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Applied Asymptotic Methods in Nonlinear Oscillations : SOLID MECHANICS AND ITS APPLICATIONS - IU.A. Mitropol'skii

Applied Asymptotic Methods in Nonlinear Oscillations

SOLID MECHANICS AND ITS APPLICATIONS

Hardcover Published: 31st July 1997
ISBN: 9780792346050
Number Of Pages: 342

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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. BogoliĀ­ 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 basiĀ­ 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.

Preface
Free Oscillation of Quasi-Linear Systemsp. 1
Self-excited Oscillationsp. 58
Forced Oscillationsp. 107
Parametrically-excited Oscillationsp. 196
Interaction of Nonlinear Oscillationsp. 245
Averaging Methodp. 282
Principal Coordinatesp. 327
Some Trigonometric Formulae Often Used in the Averaging Methodsp. 331
Referencesp. 332
Indexp. 336
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792346050
ISBN-10: 079234605X
Series: SOLID MECHANICS AND ITS APPLICATIONS
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 342
Published: 31st July 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 2.54
Weight (kg): 0.68