Bifurcation and Chaos in Nonsmooth Mechanical Systems
Bifurcation and Chaos in Nonsmooth Mechanical Systems

Author: Jan Awrejcewicz

Publisher: World Scientific

Published: 2003

Total Pages: 564

ISBN-13: 9812384596

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This 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.

Applied Nonlinear Dynamics And Chaos Of Mechanical Systems With Discontinuities
Applied Nonlinear Dynamics And Chaos Of Mechanical Systems With Discontinuities

Author: Bram De Kraker

Publisher: World Scientific

Published: 2000-04-28

Total Pages: 462

ISBN-13: 9814497908

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Rapid developments in nonlinear dynamics and chaos theory have led to publication of many valuable monographs and books. However, most of these texts are devoted to the classical nonlinear dynamics systems, for example the Duffing or van der Pol oscillators, and either neglect or refer only briefly to systems with motion-dependent discontinuities. In engineering practice a good part of problems is discontinuous in nature, due to either deliberate reasons such as the introduction of working clearance, and/or the finite accuracy of the manufacturing processes.The main objective of this volume is to provide a general methodology for describing, solving and analysing discontinuous systems. It is compiled from the dedicated contributions written by experts in the field of applied nonlinear dynamics and chaos.The main 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.

Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos

Author: Steven H. Strogatz

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 532

ISBN-13: 0429961111

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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Author: John Guckenheimer

Publisher: Springer Science & Business Media

Published: 2013-11-21

Total Pages: 475

ISBN-13: 1461211409

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An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Chaos, Bifurcations And Fractals Around Us: A Brief Introduction
Chaos, Bifurcations And Fractals Around Us: A Brief Introduction

Author: Wanda Szemplinska-stupnicka

Publisher: World Scientific

Published: 2003-11-11

Total Pages: 117

ISBN-13: 981448363X

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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.

Bifurcation and Chaos in Nonsmooth Mechanical Systems
Bifurcation and Chaos in Nonsmooth Mechanical Systems

Author: Jan Awrejcewicz

Publisher: World Scientific

Published: 2003

Total Pages: 566

ISBN-13: 9789812564801

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This book presents the theoretical frame for studying lumped nonsmoothdynamical systems: the mathematical methods are recalled, and adaptednumerical methods are introduced (differential inclusions, maximalmonotone operators, Filippov theory, Aizerman theory, etc.

Nonlinearity, Bifurcation and Chaos
Nonlinearity, Bifurcation and Chaos

Author: Jan Awrejcewicz

Publisher: BoD – Books on Demand

Published: 2012-10-24

Total Pages: 360

ISBN-13: 9535108166

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Nonlinearity, Bifurcation and Chaos - Theory and Application is an edited book focused on introducing both theoretical and application oriented approaches in science and engineering. It contains 12 chapters, and is recommended for university teachers, scientists, researchers, engineers, as well as graduate and post-graduate students either working or interested in the field of nonlinearity, bifurcation and chaos.

IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics
IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics

Author: Francis C. Moon

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 559

ISBN-13: 9401153205

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This book presents the latest research results in the area of applied nonlinear dynamics and chaos theory. Papers by three academic generations address new applications of nonlinear dynamics to mechanics, including fluid-structure interaction, machining and mechanics of solids, and many other applications.

Bifurcation and Chaos
Bifurcation and Chaos

Author: Jan Awrejcewicz

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 281

ISBN-13: 3642793290

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A collection of especially written articles describing the theory and application of nonlinear dynamics to a wide variety of problems encountered in physics and engineering. Each chapter is self-contained and includes an elementary introduction, an exposition of the state of the art, as well as details of recent theoretical, computational and experimental results. Included among the practical systems analysed are: hysteretic circuits, Josephson circuits, magnetic systems, railway dynamics, rotor dynamics and nonlinear dynamics of speech. This book provides important information and ideas for all mathematicians, physicists and engineers whose work in R & D or academia involves the practical consequences of chaotic dynamics.

Dynamics and Bifurcations of Non-Smooth Mechanical Systems
Dynamics and Bifurcations of Non-Smooth Mechanical Systems

Author: Remco I. Leine

Publisher: Springer Science & Business Media

Published: 2013-03-19

Total Pages: 245

ISBN-13: 3540443983

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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.