Analysis of Chaotic Dynamics. 1. Spacemodel

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Description: Unbalanced rotors exhibit a characteristic mechanical oscillation. Using non-linear Duffing equations the dynamics are recreated in a computer model with springing and damping depending on the excitation amplitude. The curve is supplemented by synthesizer acoustics. Analysis using phase curve, trajectories, Poincaré sections, the 3D-Model of a strange attractor and Ueda-diagram.
Duration: 21 mins 47 secs
Director: Edwin Kreuzer (Hamburg)
Credits: Year of publication: 1990
Year: 1988
Subjects: Mathematical analysis, Mathematical models, Computer graphics, Calculus
Segment 1: Determinstic non-linear dynamic systems show many different kinds of behaviour ranging from periodic oscillations to irregular chaotic motions. The last-named are fascinating but difficult to study. Normal modes of study often fail. Duffing's equation is shown and discussed. A physical model is shown to demonstrate further using various constant parametres, with the forcing amplitude varying.
Segment 2: An oscillation of period 1 a = 4. An oscillation of period 3 a = 9. Chaotic motions for 1 = 12. Stability diagrams. An acoustic experiment to demonstrate the different oscillation frequencies.
Segment 3: Graphs alone cannot always demonstrate the complexity of the situation. Poincare's so-called State Space does this. Two-dimensional representations of three-dimensional portraits.
Segment 4: Other representations of the various periods including a three-dimensional ring, and then a more complex model and the Poincare map. The development of the Strange Attractor and the difference bettween this and the Poincare Map.
Segment 5: Analysing a series of planes through the ring, we eventually return to our starting position. Credits.
Persistent URL: http://edina.ac.uk/purl/isan/0014-0000-3402-0000-0-0000-0000-0
Written and compiled by the British Universities Film & Video Council © BUFVC 2005
Subject classification by University of Edinburgh Library © 2006