Applied Asymptotic Methods in Nonlinear Oscillations: 55 (Solid Mechanics and Its Applications, 55) - Hardcover

Mitropolsky, Yuri A.; Nguyen Van Dao

Hardcover

ISBN 10: 079234605X ISBN 13: 9780792346050

Publisher: Springer, 1997

Synopsis

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.

About this title

Synopsis

This volume addresses the application of asymptotic methods in nonlinear oscillations. Such methods see a large variety of applications in physics, mechanics and engineering. The advantages of using asymptotic methods in solving nonlinear problems are firstly simplicity, especially for computing higher approximations, and secondly their applicability to a large class of quasi-linear systems. The book is concerned with the applied aspects of the methods concerned and also contains problems relevant to the everyday practice of engineers, physicists and mathematicians. Usually, dynamics systems are classified and examined by their degrees of freedom. This text is constructed from another point of view based upon the originating mechanism of the oscillations: free oscillation, self-excited oscillation, forced oscillation, and parametrically excited oscillation. The text has been designed to cover material from the elementary to the more advanced, in increasing order of difficulty. It should be of intereest to both students and researchers in applied mathematics, physical and mechanical sciences, and engineering.

Edition details

• Publisher: Springer
• Publication date: 1997
• Language: English
• ISBN 10: 079234605X
• ISBN 13: 9780792346050
• Binding: Hardcover
• Number of pages: 352