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Author: Markus Kunze
Publisher: Springer
Published: 2014-01-15
Total Pages: 244
ISBN-13: 9783662206102
DOWNLOAD EBOOKThe 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.
Author: Vincent Acary
Publisher: Springer Science & Business Media
Published: 2008-01-30
Total Pages: 529
ISBN-13: 3540753923
DOWNLOAD EBOOKThis 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.
Author: Bernard Brogliato
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 565
ISBN-13: 1447105575
DOWNLOAD EBOOKThank you for opening the second edition of this monograph, which is devoted to the study of a class of nonsmooth dynamical systems of the general form: ::i; = g(x,u) (0. 1) f(x, t) 2: 0 where x E JRn is the system's state vector, u E JRm is the vector of inputs, and the function f (-, . ) represents a unilateral constraint that is imposed on the state. More precisely, we shall restrict ourselves to a subclass of such systems, namely mechanical systems subject to unilateral constraints on the position, whose dynamical equations may be in a first instance written as: ii= g(q,q,u) (0. 2) f(q, t) 2: 0 where q E JRn is the vector of generalized coordinates of the system and u is an in put (or controller) that generally involves a state feedback loop, i. e. u= u(q, q, t, z), with z= Z(z, q, q, t) when the controller is a dynamic state feedback. Mechanical systems composed of rigid bodies interacting fall into this subclass. A general prop erty of systems as in (0. 1) and (0. 2) is that their solutions are nonsmooth (with respect to time): Nonsmoothness arises primarily from the occurence of impacts (or collisions, or percussions) in the dynamical behaviour, when the trajectories attain the surface f(x, t) = O. They are necessary to keep the trajectories within the subspace = {x : f(x, t) 2: O} of the system's state space.
Author: Mario Bernardo
Publisher: Springer Science & Business Media
Published: 2008-01-01
Total Pages: 497
ISBN-13: 1846287081
DOWNLOAD EBOOKThis 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.
Author: Remco I. Leine
Publisher: Springer Science & Business Media
Published: 2013-03-19
Total Pages: 245
ISBN-13: 3540443983
DOWNLOAD EBOOKThis 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.
Author: Mike R. Jeffrey
Publisher: Springer Nature
Published: 2020-02-22
Total Pages: 104
ISBN-13: 3030359875
DOWNLOAD EBOOKThis 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.
Author: Jan Awrejcewicz
Publisher: World Scientific
Published: 2003
Total Pages: 564
ISBN-13: 9812384596
DOWNLOAD EBOOKThis book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.
Author: Vincent Acary
Publisher: Springer Science & Business Media
Published: 2010-10-19
Total Pages: 295
ISBN-13: 9048196817
DOWNLOAD EBOOKNonsmooth Modeling and Simulation for Switched Circuits concerns the modeling and the numerical simulation of switched circuits with the nonsmooth dynamical systems (NSDS) approach, using piecewise-linear and multivalued models of electronic devices like diodes, transistors, switches. Numerous examples (ranging from introductory academic circuits to various types of power converters) are analyzed and many simulation results obtained with the INRIA open-source SICONOS software package are presented. Comparisons with SPICE and hybrid methods demonstrate the power of the NSDS approach. Nonsmooth Modeling and Simulation for Switched Circuits is intended to researchers and engineers in the field of circuits simulation and design, but may also attract applied mathematicians interested by the numerical analysis for nonsmooth dynamical systems, as well as researchers from Systems and Control.
Author: Francis H. Clarke
Publisher: Springer Science & Business Media
Published: 2008-01-10
Total Pages: 288
ISBN-13: 0387226257
DOWNLOAD EBOOKA 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.
Author: B. Fiedler
Publisher: Gulf Professional Publishing
Published: 2002-02-21
Total Pages: 1099
ISBN-13: 0080532845
DOWNLOAD EBOOKThis handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others.While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.
