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Old 10-03-2006, 10:29 PM   #122
Erick Mead
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Dojo: Big Green Drum (W. Florida Aikikai)
Location: West Florida
Join Date: Jun 2005
Posts: 2,619
Re: What is "Aikido"?

David Skaggs wrote:
A link that explains in simple terms about human balance and motor control.

In your explanation of balancing the human body with gyroscopic movement of a chaotic figure eight, what is the direction of movement of the pattern?
I judge the shape from my own sense of the hip movement I feel and this is corroborated by the cyclic pattern in Figure 1 in the "Correlated Hip Motion" study, p. 3. you see one perspective of this motion in 2 dimensions. There is also the fact that the traverse across the leg quadrants provide two opposed points of static constraint -- driving all tracks to the center. The traverses across the shikaku quadrants have to be recovered in some cyclic dynamic, therefore strongly suggesting two major loops joined at the center.

To see the shape clearly you need a long observation time for the system to fill up its typical phase space, or path history. A 3D graph in the complex plane is usually the best manner of seeing the pattern dynamic. I understand what this sort of transform does, but I cannot do it.

A chaotic system observed long enough will fill up its characteristic phase space. In this case, it should be a fuzzy looking figure eight figure made up of full loops, minor loops and tightly folded reversal loops. The motion is reversible at any time without much loss of momentum (because the two eccentric points of rotation are in constant parity) in which case the path tracks back in reverse either along its immediate past trajectory as a closely folded loop in the same approximate curvature as the full loop, or as a minor excursion loop.

You can see major cycles as well as the minor cycles in that diagram. That may indicate a cardioid shape of the minor (interior loops) loops or a sort of floral shape (exterior loops). That level of detail would be difficult to guess at without a lot of data.


Erick Mead
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