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Asymptotic Approaches in Nonlinear Dynamics

New Trends and Applications

  • Book
  • © 1998

Overview

Authors:
  1. Jan Awrejcewicz

    1. Division of Control and Biomechanics (I-10), Technical University of Lódz, Lódz, Poland

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  2. Igor V. Andrianov

    1. Pridneprovye State Academy of Civil Engineering and Architecture, Dnepropetrovsk, Ukraine

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    You can also search for this author in PubMed   Google Scholar

  3. Leonid I. Manevitch

    1. Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia

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  • This book does not require sophisticated math-training.
  • It teaches by examples and gives the recipes for the practitioner.
  • This makes it a unique text in the nonlinear dynamic literature.

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

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introduction: Some General Principles of Asymptotology

    • Jan Awrejcewicz, Igor V. Andrianov, Leonid I. Manevitch
    Pages 1-12

  3. Discrete Systems

    • Jan Awrejcewicz, Igor V. Andrianov, Leonid I. Manevitch
    Pages 13-150

  4. Continuous Systems

    • Jan Awrejcewicz, Igor V. Andrianov, Leonid I. Manevitch
    Pages 151-251

  5. Discrete—Continuous Systems

    • Jan Awrejcewicz, Igor V. Andrianov, Leonid I. Manevitch
    Pages 253-289

  6. Back Matter

    Pages 291-311
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Keywords

About this book

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.

Authors and Affiliations

  • Division of Control and Biomechanics (I-10), Technical University of Lódz, Lódz, Poland

    Jan Awrejcewicz

  • Pridneprovye State Academy of Civil Engineering and Architecture, Dnepropetrovsk, Ukraine

    Igor V. Andrianov

  • Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia

    Leonid I. Manevitch

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