Contents -- Preface -- List of Equations -- Chapter 1 Pendulum Equations -- 1.1 Mathematical pendulum -- 1.2 Period of oscillations -- 1.3 Underdamped pendulum -- 1.4 Nonlinear vs linear equation -- 1.5 Isomorphic models -- 1.5.1 Brownian motion in a periodic potential -- 1.5.2 Josephson junction -- 1.5.3 Fluxon motion in superconductors -- 1.5.4 Charge density waves -- 1.5.5 Laser gyroscope -- 1.5.6 Synchronization phenomena -- 1.5.7 Parametric resonance in anisotropic systems -- 1.5.8 Phase-locked loop -- 1.5.9 Dynamics of adatom subject to a time-periodic force -- 1.5.10 The Frenkel-Kontorova model (FK) -- 1.5.11 Solitons in optical lattices -- 1.5.12 Other applications -- 1.6 General concepts -- 1.6.1 Phase space -- 1.6.2 Poincare sections and strange attractors -- 1.6.3 Lyapunov exponent -- 1.6.4 Correlation function -- 1.6.5 Spectral analysis -- Chapter 2 Deterministic Chaos -- 2.1 Damped, periodically driven pendulum -- 2.1.1 Transition to chaos -- 2.1.2 Two external periodic fields -- 2.1.3 Dependence on driving frequency -- 2.1.4 Role of damping -- 2.1.5 Symmetry and chaos -- 2.1.6 Diffusion in a chaotic pendulum -- 2.2 Analytic methods -- 2.2.1 Period-doubling bifurcations -- 2.2.2 Melnikov method -- 2.3 Parametric periodic force -- 2.3.1 Pendulum with vertically oscillating suspension point -- 2.3.2 Transition to chaos -- 2.3.3 Melnikov method -- 2.3.4 Parametric periodic non-harmonic force -- 2.3.5 Downward and upward equilibrium configurations -- 2.3.6 Boundary between locked and running solutions -- 2.3.7 Pendulum with horizontally oscillating suspension point -- 2.3.8 Pendulum with both vertical and horizontal oscillations of the suspension point -- 2.4 Parametrically driven pendulum -- 2.5 Periodic and constant forces -- 2.5.1 Melnikov method -- 2.6 Parametric and constant forces -- 2.6.1 Harmonic balance method.

2.6.2 Heteroclinic and homoclinic trajectories -- 2.6.3 Numerical calculations -- 2.7 External and parametric periodic forces -- Chapter 3 Pendulum subject to a Random Force -- 3.1 Noise -- 3.1.1 White noise and colored noise -- 3.1.2 Dichotomous noise -- 3.1.3 Langevin and Fokker-Planck equations -- 3.2 External random force -- 3.3 Constant and random forces -- 3.4 External periodic and random forces -- 3.4.1 Two sources of noise -- 3.4.2 Fokker-Planck equation -- 3.4.3 Ratchets -- 3.4.4 Absolute negative mobility -- 3.5 Pendulum with multiplicative noise -- 3.6 Parametric periodic and random forces -- 3.7 Damped pendulum subject to a constant torque, periodic force and noise -- 3.8 Overdamped pendulum -- 3.8.1 Additive white noise -- 3.8.2 Additive dichotomous noise -- 3.8.3 Multiplicative dichotomous noise -- 3.8.4 Additive and multiplicative white noise -- 3.8.5 Multiplicative dichotomous noise and additive white noise -- 3.8.6 Correlated additive noise and multiplicative noise -- Chapter 4 Systems with Two Degrees of Freedom -- 4.1 Spring pendulum -- 4.1.1 Dynamic equations -- 4.1.2 Chaotic behavior of a spring pendulum -- 4.1.3 Driven spring pendulum -- 4.2 Double pendulum -- 4.3 Spherical pendulum -- Chapter 5 Conclusions -- Bibliography -- Glossary -- Index.