Affiliation:
1. Physikalisches Institut der Universität Frankfurt am Main, D-60054 Frankfurt am Main 1, Germany
Abstract
Using a driven damped pendulum as a demonstration model we illustrate some fundamental concepts of nonlinear dynamics. We find deterministic chaos in the motion of the pendulum by observing its sensitive dependence on the initial state. We calculate the corresponding Lyapunov exponents from the equation of motion. The largest exponent gives the average predictability time scale. We estimate fractal dimensions of the attractor by determining the Kaplan Yorke dimension. Further we investigate the organization of unstable periodic orbits embedded in the attractor of the pendulum.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)
Cited by
12 articles.
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2. Bibliography;Simulations of Oscillatory Systems;2015-02-05
3. Bibliography;Non-smooth Deterministic or Stochastic Discrete Dynamical Systems;2013-03-20
4. Extraordinary oscillations of an ordinary forced pendulum;European Journal of Physics;2008-01-17
5. INVESTIGATION OF TRIPLE PENDULUM WITH IMPACTS USING FUNDAMENTAL SOLUTION MATRICES;International Journal of Bifurcation and Chaos;2004-12