Front Cover; Nonlinear System Analysis; Copyright Page; Foreword; Preface; Table of Contents; Chapter I. Linearity and Nonlinearity; 1. An Example of a Nonlinear System: The Simple Pendulum; 2. Conservative Oscillators; 3. Approximate Solutions of the Pendulum Equation; 4. Exact Solution by Elliptic Integral; 5. Representation in a Phase Plane; 6. Nonlinear Oscillator with Damping; 7. Simple Pendulum with Forcing Function. Resonance; References; Chapter II. Self-Oscillatory Systems; Introduction; 1. Electronic Oscillators; 2. Phase-Plane Representation; 3. Cauchy-Lipschitz Theorem. 4. Geometric Study of Periodic Solutions5. Analytic Approaches to Periodic Phenomena; 6. Synchronization of Self-Oscillators; 7. Subharmonic Response; References; Chapter III. Classification of Singularities; 1. Singular Points; 2. Distribution of Singular Points in Phase-Plane R2; 3. Static and Dynamic Systems; 4. Extension of the Theory: Sources, Sinks, and Transformation Points; 5. Transformations of the Vector Field; 6. Three-Dimensional Singularities; References; Chapter IV. Systems with Several Degrees of Freedom; 1. Introduction; 2. Example of a Conservative Oscillator. 3. Nonlinear Oscillations in a Particle Accelerator4. Self-Sustained Oscillators with Two Degrees of Freedom; 5. Normal Vibrations on Nonlinear Systems; References; Chapter V. Equivalent Linearization; 1. Stating the Problem; 2. A Model in Classical Optics; 3. Introduction to the Optimal Linearization Method; 4. Similarity with Fourier's Method; 5. Optimal Linear Operator; 6. Iteration of the Procedure; 7. The Describing Function; 8. Additive Property of the Describing Function; 9. Matrix Calculus in the Analysis of Nonlinear Systems; References; Chapter VI. The Describing Function Method. 1. Equation of Feedback Loops2. Linear and Nonlinear Feedback Loops; 3. Nyquist's Diagram; 4. Mikaïlov's Hodograph; 5. Generalization of Mikaïlov's Hodograph for Nonlinear Systems; 6. Applications to Autonomous Systems; 7. Applications to Nonautonomous Systems; 8. Sensitivity with Respect to Small Changes in Parameters; 9. Retarded Actions; 10. Multiple-Input Describing Function; References; Chapter VII. Nonlinear Equations with Periodic Coefficients; Introduction; 1. Perturbation Method; 2. Stepwise Method: Application to the Orbital Stability Problem in a Synchrotron. 3. Hamiltonian Representation4. The Smooth Approximation; References; Chapter VIII. System Response to Random Inputs; 1. Campbell's Theorem; 2. Fokker-Planck-Kolmogorov Method; 3. Solution of the Fokker-Planck-Kolmogorov Equation Based on Campbell's Theorem; References; Chapter IX. Random Fluctuations of Self-Oscillators; Introduction; 1. Berstein's Method; 2. Blaquiere's Method; 3. Lerner's Quasi-Linear Method; 4. Flicker Noise; 5. Error in Frequency Measurement Using a Finite Time t'; 6. Application to Masers; References; Appendix: Sinusoidal Modes of Electromagnetic Resonators