Overview
- First systematic description for the non smooth time transformations and related analytical and numerical algorithms
- Bridges the gap between 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
Part of the book series: Lecture Notes in Applied and Computational Mechanics (LNACM, volume 52)
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Table of contents (14 chapters)
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)
Authors and Affiliations
Bibliographic Information
Book Title: Nonlinear Dynamics
Book Subtitle: Between Linear and Impact Limits
Authors: Valery N. Pilipchuk
Series Title: Lecture Notes in Applied and Computational Mechanics
DOI: https://doi.org/10.1007/978-3-642-12799-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2010
Softcover ISBN: 978-3-642-26353-8Published: 28 June 2012
eBook ISBN: 978-3-642-12799-1Published: 09 May 2010
Series ISSN: 1613-7736
Series E-ISSN: 1860-0816
Edition Number: 1
Number of Pages: XI, 364
Topics: Classical Mechanics, Vibration, Dynamical Systems, Control, Engineering, general, Complexity