An Introduction To Nonlinear Oscillations

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Introduction To Nonlinear Oscillations

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Author : Vladimir I. Nekorkin
language : en
Publisher: John Wiley & Sons
Release Date : 2015-04-01

Introduction To Nonlinear Oscillations written by Vladimir I. Nekorkin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-01 with Science categories.

A systematic outline of the basic theory of oscillations, combining several tools in a single textbook. The author explains fundamental ideas and methods, while equally aiming to teach students the techniques of solving specific (practical) or more complex problems. Following an introduction to fundamental notions and concepts of modern nonlinear dynamics, the text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications. With each chapter including exercises and solutions, including computer problems, this book can be used in courses on oscillation theory for physics and engineering students. It also serves as a good reference for students and scientists in computational neuroscience.

An Introduction To Nonlinear Oscillations

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Author : Ronald E. Mickens
language : en
Publisher: CUP Archive
Release Date : 1981

An Introduction To Nonlinear Oscillations written by Ronald E. Mickens and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Science categories.

An introductory account of the equations describing nonlinear oscillations & the methods for solving them.

Nonlinear Oscillations Dynamical Systems And Bifurcations Of Vector Fields

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Author : John Guckenheimer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21

Nonlinear Oscillations Dynamical Systems And Bifurcations Of Vector Fields written by John Guckenheimer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Mathematics categories.

From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2

Nonlinear Oscillations And Waves In Dynamical Systems

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Author : Polina Solomonovna Landa
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-02-29

Nonlinear Oscillations And Waves In Dynamical Systems written by Polina Solomonovna Landa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-02-29 with Mathematics categories.

This volume is an up-to-date treatment of the theory of nonlinear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified point of view. Also, the relation between the theory of oscillations and waves, nonlinear dynamics and synergetics is discussed. One of the purposes of this book is to convince readers of the necessity of a thorough study of the theory of oscillations and waves, and to show that such popular branches of science as nonlinear dynamics, and synergetic soliton theory, for example, are in fact constituent parts of this theory. Audience: This book will appeal to researchers whose work involves oscillatory and wave processes, and students and postgraduates interested in the general laws and applications of the theory of oscillations and waves.

Nonlinear Oscillations In Mechanical Engineering

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Author : Alexander Fidlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-19

Nonlinear Oscillations In Mechanical Engineering written by Alexander Fidlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-19 with Technology & Engineering categories.

"Nonlinear Oscillations in Mechanical Engineering" explores the effects of nonlinearities encountered in applications in that field. Since the nonlinearities are caused, first of all, by contacts between different mechanical parts, the main part of this book is devoted to oscillations in mechanical systems with discontinuities caused by dry friction and collisions. Another important source of nonlinearity which is covered is that caused by rotating unbalanced parts common in various machines as well as variable inertias occurring in all kinds of crank mechanisms. This book is written for advanced undergraduate and postgraduate students, but it may be also helpful and interesting for both theoreticians and practitioners working in the area of mechanical engineering at universities, in research labs or institutes and especially in the R and D departments within industrial firms.

An Introduction To Nonlinear Chemical Dynamics

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Author : Irving R. Epstein
language : en
Publisher: Oxford University Press
Release Date : 1998-10-22

An Introduction To Nonlinear Chemical Dynamics written by Irving R. Epstein and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-22 with Science categories.

Just a few decades ago, chemical oscillations were thought to be exotic reactions of only theoretical interest. Now known to govern an array of physical and biological processes, including the regulation of the heart, these oscillations are being studied by a diverse group across the sciences. This book is the first introduction to nonlinear chemical dynamics written specifically for chemists. It covers oscillating reactions, chaos, and chemical pattern formation, and includes numerous practical suggestions on reactor design, data analysis, and computer simulations. Assuming only an undergraduate knowledge of chemistry, the book is an ideal starting point for research in the field. The book begins with a brief history of nonlinear chemical dynamics and a review of the basic mathematics and chemistry. The authors then provide an extensive overview of nonlinear dynamics, starting with the flow reactor and moving on to a detailed discussion of chemical oscillators. Throughout the authors emphasize the chemical mechanistic basis for self-organization. The overview is followed by a series of chapters on more advanced topics, including complex oscillations, biological systems, polymers, interactions between fields and waves, and Turing patterns. Underscoring the hands-on nature of the material, the book concludes with a series of classroom-tested demonstrations and experiments appropriate for an undergraduate laboratory.

Nonlinear Oscillations

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Author : Ali H. Nayfeh
language : en
Publisher: John Wiley & Sons
Release Date : 2008-09-26

Nonlinear Oscillations written by Ali H. Nayfeh and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-26 with Science categories.

Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses simple physical examples to explain nonlinear dispersive and nondispersive waves. The notation is unified and the analysis modified to conform to discussions. Solutions are worked out in detail for numerous examples, results are plotted and explanations are couched in physical terms. The book contains an extensive bibliography.

Nonlinear Oscillations In Physical Systems

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Author : Chihiro Hayashi
language : en
Publisher:
Release Date : 1985

Nonlinear Oscillations In Physical Systems written by Chihiro Hayashi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Science categories.

Many of today's most exciting questions in the physical and life sciences concern the behavior of nonlinear systems, especially the onset of chaotic behavior under deterministic conditions. Available for the first time in paperback, this book offers a fundamental explanation of nonlinear oscillations in physical systems. Originally intended for electrical engineers, this book remains an important reference for the increasing numbers of researchers studying nonlinear phenomena in physics, chemical engineering, biology, medicine, and other fields. All problems in mechanics are basically nonlinear from the outset, and the linearizations commonly practiced are approximating devices. Focusing attention on those features of problems where nonlinearity results in distinctive new phenomena, the author stresses the relationship between analysis and experiment.

Truly Nonlinear Oscillations

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Author : Ronald E. Mickens
language : en
Publisher: World Scientific
Release Date : 2010

Truly Nonlinear Oscillations written by Ronald E. Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

This unique book provides a concise presentation of many of the fundamental strategies for calculating approximations to the oscillatory solutions of truly nonlinear (TNL) oscillator equations. The volume gives a general overview of the author''s work on harmonic balance, iteration and combined linearization-averaging methods. However, full discussions are also presented on parameter expansion procedures and a first-order averaging technique for TNL oscillators. The calculational basis of each method is clarified by applying them to a set of standard TNL oscillator equations. This allows a direct comparison to be made among the various methods. The book is self-contained and therefore suitable for both classroom use and self-study by students and professionals who desire to learn, understand, and apply these technique to the field of nonlinear oscillations.

Introduction To Nonlinear Dynamics For Physicists

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Author : H. D. I. Abarbanel
language : en
Publisher: World Scientific
Release Date : 1993

Introduction To Nonlinear Dynamics For Physicists written by H. D. I. Abarbanel and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.

This series of lectures aims to address three main questions that anyone interested in the study of nonlinear dynamics should ask and ponder over. What is nonlinear dynamics and how does it differ from linear dynamics which permeates all familiar textbooks? Why should the physicist study nonlinear systems and leave the comfortable territory of linearity? How can one progress in the study of nonlinear systems both in the analysis of these systems and in learning about new systems from observing their experimental behavior? While it is impossible to answer these questions in the finest detail, this series of lectures nonetheless successfully points the way for the interested reader. Other useful problems have also been incorporated as a study guide. By presenting both substantial qualitative information about phenomena in nonlinear systems and at the same time sufficient quantitative material, the author hopes that readers would learn how to progress on their own in the study of such similar material hereon.