Skip to main content
SpringerLink
Log in
Book cover

Strongly Nonlinear Oscillators

Analytical Solutions

  • Textbook
  • © 2014

Overview

Authors:
  1. Livija Cveticanin

    1. Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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
  • Includes supplementary material: sn.pub/extras

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (8 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • Livija Cveticanin
    Pages 1-3

  3. Nonlinear Oscillators

    • Livija Cveticanin
    Pages 5-15

  4. Pure Nonlinear Oscillator

    • Livija Cveticanin
    Pages 17-48

  5. Free Vibrations

    • Livija Cveticanin
    Pages 49-85

  6. Oscillators with Time Variable Parameters

    • Livija Cveticanin
    Pages 87-126

  7. Forced Vibrations

    • Livija Cveticanin
    Pages 127-160

  8. Two-Degree-of-Freedom Oscillator

    • Livija Cveticanin
    Pages 161-189

  9. Chaos in Oscillators

    • Livija Cveticanin
    Pages 191-221

  10. Back Matter

    Pages 223-239
    Download chapter PDF
Back to top

Keywords

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.

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)

Authors and Affiliations

  • Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

    Livija Cveticanin

About the author

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

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation