Authors:
- Clearly illustrates the nature of nonlinear phenomena by introducing a real mechanical model, the SD oscillator, which offers an effectives model for describing geometrical nonlinearities
- Opens a new perspective on the inner workings of the real world through this simple actual mechanical model without any truncation
- Offers an opportunity to broaden our conventional nonlinear understanding to the unconventional nonlinear systems with applications in engineering and interdisciplinary areas
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Tracts in Mechanical Engineering (STME)
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Table of contents (17 chapters)
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Front Matter
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Back Matter
About this book
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 the 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.
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Authors and Affiliations
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School of Astronautics, Harbin Institute of Technology, Harbin, China
Qingjie Cao
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Laboratoire de Mcanique et d’Acoustique , Marseille Cedex 20, France
Alain Léger
Bibliographic Information
Book Title: A Smooth and Discontinuous Oscillator
Book Subtitle: Theory, Methodology and Applications
Authors: Qingjie Cao, Alain Léger
Series Title: Springer Tracts in Mechanical Engineering
DOI: https://doi.org/10.1007/978-3-662-53094-8
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2017
Hardcover ISBN: 978-3-662-53092-4Published: 18 April 2017
Softcover ISBN: 978-3-662-57110-1Published: 25 July 2018
eBook ISBN: 978-3-662-53094-8Published: 27 September 2016
Series ISSN: 2195-9862
Series E-ISSN: 2195-9870
Edition Number: 1
Number of Pages: XIX, 262
Number of Illustrations: 77 b/w illustrations, 54 illustrations in colour
Topics: Vibration, Dynamical Systems, Control, Applications of Nonlinear Dynamics and Chaos Theory, Classical Mechanics, Mathematical Modeling and Industrial Mathematics