Asymptotic Methods in the Theory of Non-linear Oscillations PDF Download
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Author: Nikolaĭ Nikolaevich Bogoli︠u︡bov
Publisher: CRC Press
ISBN: 9780677200507
Category : Science
Languages : en
Pages : 556
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Book Description
Author: Nikolaĭ Nikolaevich Bogoli︠u︡bov
Publisher: CRC Press
ISBN: 9780677200507
Category : Science
Languages : en
Pages : 556
Get Book Here
Book Description
Author: Vladimir I. Nekorkin
Publisher: John Wiley & Sons
ISBN: 3527685421
Category : Science
Languages : en
Pages : 264
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Book Description
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.
Author: Johan Grasman
Publisher: Springer Science & Business Media
ISBN: 1461210569
Category : Science
Languages : en
Pages : 229
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Book Description
In various fields of science, notably in physics and biology, one is con fronted with periodic phenomena having a remarkable temporal structure: it is as if certain systems are periodically reset in an initial state. A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation oscillations requires a mathematical analysis which differs strongly from the well-known theory of almost linear oscillations. In this monograph the method of matched asymptotic expansions is employed to approximate the periodic orbit of a relaxation oscillator. As an introduction, in chapter 2 the asymptotic analysis of Van der Pol's equation is carried out in all detail. The problem exhibits all features characteristic for a relaxation oscillation. From this case study one may learn how to handle other or more generally formulated relaxation oscillations. In the survey special attention is given to biological and chemical relaxation oscillators. In chapter 2 a general definition of a relaxation oscillation is formulated.
Author: N. N. Bogoliubov
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: N. A. Bobylev
Publisher: Walter de Gruyter
ISBN: 9783110141320
Category : Mathematics
Languages : en
Pages : 292
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Book Description
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jürgen Appell, Würzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Toruń, Poland Vicenţiu D. Rădulescu, Kraków, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jürgen Appell. Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Tomasz W. Dłotko and Yejuan Wang, Critical Parabolic-Type Problems (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)
Author: Nikolaĭ Nikolaevich Bogoli︠u︡bov
Publisher:
ISBN:
Category : Asymptotes
Languages : en
Pages : 898
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Book Description
Author: D.M. Klimov
Publisher: CRC Press
ISBN: 1482265222
Category : Mathematics
Languages : en
Pages : 239
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Book Description
Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. Group-Theoretic Methods in Mechanics and Applied Mathematics systematizes the group analysis of the main postulates of classical and relativistic mechanics. Exact solutions are given for the following equations: dynamics of rigid body, heat transfer, wave, hydrodynamics, Thomas-Fermi, and more. The author pays particular attention to the application of group analysis to developing asymptotic methods for problems with small parameters. This book is designed for a broad audience of scientists, engineers, and students in the fields of applied mathematics, mechanics and physics.
Author: Nguyen Van Dao
Publisher: Springer Science & Business Media
ISBN: 9401141509
Category : Technology & Engineering
Languages : en
Pages : 341
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Book Description
This volume contains selected papers presented at the Symposium on "Recent Developments in Non-linear Oscillations of Mechanical Systems", held in Hanoi, Vietnam, from 2 - 5 March 1999. This Symposium was initiated and sponsored by the International Union of Theoretical and Applied Mechanics (lUI AM) and organised in conjunction with Vietnam National University, Hanoi. Ihe purpose of the Symposium was to bring together scientists active in different fields of oscillations with the aim to review the recent progress in theory of oscillations and engineering applications and to outline the prospects in its further achievements to then co-ordinate and direct research in this field to further co-operation between scientists and various scientific institutions. An International Scientific Committee was appointed by the Bureau of IUI AM with the following members: Nguyen Van Dao (Vietnam, Co-Chairman) E.J. Kreuzer (Germany, Co-Chairman) D.H. van Campen (The Netherlands) F.L. Chernousko (Russia) A.H. Nayfeh (U.S.A) Nguyen Xuan Hung (Vietnam) W.O. Schiehlen (Germany) J.M.T. Thompson (U.K) Y. Veda (Japan). This Committee selected the participants to be invited and the papers to be presented at the Symposium. As a result of this procedure, 52 active scientists from 16 countries responded to the invitation, and 42 papers were presented in lecture and poster discussion sessions.
Author: Ronald E Mickens
Publisher: World Scientific
ISBN: 9814466042
Category : Mathematics
Languages : en
Pages : 261
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Book Description
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.
Author: Leonid P. Shilnikov
Publisher: World Scientific
ISBN: 9789810233822
Category : Science
Languages : en
Pages : 420
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Book Description
Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need. Following the footsteps of Poincare, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form. In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced studentsof nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.
