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A Smooth and Discontinuous Oscillator

Theory, Methodology and Applications

  • Qingjie Cao
  • Alain Léger

Part of the Springer Tracts in Mechanical Engineering book series (SPTME)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Qingjie Cao, Alain Léger
    Pages 1-10
  3. Qingjie Cao, Alain Léger
    Pages 11-22
  4. Qingjie Cao, Alain Léger
    Pages 23-41
  5. Qingjie Cao, Alain Léger
    Pages 43-51
  6. Qingjie Cao, Alain Léger
    Pages 53-65
  7. Qingjie Cao, Alain Léger
    Pages 67-88
  8. Qingjie Cao, Alain Léger
    Pages 89-102
  9. Qingjie Cao, Alain Léger
    Pages 103-120
  10. Qingjie Cao, Alain Léger
    Pages 121-138
  11. Qingjie Cao, Alain Léger
    Pages 139-153
  12. Qingjie Cao, Alain Léger
    Pages 155-186
  13. Qingjie Cao, Alain Léger
    Pages 187-204
  14. Qingjie Cao, Alain Léger
    Pages 205-213
  15. Qingjie Cao, Alain Léger
    Pages 215-236
  16. Qingjie Cao, Alain Léger
    Pages 237-249
  17. Qingjie Cao, Alain Léger
    Pages 251-253
  18. Qingjie Cao, Alain Léger
    Pages E1-E1
  19. Back Matter
    Pages 255-262

About this book

Introduction

This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963.

This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and th

e perturbed chaotic attractors without any truncation, is of particular interest. 

Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.

Keywords

Bifurcation Behaviour Chaotic Motions Engineering Isolation Nonlinear Dynamics Nonlinear Systems Smooth and Discontinuous (SD) Smooth and Discontinuous (SD) Oscillator Structural Dynamics

Authors and affiliations

  • Qingjie Cao
    • 1
  • Alain Léger
    • 2
  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinChina
  2. 2.Laboratoire de Mcanique et d’Acoustique Marseille Cedex 20France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-53094-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2017
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-662-53092-4
  • Online ISBN 978-3-662-53094-8
  • Series Print ISSN 2195-9862
  • Series Online ISSN 2195-9870
  • Buy this book on publisher's site
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