximations of the models. Such an approach is still not very popular nevertheless, even though it could be very useful for many models of numerous fields (e.g. mechanics, vibrations, etc.). This book is especially suited for people both in research and industry interested in the modeling and numerical simulation of discrete mechanical systems with friction or impact phenomena occurring in the presence of classical (linear elastic) or non-classical constitutive laws (delay, memory effects, etc.). It aims to close the gap between highly specialized mathematical literature and engineering applications, as well as to also give tools in the framework of non-smooth stochastic differential systems: thus, applications involving stochastic excitations (earthquakes, road surfaces, wind models etc.) are considered. Contents 1. Some Simple Examples. 2. Theoretical Deterministic Context. 3. Stochastic Theoretical Context. 4. Riemannian Theoretical Context. 5. Systems with Friction. 6. Impact Systems. 7. Applications–Extensions. About the Authors Jérôme Bastien is Assistant Professor at the University Lyon 1 (Centre de recherche et d'Innovation sur le sport) in France. Frédéric Bernardin is a Research Engineer at Département Laboratoire de Clermont-Ferrand (DLCF), Centre d'Etudes Techniques de l'Equipement (CETE), Lyon, France. Claude-Henri Lamarque is Head of Laboratoire Géomatériaux et Génie Civil (LGCB) and Professor at Ecole des Travaux Publics de l'Etat (ENTPE), Vaulx-en-Velin, France.

Qualitative Analysis of Nonsmooth Dynamics

Alain Léger,Elaine Pratt
Qualitative Analysis of Nonsmooth Dynamics Book PDF

Author : Alain Léger,Elaine Pratt
Publisher : Elsevier
Page : 222 pages
File Size : 43,5 Mb
Release : 2016-04-26
Category : Technology & Engineering
ISBN : 9780081012017

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Qualitative Analysis of Nonsmooth Dynamics by Alain Léger,Elaine Pratt Pdf

Qualitative Analysis of Nonsmooth Dynamics: A Simple Discrete System with Unilateral Contact and Coulomb Friction explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems. By analyzing these non-regularities successively this work explores the set of equilibria and properties of periodic solutions of elementary mechanical systems, where no classical results issued from the theory of ordinary differential equations are readily available, such as stability, continuation or approximation of solutions. The authors focus on unilateral contact in presence of Coulomb friction and show, in particular, how any regularization would greatly simplify the mathematics but lead to unacceptable physical responses. Explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems Includes theoretical results concerning the full investigation of the behavior under constant or oscillating loadings, even in the case of the simplest mechanical systems Provides a focus on unilateral contact in presence of Coulomb friction Helps you gain an accurate understanding of how the transition occurs to ensure the safe use of any machine involving rotating or sliding mechanisms

Nonsmooth Analysis and Control Theory

Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski
Nonsmooth Analysis and Control Theory Book PDF

Author : Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 43,6 Mb
Release : 2008-01-10
Category : Mathematics
ISBN : 9780387226255

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Nonsmooth Analysis and Control Theory by Francis H. Clarke,Yuri S. Ledyaev,Ronald J. Stern,Peter R. Wolenski Pdf

A clear and succinct presentation of the essentials of this subject, together with some of its applications and a generous helping of interesting exercises. Following an introductory chapter with a taste of what is to come, the next three chapters constitute a course in nonsmooth analysis and identify a coherent and comprehensive approach to the subject, leading to an efficient, natural, and powerful body of theory. The whole is rounded off with a self-contained introduction to the theory of control of ordinary differential equations. The authors have incorporated a number of new results which clarify the relationships between the different schools of thought in the subject, with the aim of making nonsmooth analysis accessible to a wider audience. End-of-chapter problems offer scope for deeper understanding.