Regular and Chaotic Oscillations of a Rotating Pendulum

Backhaus, Udo; Schlichting, H. Joachim. In: G. Marx (Ed.): Chaos in Education II. Vesprem (Hungary) 1987, pp. 312-317.

One reason of the great success of classical physics is the ability to predict the evolution of a system from which the dynamics (equation of motion) and the initial values are known. But this ability falls with  chaotic systems.  Because of the exponential Increase of small errors in the initial conditions of a chaotic system every prediction of its behaviour becomes Impossible in shortest time. For a long time physicists thought that the chaotic behaviour of a system is due to its complexity. But recently, one found that very simple systems may become chaotic, too. As important as this realisation is the manner of the transition from order to chaos. This transition follows some general patterns: the system announces the breakdown of the deterministic behaviour. Of course, the knowledge of these patterns is of great practical Interest. The rotating pendulum presented here allows to study the transitions between regular and chaotic motions by means of computational simulations. Thereby, complete Feigenbaum scenarios and other transitions may be obtained. The numerical resuits are described in more detail in.

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