Re: Kokyu explanation
For our westeners the main problem with the concepts of kokyu and ki is that it is very difficult indeed to explain them verbally. The only way of understanding them is experiencing them with one's body. For our western minds it is very uncomfortable, or at least alienating, to be supposed to feel something which we cannot put into words.
When I was a beginner even more than I am now, I found it very helpful to think of the concept of ki in terms of energy of intention, the energy of wanting to go somewhere. There are many simple exercises to demonstrate this. It is also visible all the time in daily life. When people walk on a crowded sidewalk, trying not to bump into one another, there is a lot of projection of ki: people have a certain energy that originates from their intention to pass another person either at the left or at the right hand side and the other person easily percieves this as such from a distance. It is this kind of energy one feels even more when one is touching the other person while he is moving or even wanting to move. The advantage, I found, of this kind of definition of ki is that energy of movement and intention is something that can be understood to a certain extent in terms of western physics. Later I realized that this idea of ki is too limited, but I still believe it is part of it.
As a beginner I found kokyu (defined in its limited sense of "breath power") less problematic to feel and understand. Once one masters the very basics of, say, irimi nage, it is very clear that the technique works better when one exhales on entering: try to inhale once and you understand immediately that it does not work. Of course, kokyu ho demonstrates (apart from many other things) exactly the same thing: the movements go with a rythm of inhaling and exhaling which cannot be reversed without seriously impeding the effectiveness of the technique. Later, of course, I realized that kokyu is much more than these simple mechanics, but the beginning was there.
I hope this helps.