Author: Nikolaĭ Nikolaevich Bogoli︠u︡bovPublisher: CRC Press
ISBN: 9780677200507
Category : Science
Languages : en
Pages : 556
Book Description
Asymptotic Methods in the Theory of Non-linear Oscillations
Author: Nikolaĭ Nikolaevich Bogoli︠u︡bovPublisher: CRC Press
ISBN: 9780677200507
Category : Science
Languages : en
Pages : 556
Book Description
Applied Asymptotic Methods in Nonlinear Oscillations
Author: Yuri A. MitropolskyPublisher: Springer Science & Business Media
ISBN: 9401588473
Category : Technology & Engineering
Languages : en
Pages : 352
Book Description
Many dynamical systems are described by differential equations that can be separated into one part, containing linear terms with constant coefficients, and a second part, relatively small compared with the first, containing nonlinear terms. Such a system is said to be weakly nonlinear. The small terms rendering the system nonlinear are referred to as perturbations. A weakly nonlinear system is called quasi-linear and is governed by quasi-linear differential equations. We will be interested in systems that reduce to harmonic oscillators in the absence of perturbations. This book is devoted primarily to applied asymptotic methods in nonlinear oscillations which are associated with the names of N. M. Krylov, N. N. Bogoli ubov and Yu. A. Mitropolskii. The advantages of the present methods are their simplicity, especially for computing higher approximations, and their applicability to a large class of quasi-linear problems. In this book, we confine ourselves basi cally to the scheme proposed by Krylov, Bogoliubov as stated in the monographs [6,211. We use these methods, and also develop and improve them for solving new problems and new classes of nonlinear differential equations. Although these methods have many applications in Mechanics, Physics and Technique, we will illustrate them only with examples which clearly show their strength and which are themselves of great interest. A certain amount of more advanced material has also been included, making the book suitable for a senior elective or a beginning graduate course on nonlinear oscillations.
Introduction to Nonlinear Oscillations
Author: Vladimir I. NekorkinPublisher: John Wiley & Sons
ISBN: 3527413308
Category : Science
Languages : en
Pages : 264
Book Description
Ein Überblick über die Methoden zu Studium der Existenz und Stabilität nichtlinearer Schwingungen. Dieses Lehrbuch präsentiert systematisch die Theorie von Bifurkationen für ein- und zweidimensionale dynamische Systeme, die die Grundlage dieser Methoden bildet.
Asymptotic Methods for Relaxation Oscillations and Applications
Author: Johan GrasmanPublisher: Springer Science & Business Media
ISBN: 1461210569
Category : Science
Languages : en
Pages : 229
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.
Asymptotic Methods in the Theory of Nonlinear Oscillations
Author: Nikolaĭ Nikolaevich Bogoli︠u︡bovPublisher:
ISBN:
Category : Asymptotes
Languages : en
Pages : 898
Book Description
Asymptotic Methods in the Theory of Non-linear Oscillations
Author: N. N. BogoliubovMethods Of Qualitative Theory In Nonlinear Dynamics (Part I)
Author: Leonid P ShilnikovPublisher: World Scientific
ISBN: 9814496421
Category : Science
Languages : en
Pages : 418
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 Poincaré, 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 students of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.
ANALYTICAL METHODS IN THE THEORY OF NON-LINEAR OSCILLATIONS
Author: Timothy P. CoffeyNonlinear Differential Equations and Dynamical Systems
Author: Ferdinand VerhulstPublisher: Springer Science & Business Media
ISBN: 3642614531
Category : Mathematics
Languages : en
Pages : 324
Book Description
For lecture courses that cover the classical theory of nonlinear differential equations associated with Poincare and Lyapunov and introduce the student to the ideas of bifurcation theory and chaos, this text is ideal. Its excellent pedagogical style typically consists of an insightful overview followed by theorems, illustrative examples, and exercises.
Nonlinear System Analysis
Author: Austin BlaquierePublisher: Elsevier
ISBN: 0323151663
Category : Technology & Engineering
Languages : en
Pages : 409
Book Description
Nonlinear System Analysis focuses on the study of systems whose behavior is governed by nonlinear differential equations. This book is composed of nine chapters that cover some problems that play a major role in engineering and physics. The opening chapter briefly introduces the difference between linear and nonlinear systems. Considerable chapters are devoted to engineering and physics related problems and their applications to particle accelerators, frequency measurements, and masers. Included in these chapters are important practical problems, such as synchronization, stability of systems with periodic coefficients, and effect of random disturbances. The remaining chapters examine random fluctuations of the motion and self-oscillators. This book is intended primarily for engineers and physicists.