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Asymptotic Approaches in Nonlinear Dynamics

New Trends and Applications

  • Jan Awrejcewicz
  • Igor V. Andrianov
  • Leonid I. Manevitch

Part of the Springer Series in Synergetics book series (SSSYN, volume 69)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Jan Awrejcewicz, Igor V. Andrianov, Leonid I. Manevitch
    Pages 1-12
  3. Jan Awrejcewicz, Igor V. Andrianov, Leonid I. Manevitch
    Pages 13-150
  4. Jan Awrejcewicz, Igor V. Andrianov, Leonid I. Manevitch
    Pages 151-251
  5. Jan Awrejcewicz, Igor V. Andrianov, Leonid I. Manevitch
    Pages 253-289
  6. Back Matter
    Pages 291-311

About this book

Introduction

How well is Nature simulated by the varied asymptotic models that imaginative scientists have invented? B. Birkhoff [52J This book deals with asymptotic methods in nonlinear dynamics. For the first time a detailed and systematic treatment of new asymptotic methods in combination with the Pade approximant method is presented. Most of the basic results included in this manuscript have not been treated but just mentioned in the literature. Providing a state-of-the-art review of asymptotic applications, this book will prove useful as an introduction to the field for novices as well a reference for specialists. Asymptotic methods of solving mechanical and physical problems have been developed by many authors. For example, we can refer to the excel­ lent courses by A. Nayfeh [119-122]' M. Van Dyke [154], E.J. Hinch [94J and many others [59, 66, 95, 109, 126, 155, 163, 50d, 59dJ. The main features of the monograph presented are: 1) it is devoted to the basic principles of asymp­ totics and its applications, and 2) it deals with both traditional approaches (such as regular and singular perturbations, averaging and homogenization, perturbations of the domain and boundary shape) and less widely used, new approaches such as one- and two-point Pade approximants, the distributional approach, and the method of boundary perturbations.

Keywords

Degrees of freedom Soliton asymptotic methods calculus linearity mechanics nonlinear dynamics oscillation

Authors and affiliations

  • Jan Awrejcewicz
    • 1
  • Igor V. Andrianov
    • 2
  • Leonid I. Manevitch
    • 3
  1. 1.Division of Control and Biomechanics (I-10)Technical University of LódzLódzPoland
  2. 2.Pridneprovye State Academy of Civil Engineering and ArchitectureDnepropetrovskUkraine
  3. 3.Institute of Chemical PhysicsRussian Academy of SciencesMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-72079-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-72081-9
  • Online ISBN 978-3-642-72079-6
  • Series Print ISSN 0172-7389
  • Buy this book on publisher's site
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