Re: Kokyu explanation
My dojo (Ki Society) doesn't talk about closing the armpits, but the continual admonition to have "weight underside" in arms and shoulders has exactly that effect.
I was working on this with a senior this week. When he holds me as if he's about to apply kotagaeshi, his elbows are very solidly down and his armpits closed. If I try to lift up on his arms there is relaxed but very strong resistance. It's immediately obvious by feel that when he chooses to throw me, I'm going to have to fall. If the arms are lighter and the armpits more open--the way I naturally try to do this, unfortunately--uke can center himself and stand, even against a much stronger nage.
From a novice's perspective it's really hard to tell which of the differences between styles are vocabulary and which actually reflect a different physical experience. This is something I hope to learn more about as I go along. Currently when I train in other styles of aikido I alternate between thinking "Gosh, this is just the same" and "Gosh, this is totally different" but I'm not sure either perception is at all accurate.