Undergraduate Lecture Notes in Physics

Strongly Nonlinear Oscillators

Analytical Solutions

Authors: Cveticanin, Livija

  • Provides the unique analytical solving procedure for any strong nonlinear oscillator
  • Includes many examples for practical applications
  • Discusses chaos in ideal and nonlinear pure nonlinear oscillators
  • Supports learning with end-of-chapter exercises and a solution manual
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  • ISBN 978-3-319-05272-4
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About this Textbook

This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for professionals and engineers who apply these techniques to the field of nonlinear oscillations.

About the authors

Prof. Dr. Livija Cveticanin (Mrs.)
University of Novi Sad
Faculty of Technical Sciences
Trg. D. Obradovica 6
21000 Novi Sad
Serbia
phone: +381-21-485-2237
affiliation: University of Novi Sad, Serbia

Reviews

From the book reviews:

“This book is devoted to analysis of solutions of the second-order ordinary differential equations (or systems) which describe oscillations of mechanical (and related) systems. … the book can be recommended to engineers as a good source of methods and examples.” (Henryk Żołądek, Mathematical Reviews, January, 2015)


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Table of contents (8 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-05272-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Strongly Nonlinear Oscillators
Book Subtitle
Analytical Solutions
Authors
Series Title
Undergraduate Lecture Notes in Physics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-05272-4
DOI
10.1007/978-3-319-05272-4
Series ISSN
2192-4791
Edition Number
1
Number of Pages
IX, 239
Number of Illustrations and Tables
62 b/w illustrations, 12 illustrations in colour
Topics