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Old 08-05-2009, 01:20 PM   #579
Eric Joyce
Dojo: Budoshingikan
Location: Gilbert, AZ
Join Date: Dec 2002
Posts: 179
United_States
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Re: Is It Missing In Everybody's Aikido?

Quote:
Erick Mead wrote: View Post
"What's the Frequency, Kenneth?" Success is always proportional to skill even in this framework. I agree there is a driven frequency. I agree there is a chaotic collapse. I do not necessarily agree that the two rhythms are discordant. They are in fact harmonic.

While it is true that a discordant chaotic pulse (also known, technically speaking, as "hammering the crap out of somebody") can create a resulting chaotic movement, it also just naturally results from a driven harmonic at a fundamental frequency, which erupts into a resonant chaos.

The result suggests the latter -- and the reflexive head bob is, in my view, conclusive, and the reflexive triggering of the leg extensors ( ryote) and flexors (katate) in succession is quite apparent. The grossly noticeable buckling/shimmy thing going on is a sure sign. Just arbitrarily snatching on or beating into someone's structure does not do that. Of course, if you know what is happening and can do it, you can damp it by a similar means, which involves no leverage.

Ark is popping the guy's gamma motor spindles and Golgi tendon organs. Think of them like structural circuit breakers. Driven resonance goes asymptotic and becomes destructive very quickly. The body does not have the margin to wait for conscious feedback in that case. Either it reflexively acts or it risks a stability loss (or structural damage) that is not recoverable.

Simple harmonic action is linear. Complex harmonic action is non-linear and resonant. http://en.wikipedia.org/wiki/Double_pendulum
My arm is a double pendulum. The upper and lower centers form a double inverted pendulum Two people (simplified) can be considered double inverted pendulums. A multiple n-pendulum as n becomes > ~ 3 is a chain.

Driven resonance (90 degrees out of phase -- temporally, spatially or BOTH ) at a whole number frequency within the pahse space leads to chaotic movement. Resonance (at the fundamental frequency of a structure) will find any discontinuity in a the shear path in that system and collapse it at that point. Furitama is that fundamental frequency. Funetori undo, ude furi, sayu undo, happo undo, all define the limits of a moving phase space for a periodic dynamic stability region (the length of one simple natural pendulum swing) all of which can be made harmonic spatially (i.e -- 90 degree or Juuji 十字] relationship) with connected another phase space when they interact -- as the the two pendulums do when linked.

On the third one, that you did not mention, Mr. Chen. In the animation above, if the two pendulum are seen as crude representations of the two bodies connected, the periods where the system undergoes the single or doubled "whoop-de-do" rotations of the lower pendulum -- correspond to the throwing opportunities in the complex phase space, as used by Mr. Chen. The other periodic back and forth in-phase, leading phase or lagging phase oscillations where there is no full rotation are the "wait for it" part. Where it is commencing a full rotation -- that suddenly becomes "downhill" in the phase space for a throw -- and a throw if you go with it. Surf the break, man. If you attempt a throw anywhere else in that phase space -- you are working seriously uphill, and are likely to get caught inside.

The boundary of the above 2D pendulums figure may viewed as a the projection of a limacon, (the pedal of a circle) rotated around the axis of its cusp. Roughly, imagine seeing the profile of a squat apple shape constructed of loops of yarn with a deep cusp at the stem and a hollow teardrop core -- See below), or like a doughnut contracted to the point that the inner ring overlaps itself to make the center hole an internal lozenge or teardrop volume.

If you consider and look for the related bounding figures (cycloids and trochoids) of this kind of action. you have some better concrete imagery to prime your intuition about the spatial boundaries of the dynamics you are trying to achieve (regardless of scale -- the cusp can be arbitrarily large or miniscule) --- and the pedal curve (below) shows the explicit presence of juuji in the relationship.

Limacon

Another family of boundary curves of useful interest where cusp discontinuity and shear are immediately evident and yet have a seamless transition are the hyperboloids, catenoids and helicoids:
Wow!! That is some cool stuff Erick. I hope you work for NASA or something. Simply fascinating.

Eric Joyce
Otake Han Doshin Ryu Jujutsu
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