Dave Findlay wrote:
Thanks for your time with the reply! Much to my surprise I pretty much followed the logic of the description
, but to be honest I was kinda left a bit unconvinced about the effect (magnitude?) of a gryoscopic resultant force, given that the accelerations involved are prtty small, relative to an actual gyroscope. Maybe that will be something to fall out of the discussion about Mike's question about throwing someone away.
Yes --- small. "Judge me by my size, do you." Sorry, likewise couldn't resist.
The resultant is determined by relative moment, and the moments are of the same order of magnitude. No, it is not a gyrocompass moment (ca. 20k rpm), but the physics is the same. The scale of proportion between the rotary moment and input moment in the example is much closer to par. And there is no moment on the off-axis to resist the input.
The more significant differnce, though, is that human balance is chaotic. The semi-cyclic wobble of the hips for stability is chaotic -- in the mathematical sense -- it can circuit one or the other loop of of its roughly figure eight loop path or back again at a moment's notice (pun intended) and reversing loops as well, never QUITE following the same path twice. Swivel your hips around and the shape of the motion of your center in stabilizing you is quite obvious.
The shape of the stability path of the center of mass is a loose collection of figure-eight paths very similar to (but different shape) as the Lorenz attrractor. The Lorenz attractor is the "butterfly" shape on the opening page of this paper: https://dspace.mit.edu/bitstream/172...n%20diagram%22
The dripping faucet bifurcation diagram, illustrates the consequence of this chaotic mechinasm. (Bear with me). At a low flow rate (acceleration) a faucet drips at one frequency (velocity). Increase the flow and it breaks into two discrete, but widely separated frequencies of drip. Increase it again and it breaks into four simultaneous rhythms, but closer together; eight and even closer together; 16 and ... and so on.
At a point, the diagram is almost black with discrete frquencies among which the drips actually fall, and the system is defined as "chaotic." Typically, this is almost immediatly after it undergoes its third period doubling, or "Period Three." You can see the bifurcation diagram on page 13 of the cited paper, figure 10.
"The Tao begets One; One begets Two, Two begets Three and Three beget the Ten Thousand Things." We have just quantified it folks, that is all.
In a chaotic system acted on by vanishingly small perturbations like a dripping faucet, at high acceleration, the range of discrete frequencies available is such that instantaneous, (seemingly) discontinuous and highly disproportionate shifts of state can occur.
Because the frequency of wobble in the hip path (velocity) (time between drips) is chaotic, and the system is under a relatively large constant acceleration input (gravity) (flow of water) ( ie. -- a squared velocity term), the frequency of the wobble can change discontinuously and dispropotionately with arbitrarily small inputs among a very large range of discrete frequency values. That frequency is velocity. Kinetic energy increases by the square of velocity.
The "perpetual motion" objections come next Eeeek! We are increasing energy in the technique, by increasing frequency at constant ampitude without any obvious source, and thus violating entropy.
Not so. There is a source of energy -- right underneath us. We drop our hips as we perform technique, thus "stealing" energy from the earth (converting gravitational potential into actual kinetic energy.
Then, because our stabilizing system loops back on itself, we store that energy "momentarily" -- in our hip sway moment, and as the cyclic phase of the sytem comes back around we add back in more energy from the recovery push off from the drop we just made. We then can applying that additional moment energy to uke in the technique. All of that energy is now ready to dump into the side of uke's attack, adding moment gyroscopically and dispacing him out of his plane of action, .
Notably, there are gaps in the bifurcation diagram where the added acceleration becomes unsupportable and state of the system just collapses to one or a few values at that level of energy.
There is definitely resonance with aikido and kuzushi in that model.
The resultants are as suitably "spooky" (but entirely mathematically determinate) as aikido can be in practice.