Lecture Notes in Applied and Computational Mechanics

Nonlinear Dynamics

Between Linear and Impact Limits

Authors: Pilipchuk, Valery N.

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  • Offers a systematic description for non-smooth time transformations and related analytical and numerical algorithms
  • Bridges linear and strongly nonlinear dynamics by showing how to switch the physical basis when approaching the area of severe (impact) nonlinearities
  • Presents a unified physical basis for analyses of vibrations with essentially non-harmonic or discontinuous temporal shapes
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Hardcover $249.99
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Softcover $199.99
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About this book

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.

Reviews

From the reviews:

“This book is based on a series of papers which the author published earlier. The main subject of this book is the concept of non-smooth time transformations (NSTT) to describe periodic solutions of essentially nonlinear differential equations. … This book is suitable for scientists interested in applied mathematics, in particular those interested in constructing (approximations of) periodic solutions for differential equations.” (Wim T. van Horssen, Mathematical Reviews, Issue 2012 j)

“The content of this book is built on a new physical idea that the effectiveness of linear and weakly nonlinear dynamic theories is due to the spatio-temporal nature of harmonic motions associated with subgroup of rigid-body rotations. … this original book will be of interest to the experts, professors and post-graduate students in various areas of nonlinear physics, fundamental and engineering mechanics, applied mathematics, and other fields of research dealing with nonlinear dynamic models, non-smooth or discontinuous processes.” (Anatoly Martynyuk, Zentralblatt MATH, Vol. 1202, 2011)


Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $149.00
price for USA in USD
  • ISBN 978-3-642-12799-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $249.99
price for USA in USD
  • ISBN 978-3-642-12798-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $199.99
price for USA in USD
  • ISBN 978-3-642-26353-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Dynamics
Book Subtitle
Between Linear and Impact Limits
Authors
Series Title
Lecture Notes in Applied and Computational Mechanics
Series Volume
52
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-12799-1
DOI
10.1007/978-3-642-12799-1
Hardcover ISBN
978-3-642-12798-4
Softcover ISBN
978-3-642-26353-8
Series ISSN
1613-7736
Edition Number
1
Number of Pages
XI, 364
Topics