Analysis of Chaotic Dynamics. 1. Spacemodel
Description
| Title | Analysis of Chaotic Dynamics. 1. Spacemodel |
|---|---|
| Duration | 21 mins 47 secs |
| Collection | IWF Knowledge and Media GmbH |
| Language | |
| Country View on map | |
| Director | |
| Subjects | |
| Terms of Use | more… |
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.Credits
Year of publication: 1990
Segments
?Segment 1
Starts: 0:00
(4:05)
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
Starts: 4:05
(5:33)
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
Starts: 9:38
(5:28)
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
Starts: 15:06
(5:00)
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
Starts: 20:06
(1:41)
Analysing a series of planes through the ring, we eventually return to our starting position. Credits.
