Introduction to nonlinear oscillations /

• Main Author: Nekorkin, Vladimir I.
• Format: eBook
• Language: English
• Published: Weinheim : Wiley-VCH, 2015.
• Subjects: Nonlinear oscillations.; Science.; SCIENCE > Physics > Mathematical & Computational.; SCIENCE > Mechanics > General.; SCIENCE > Mechanics > Solids.; Electronic books.

A systematic outline of the basic theory of oscillations, combining several tools in a single textbook. The author explains fundamental ideas and methods, while equally aiming to teach students the techniques of solving specific (practical) or more complex problems. Following an introduction to fund...

Table of Contents:

• Introduction to the Theory of Oscillations
• One-Dimensional Dynamics
• Stability of Equilibria. A Classification of Equilibria of Two-Dimensional Linear Systems
• Analysis of the Stability of Equilibria of Multidimensional Nonlinear Systems
• Linear and Nonlinear Oscillators
• Basic Properties of Maps
• Limit Cycles
• Basic Bifurcations of Equilibria in the Plane
• Bifurcations of Limit Cycles. Saddle Homoclinic Bifurcation
• The Saddle-Node Homoclinic Bifurcation. Dynamics of Slow-Fast Systems in the Plane
• Dynamics of a Superconducting Josephson Junction
• The Van der Pol Method. Self-Sustained Oscillations and Truncated Systems
• Forced Oscillations of a Linear Oscillator
• Forced Oscillations in Weakly Nonlinear Systems with One Degree of Freedom
• Forced Synchronization of a Self-Oscillatory System with a Periodic External Force
• Parametric Oscillations
• Answers to Selected Exercises.