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Nonlinear Dynamics

Between Linear and Impact Limits

  • Valery N. Pilipchuk

Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 52)

Table of contents

  1. Front Matter
  2. Valery N. Pilipchuk
    Pages 1-36
  3. Valery N. Pilipchuk
    Pages 37-49
  4. Valery N. Pilipchuk
    Pages 51-91
  5. Valery N. Pilipchuk
    Pages 93-129
  6. Valery N. Pilipchuk
    Pages 131-144
  7. Valery N. Pilipchuk
    Pages 145-178
  8. Valery N. Pilipchuk
    Pages 195-239
  9. Valery N. Pilipchuk
    Pages 241-244
  10. Valery N. Pilipchuk
    Pages 245-264
  11. Valery N. Pilipchuk
    Pages 265-273
  12. Valery N. Pilipchuk
    Pages 275-294
  13. Valery N. Pilipchuk
    Pages 295-303
  14. Valery N. Pilipchuk
    Pages 305-337
  15. Back Matter

About this book

Introduction

Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of “unusual” physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of Nonlinear Dynamics appeared to be very diverse, individual and technically complicated. This book makes an attempt to find a common ground for nonlinear dynamic analyses based on the existence of strongly nonlinear but quite simple counterparts to the linear models and tools. It is shown that, since the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, then translations and reflections, impact oscillators, and hyperbolic (Clifford’s) algebras must give rise to some “quasi impact” methodology. Such strongly nonlinear methods are developed in several chapters of this book based on the idea of non-smooth time substitutions. Although most of the illustrations are based on mechanical oscillators, the area of applications may include also electric, electro-mechanical, electrochemical and other physical models generating strongly anharmonic temporal signals or spatial distributions. Possible applications to periodic elastic structures with non-smooth or discontinuous characteristics are outlined in the final chapter of the book.

Keywords

NSTT Non-Smooth Processes Non-Smooth Temporal Transformations Nonlinear Dynamics Nonlinear Processes rotation vibration

Authors and affiliations

  • Valery N. Pilipchuk
    • 1
  1. 1.Professor (Research) Mechanical EngineeringWayne State UniversityDetroitUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-12799-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-12798-4
  • Online ISBN 978-3-642-12799-1
  • Series Print ISSN 1613-7736
  • Series Online ISSN 1860-0816
  • Buy this book on publisher's site