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Strongly nonlinear oscillators : analytical solutions / Livija Cveticanin.

By: Material type: TextTextSeries: Undergraduate lecture notes in physicsPublication details: Switzerland : Springer, 2014.Description: ix, 239 p. ; illISBN:
  • 9783319052717
Subject(s): DDC classification:
  • 621.381533 23 C993
Contents:
1. Introduction -- 2. Nonlinear Oscillators -- 3. Pure Nonlinear Oscillator -- 4. Free Vibrations -- 5. Oscillators with Time-Variable Parameters -- 6. Forced Vibrations -- 7. Two-Degree-Of-Freedom Oscillator -- 8. Chaos in Oscillators-- Appendices-- Index.
Summary: 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 authors 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 621.381533 C993 (Browse shelf(Opens below)) Available 136039
Total holds: 0

Includes index.

1. Introduction --
2. Nonlinear Oscillators --
3. Pure Nonlinear Oscillator --
4. Free Vibrations --
5. Oscillators with Time-Variable Parameters --
6. Forced Vibrations --
7. Two-Degree-Of-Freedom Oscillator --
8. Chaos in Oscillators--
Appendices--
Index.

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 authors 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.

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