Description
Book SynopsisPendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom. This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multiplicative periodic and random forces. No preliminary knowledge, such as complex mathematical or numerical methods, is required from a reader other than undergraduate courses in mathematical physics. A wide group of researchers, along with students and teachers will, thus, benefit from this definitive book on nonlinear dynamics.
Table of ContentsPendulum Equations; Applications; Phase Space; Poincare Sections; Lyapunov Exponents; Spectral Analysis; Transition to Chaos; Analytic Methods (Feigenbaum, Melnikov); Parametric Driving; Brownian Motion; Overdamped; Spring; Double and Spherical Pendula.
