© 2014

Strongly Nonlinear Oscillators

Analytical Solutions


Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Livija Cveticanin
    Pages 1-3
  3. Livija Cveticanin
    Pages 5-15
  4. Livija Cveticanin
    Pages 17-48
  5. Livija Cveticanin
    Pages 49-85
  6. Livija Cveticanin
    Pages 87-126
  7. Livija Cveticanin
    Pages 127-160
  8. Livija Cveticanin
    Pages 161-189
  9. Livija Cveticanin
    Pages 191-221
  10. Back Matter
    Pages 223-239

About this book


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.


Chaos in Oscillators Deterministic Chaos Non-ideal Mechanical System Oscillators with Time-Variable Parameters Solving Nonlinear Oscillator Equations Strong Nonlinear Vibration Two-Degree-Of-Freedom Oscillator Waves and Oscillations

Authors and affiliations

  1. 1.Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia

About the authors

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

Bibliographic information


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)