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In a number of discussions, I have addressed the issue of angular momentum and the nature of its use according to aiki principles. This entry will sum up some of those thoughts.
I have observed that a mechanical model for the relaxed human structure is that of a linked chain of bones. This has very significant impact in the use, magnification and dissipation of forces in encounters involving aikido. The tip of a folded chain, if allowed to fall freely from the support, accelerates with nothing bu the force of gravity. And yet, the chain tip actually accelerates faster than a ball dropped simultaneously from the same height.
The reason this occurs is because of conservation of angular momentum in the free end of the chain and the addition of each increment of momentum from the successive links to those still falling as they are each brought to a halt by the tension against the support. In the limit the speed of the falling chain would go to inifitnyt but limited by the material and its dimension, it merely becomes very, very fast until it suddenly goes to zero, and rebounds against the support.
The whip operates on the same principle: a coil or loop (technically, a spiral wave) of the whip constantly decreasing in radius -- thus increasing in angular velocity by the inverse square of the radius, The kinetic energy embodied in that progression increases as the square of the velocity. The tip of the whip at full extension exceeds the sound barrier, which forms a limiting boundary on what would otherwise be a mathematically infinite angular velocity as it approached zero radius.
Chris Thralls wrote of Terry Dobson, who he reports frequently used the training example of a whip to illustrate his views of aiki priniciples in action.
Chris Thralls AikiWeb/Forums/Weapons/ "Rope or Whip?" 07-11-2006, 02:56 AM wrote:
I had the privilege of training with Terry Dobson a lot, and he used a bullwhip to demonstrate several things. The most important thing was the demonstration of leading one's partner by their Ki, instead of pushing them around. .... He was adamant that Aikido is the art of Nonresistance, of joining with and leading Uke's energy to a peaceful resolution. .... He then demonstrated the effectiveness of circular and spirallic movements in generating very strong forces. He showed how changing directions dynamically caused the tip of the whip to move so fast that it broke the sound barrier, hence the "crack" of the whip.
One can see the principle in operation in many aspects of ki no kokyu action in aikido. The dynamic form of sumi-otoshi can be duplicated in form with a rope the length of a human body plus the length of the arm. Holding one end and placing a spiral wave in this rope, will lift the free end of the rope off the ground and cause it to rotate vertically end for end, just like uke's body does in sumi-otoshi.
Likewise, much of sword cutting follows these same principles. Even though the sword is relatively rigid (just like the bones of your forearm), it can be treated just exactly like one more of the bony bits in the body's chain of links. Realizing and seeing the form in operation this allows you to increase cutting power through proper form rather than strength. But it also allows for greater control and precision because of the same principles that cause the snapped whip to dissipate it energy into mathematically zero radius but infinite velocity simultaneously as it reaches the limits of its length.
The principle operates equally well in reverse to dissipate rather than concentrate angular momentum. Even in relatively static forms such as kokyu tanden ho, the limbs must rotate around the joints to exert power, making them the slow motion equivalent of the falling chain or snapping whip. IN the same way that the falling chain at the end of its fall lifts itself (chaotically) by rebound of its own acceleration agaisnt the tension of its support, a similar reversal of momentum can be applied to the partner's body causing him to lift, which is . in fact, what is done in kokyu tanden ho.
That expression of power can be dissipated by use of these principles in a couple of ways. In tekubi furi undo (hand shaking exercise) you can feel the oscillation of the waves of positivca and negative angular momentum generated at your hands reverberate right back down into your center. That is in my opinion why we do it, to train that sensation in the body more keenly. If you fling your hands at the ground in the tekubi furi exercise while standing up, you will in fact feel you heels lift slightly off the ground, this is the combined angular momentum of your flung hands being counterpoised and the shoulder/neck, lifting the body with the reaction to the force that you just threw at the ground. Uke's body can be affected in much the same way and in different configuraiton to reverse his applied energy back into him in the same form of reaction -- all by the manipulation of the angular momentum he is using to try top push you.
In kokyu tanden ho exercise, you also are finding the path to "push" with this chain (yes, you can push on a chain of tangent spheres without it collapsing, but only along one supercritical path, which is unique to every load condition, which is called the "funicular" path (hanging cable shape) for that set of loads. What is often called in Japanese "hiriki" or "elbow power" is an expression or observation of this load path where the elbow becomes the focal point of the coordinated movement, like a single weight hanging from a cable brings the cable to less of a curve and more of a point -- like the elbow.
In unliftable body exercises you are finding the path that does not allow this chain to be pushed -- allowing the chain to collapse under the lifting loads, which is relatively easy since it is supercritical to begin with. This allows you to form a set of four hinges across the joints of the body from grasp to grasp. This is a mechanism subject to collapse merely under its own weight. The body is therefore not liftable simply by the addition of more lifting effort. Conversely, if you allow your arms and shoulders to become relatively rigid, they will pin together at your neck and you can be lifted, because a three hinge arch is quite strong. This is the reason why bodies that are floppy because they are unconscious (or dead) are thought to be heavier than live "stiffs." People who are aware and alert have enough normal tone in their limbs and torso to actually be easier to lift, than they would be otherwise.
So, get a length of rope. Play with it. See what shapes you can make with it. See how they may relate to your expression of kokyu and aiki principles in your practice.