Berlin 2005 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 40: Statistical Physics (General) I

DY 40.3: Vortrag

Dienstag, 8. März 2005, 10:45–11:00, TU H3010

The driven mathematical pendulum revisited: precision analysis of the stability — •C. Jung, S. Hankemeier, H. Hübener, A. Struck und B. Kramer — 1. Institut für theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany

The dynamics of the damped mathematical pendulum with a periodic driving force renders the important features in many even non-classical systems suchs as Josephson junctions or Bose-Einstein condensates. The nonlinear equation of motion reveals periodic and chaotic motion for different choices of parameters and initial conditions.

We investigate the stability of trajectories by integrating the equation of motion using highly accurate numerical algorithms. The dependence of the Lyapunov exponents on the damping constant and amplitude A and frequency ω of the driving force is systematically analyzed.

Regions of regular and chaotic motion are identified. We discuss a possible self-similar structure in a systematic map of Lyapunov exponents in the A-ω-plane.