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In this series of blogposts, on understanding aiki from a bio-mechanical perspective, I have made reference to key aspects of angular momentum and the behaviors of chains -- particularly the bones considered as a chain of linked rods:
While a popular and instructive video, the author's conservation of momentum theory proposed as an explanation is wrong. The correct explanation is an understanding of the effect of DYNAMIC rigidity that occurs when a chain of rods is lifted by a continuous rotation:
[T]he chain is more like a series of short, rigid 'rods', say the authors, who publish their results today in Proceedings of the Royal Society A1. In their model, each rod is made up of three beads and two connectors. The size of a rod corresponds to the number of beads it takes to turn a section of chain back on itself by 180 degrees (it takes six).
Picking up a portion of rod from the pot with an upward force on one of its ends causes two things to happen, says Biggins. It makes the rod lift, but it also causes it to rotate. The end that is not picked up pushes downwards, and the pot provides a reaction force, he says. "The far end of the rod under those two motions actually goes down, and therefore pushes down. And that gives rise to this extra kick from the pot which drives the fountain.
In other words, once one end of a chain of rods begins a cascade dynamically, the chain of rods as a whole begins to lift and rotate at the other end in a complementary manner. Under gravity, the induced drop over the lip of the cup on one end, is compensated by the lift on the other end, and because the chain under tension is dynamically rigid, a rotation is caused by the immediately lifting segment PUSHING down on the vessel -- which reacts with an equal push UPWARD -- not only adding momentum but because of the rotation of the lifting portion of the segment -- the reaction is a counter-rotation on the resting end of the segment up and outward.
This is a coincidence of contradictory forces in a spiral dynamic (aiki) - the pull on the chain coming out of the bucket (tension), resulting rigidity and reaction forces giving added push (compression) on the chain out of the bucket, and giving it rotation in addition to the added momentum.
In the chain shown in the video demonstration we see the operations of aiki age in the chain rising from the cup, and the action of aiki sage in the descending elements of the chain. In free action these same principles may be deployed laterally and spirally using one's center of mass (dantien/hara ) to the same effect as the more simplistic up-down dynamic of the chain trick under gravity. These dynamics are, by turn, the stiffer, whole body dynamics dominated by torsional stresses, or respectively by the looser, pendulum action as with free chains -- and freely shifting between the two modes -- which are, mathematically speaking, directly related.
Aiki is the development of the body's ability to naturally -- and ultimately reflexively -- modulate its own rigidities and flexibilities of structure under dynamic conditions to form -- or to defeat the formation of -- these kinds of dynamics in connected structures (another person's body/weapon).