Chaotic Mechanics in Systems with Impacts and Friction

Chaotic Mechanics in Systems with Impacts and Friction PDF

Author: Barbara Blazejczyk-Okolewska

Publisher: World Scientific

Published: 1999

Total Pages: 194

ISBN-13: 9789810237165

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This book is devoted to the theory of chaotic oscillations in mechanical systems. Detailed descriptions of the basic types of nonlinearity ? impacts and dry friction ? are presented. The properties of such behavior are discussed, and the numerical and experimental results obtained by the authors are presented.The dynamic properties of systems described here can be useful in the proper design and use of mechanics where such behavior still creates problems.This book will be very useful for anyone with a fundamental knowledge of nonlinear mechanics who is beginning research in the field.

Chaotic Mechanics in Systems with Impacts and Friction

Chaotic Mechanics in Systems with Impacts and Friction PDF

Author: Barbara Blazejczyk-Okolewska

Publisher: World Scientific

Published: 1999-06-17

Total Pages: 184

ISBN-13: 9814495395

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This book is devoted to the theory of chaotic oscillations in mechanical systems. Detailed descriptions of the basic types of nonlinearity — impacts and dry friction — are presented. The properties of such behavior are discussed, and the numerical and experimental results obtained by the authors are presented. The dynamic properties of systems described here can be useful in the proper design and use of mechanics where such behavior still creates problems. This book will be very useful for anyone with a fundamental knowledge of nonlinear mechanics who is beginning research in the field. Contents:Chaotic Phenomena in Applied Mechanics:Nonlinearities in Mechanical SystemsProperties of a Dry Friction ForceChaos in Systems with Dry FrictionBasic Theory of ImpactCoefficient of RestitutionChaos in Impact OscillatorImpact Oscillator with Dry Friction:Experimental Observation of IntermittencyDynamics of Impact Oscillator with Dry FrictionAn Investigation of the Dynamic System with ImpactsSystems with Impacts:Some Aspects of the Dynamical Behavior of the Impact Force GeneratorOperation of the Multifender GeneratorSystems with Friction:Chaotic Behavior of Friction ForceComplex Behavior of a Quasiperiodically Forced Experimental System with Dry Friction Readership: Researchers in mechanical engineering and chaos/dynamical systems. Keywords:Impacts;Dry Friction;Chaotic Oscillations;Coefficient of Restitution;Nonlinear Vibrations;Grazing Impact;Impact Oscillator;Intermittency;Periodic Impact Motion;Impact Force Generator

Bifurcations and Chaos in Piecewise-smooth Dynamical Systems

Bifurcations and Chaos in Piecewise-smooth Dynamical Systems PDF

Author: Zhanybai T. Zhusubaliyev

Publisher: World Scientific

Published: 2003

Total Pages: 380

ISBN-13: 9789812564436

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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."

Synchronization in Coupled Chaotic Circuits and Systems

Synchronization in Coupled Chaotic Circuits and Systems PDF

Author: Chai Wah Wu

Publisher: World Scientific

Published: 2002-01-30

Total Pages: 188

ISBN-13: 9814490415

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This invaluable book studies synchronization of coupled chaotic circuits and systems, as well as its applications. It shows how one can use stability results in nonlinear control to derive synchronization criteria for coupled chaotic circuits and systems. It also discusses the use of Lyapunov exponents in deriving synchronization criteria. Both the case of two coupled systems and the case of arbitrarily coupled arrays of systems are considered. The book examines how synchronization properties in arrays of coupled systems are dependent on graph-theoretical properties of the underlying coupling topology. Finally, it studies some applications of synchronized chaotic circuits and systems, including spread spectrum and secure communications, coupled map lattices and graph coloring. Contents:Synchronization in Two Coupled Chaotic SystemsSynchronization in Coupled Arrays of Chaotic SystemsSynchronization in Coupled Arrays: Dynamic CouplingGraph Topology and SynchronizationLyapunov Exponents Approach to SynchronizationAppendices:Some Linear Systems Theory and Matrix TheoryGraph-Theoretical Definitions and NotationsStability, Lyapunov's Direct Method and Lyapunov ExponentsChaotic Circuits and Systems Readership: Graduate students, researchers and academics in electrical engineering and nonlinear science. Keywords:Reviews:“Wu's book presents a very readable introduction to the synchronization of chaos and its application in circuits … the book is mathematically oriented and adequately formal for anyone who is interested in getting a good background in this area.”Mathematical Reviews “The book may be useful for students and researchers interested in the synchronization theory as well as for those who are interested in practical designing of coupled chaotic circuits.”Mathematics Abstracts

Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities

Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities PDF

Author: Marian Wiercigroch

Publisher: World Scientific

Published: 2000

Total Pages: 466

ISBN-13: 9789810229276

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Annotation Consisting primarily of contributions written by engineers from Europe, Asia, and the US, this volume provides a general methodology for describing, solving, and analyzing discontinuous systems. The focus is on mechanical engineering problems where clearances, piecewise stiffness, intermittent contact, variable friction, or other forms of discontinuity occur. Practical applications include vibration absorbers, percussive drilling of hard materials, and dynamics of metal cutting. Of likely interest to new and experienced researchers working in the field of applied mathematics and physics, mechanical and civil engineering, and manufacturing. Lacks a subject index. Annotation copyrighted by Book News, Inc., Portland, OR.

Chaos for Engineers

Chaos for Engineers PDF

Author: Tomasz Kapitaniak

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 150

ISBN-13: 3642571433

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A desription of the new mathematical ideas in nonlinear dynamics in such a way that engineers can apply them to real physical systems.

The Physics of Chaos in Hamiltonian Systems

The Physics of Chaos in Hamiltonian Systems PDF

Author: George M. Zaslavsky

Publisher: World Scientific

Published: 2007

Total Pages: 337

ISBN-13: 1860947956

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This book aims to familiarize the reader with the essential properties of the chaotic dynamics of Hamiltonian systems by avoiding specialized mathematical tools, thus making it easily accessible to a broader audience of researchers and students. Unique material on the most intriguing and fascinating topics of unsolved and current problems in contemporary chaos theory is presented. The coverage includes: separatrix chaos; properties and a description of systems with non-ergodic dynamics; the distribution of Poincar‚ recurrences and their role in transport theory; dynamical models of the Maxwell's Demon, the occurrence of persistent fluctuations, and a detailed discussion of their role in the problem underlying the foundation of statistical physics; the emergence of stochastic webs in phase space and their link to space tiling with periodic (crystal type) and aperiodic (quasi-crystal type) symmetries. This second edition expands on pseudochaotic dynamics with weak mixing and the new phenomenon of fractional kinetics, which is crucial to the transport properties of chaotic motion. The book is ideally suited to all those who are actively working on the problems of dynamical chaos as well as to those looking for new inspiration in this area. It introduces the physicist to the world of Hamiltonian chaos and the mathematician to actual physical problems.The material can also be used by graduate students.

Chaos Bifurcations and Fractals Around Us

Chaos Bifurcations and Fractals Around Us PDF

Author: Wanda Szempli

Publisher: World Scientific

Published: 2003

Total Pages: 117

ISBN-13: 9812386890

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During the last twenty years, a large number of books on nonlinear chaotic dynamics in deterministic dynamical systems have appeared. These academic tomes are intended for graduate students and require a deep knowledge of comprehensive, advanced mathematics. There is a need for a book that is accessible to general readers, a book that makes it possible to get a good deal of knowledge about complex chaotic phenomena in nonlinear oscillators without deep mathematical study.Chaos, Bifurcations and Fractals Around Us: A Brief Introduction fills that gap. It is a very short monograph that, owing to geometric interpretation complete with computer color graphics, makes it easy to understand even very complex advanced concepts of chaotic dynamics. This invaluable publication is also addressed to lecturers in engineering departments who want to include selected nonlinear problems in full time courses on general mechanics, vibrations or physics so as to encourage their students to conduct further study.

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