Overview
- Opens new possibilities of the application of the averaging method to the solution of problems in mechanics, radio engineering, and control
Part of the book series: Mathematics and Its Applications (MAIA, volume 567)
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Table of contents (5 chapters)
Keywords
About this book
In contrast to other books devoted to the averaging method and the method of integral manifolds, in the present book we study oscillation systems with many varying frequencies. In the process of evolution, systems of this type can pass from one resonance state into another. This fact considerably complicates the investigation of nonlinear oscillations.
In the present monograph, a new approach based on exact uniform estimates of oscillation integrals is proposed. On the basis of this approach, numerous completely new results on the justification of the averaging method and its applications are obtained and the integral manifolds of resonance oscillation systems are studied.
This book is intended for a wide circle of research workers, experts, and engineers interested in oscillation processes, as well as for students and post-graduate students specialized in ordinary differential equations.
Reviews
From the reviews:
"The present research monograph deals with the averaging method for multifrequency nonlinear systems of ordinary differential equations. It gives a careful and detailed exposition to recent achievements by the authors and their coworkers based on exact uniform estimates of oscillatory integrals. As a result, many new results on the justification of the averaging method and its applications are obtained ... ." (G. Teschl, Monashefte für Mathematik, Vol. 146 (2), 2005)
Authors and Affiliations
Bibliographic Information
Book Title: Multifrequency Oscillations of Nonlinear Systems
Authors: A. Samoilenko, R. Petryshyn
Series Title: Mathematics and Its Applications
DOI: https://doi.org/10.1007/1-4020-2031-7
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media Dordrecht 2004
Hardcover ISBN: 978-1-4020-2030-8Published: 07 July 2004
Softcover ISBN: 978-90-481-6574-2Published: 15 December 2010
eBook ISBN: 978-1-4020-2031-5Published: 11 April 2006
Edition Number: 1
Number of Pages: VI, 317
Topics: Ordinary Differential Equations, Partial Differential Equations, Fourier Analysis, Functional Analysis, Applications of Mathematics