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Regular and Chaotic Oscillations de Polina S. Landa

Regular and Chaotic Oscillations: Foundations of Engineering Mechanics

Autor Polina S. Landa
en Limba Engleză Hardback – apr 2001
In this book the modern theory of both regular and chaotic nonlinear oscillations is set out, primarily, as applied to mechanical problems. The material is presented in a nontraditional manner with emphasis on the new results of the theory obtained partially by the author, who is one of the leading experts in the area. Among the up-to-date topics are synchronization and chaotization of self-oscillatory systems and the influence of weak random vibrations on the modification of characteristics and behavior of nonlinear systems. One of the purposes of the book is to enable readers to gain a thorough understanding of this theory and to show that it can be very useful in engineering investigations. The primary audience for this book is researchers working with different oscillatory processes and students interested in a thorough study of the general laws and applications of the theory of nonlinear oscillations.
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Specificații

ISBN-13: 9783540410010
ISBN-10: 3540410015
Pagini: 400
Ilustrații: XII, 397 p. 1 illus.
Dimensiuni: 155 x 235 x 29 mm
Greutate: 0.7 kg
Ediția:2001
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Foundations of Engineering Mechanics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

1. Introduction.- 1.1 The importance of oscillation theory for engineering mechanics.- 1.2 Classification of dynamical systems. Systems with conservation of phase volume and dissipative systems.- 1.3 Different types of mathematical models and their functions in studies of concrete systems.- 1.4 Phase space of autonomous dynamical systems and the number of degrees of freedom.- 1.5 The subject matter of the book.- 2. The main analytical methods of studies of nonlinear oscillations in near-conservative systems.- 2.1 The van der Pol method.- 2.2 The asymptotic Krylov-Bogolyubov method.- 2.3 The averaging method.- 2.4 The averaging method in systems incorporating fast and slow variables.- 2.5 The Whitham method.- I. Oscillations in Autonomous Dynamical Systems.- 3. General properties of autonomous dynamical systems.- 4. Examples of natural oscillations in systems with one degree of freedom.- 5. Natural oscillations in systems with many degrees of freedom. Normal oscillations.- 6. Self-oscillatory systems with one degree of freedom.- 7. Self-oscillatory systems with one and a half degrees of freedom.- 8. Examples of self-oscillatory systems with two or more degrees of freedom.- 9. Synchronization and chaotization of self-oscillatory systems by an external harmonic force.- 10. Interaction of two self-oscillatory systems. Synchronization and chaotization of self-oscillations.- 11. Interaction of three or more self-oscillatory systems.- II. Oscillations in Nonautonomous Systems.- 12. Oscillations of nonlinear systems excited by external periodic forces.- 13. Parametric excitation of oscillations.- 14. Changes in the dynamical behavior of nonlinear systems induced by high-frequency vibration or by noise.- A. Derivation of the approximate equation for the one-dimensional probability density.- References.

Recenzii

From the reviews of the first edition:
"The present book … gives an up to date overview of recent developments, especially focusing on work done in the countries of the former Soviet Union. In this respect it is a gold mine for readers who have already some similarity with the theory of nonlinear oscillations, because 375 references are listed. … For those readers who want to get an overview on modern developments of oscillation theory and their applications in the sciences, the book will be certainly an excellent choice." (H. Troger, Zentralblatt MATH, Vol. 980, 2002)

Textul de pe ultima copertă

In the present book the modern theory of non-linear oscilla- tions both regular and chaotic, is set out, primarily, as applied to mechanical problems. The material is presented in a non-traditional manner with emphasizing of the new results of the theory otained partially by the author, who is one of the leading experts in the area. Among the up-to-date topics are synchronization and chaotization of self-oscillatory sy- stems, the influence of weak random vibration on modificati- on of characteristics and behavior of the non-linear systems etc. One of the purposes of the book is to convince the rea- ders of the necessity of a thorough study of this theory and to show that it can be very useful in engineering investiga- tions. The primary readers for this book are researchers working with different oscillatory processes, and both un- der-graduate and post-graduate students interested in a deep study of the general laws and applications of the theory of nonlinear oscillations. The instructors can find here new materials for lecturess and optinal courses.

Caracteristici

Presented in a non-traditional manner with emphasis on the new result in the theory obtained partially by the author, who is one of the leading experts in the area Includes modern topics such as synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration Includes supplementary material: sn.pub/extras