Re: opening the joints
Even as I am typing this, I don't know why... I guess it's because you wouldn't be taking the time to prepare these detailed mathematical descriptions if you didn't have a love and appreciation for this stuff, and I respect that. I don't want these skills to disappear, and I'm working on learning and sharing them with others.
I actually waded through most of your stuff. It reads like you were one of the only people to get an A in your kinematics class. On the surface, that's a complement. But it's also a problem-- I bet there weren't many other guys (or gals) who got A's in kinematics and dynamics. Of the ones who did, a vanishingly small percentage of them could be considered martial arts enthusiasts with knowledge worth sharing.
There are several people on this board with skills which have been independently verified. They have martial knowledge worth sharing. While they are different people with different backgrounds, they have hashed out an informal language for talking about these things. The language is built around a metaphor that helps a lot of us newbies develop a conceptual model of how this stuff works. For the more advanced, they have a framework that allows them to transmit information about the finer points. I've been following the conversation for a year or two, and while the model has evolved it hasn't broken down. At this point, I feel safe saying the model is good enough for people to use to communicate their ideas about how to really "do" aikido the way the great masters did.
You have spent a great deal of time and energy trying to explain your model. It's complex. It uses a language that only a small percentage of the population understands. I have an engineering degree. I (think I) get what you are trying to say with your model. As a consultant, I also understand that no one will use it. In order to talk about these things in your terms, people would have to learn a lot of kinematics and math, spending time that would be better spent training. And that assumes the math is within their reach. If I recall correctly, Takeda didn't write. Maybe not writing or reading freed up a lot of training time!
I freely admit that I don't know how to do these things. I'm working on it, but I am very much a beginner. I mine the forums for new information daily, and increasingly you're the guy screaming (metaphorically speaking) at people in a language they don't understand. You may well know what these guys are talking about, but as long as you insist on forcing your model on them no meaningful dialogue can take place. They won't receive information from you, and you won't receive information from them.
It looks like you are dismissing a lot of what is being openly discussed as basics, and claiming that real aikido is comprised of that plus much more. I think basics is too imprecise a term. They aren't basics, they are the fundamentals. Their study appears to be limitless. I think the "much more" is like the trees that hide the forest. Techniques and strategy are easy to understand. What is hard is developing a body that has the fundamentals so deeply ingrained that the techniques create themselves and the strategy happens spontaneously. But this is the goal that every master has plainly stated.
I've been doing martial arts a long time, now. It's only recently that I have learned how much time I wasted looking at the trees. There are lots of them and some of them are really interesting. They also can be a major distraction. The fundamentals make any technique work. Technique without the fundamentals is empty. There is too much empty technique out there, and I've invested years in empty practice. I think this is one reason Ueshiba pared the techniques from Daito Ryu down to a relatively small number. He was active in solo training until he passed away. He never stopped developing the fundamentals. I believe he intended the kata practice to be paired training that would be at least as effective as the solo work. He didn't have partners to practice on his own level with. Paired kata gives us the opportunity to force skill evolution to occur. Unfortunately, it looks like most of us missed this.
Personally, I think kokyu is not a basic condition which assists in the performance of the technique. It *is* the technique. It's the root. It's not something you can ever say "I understand that and I can do it" because it can always be developed more. Maybe you know that, in which case I'd appreciate it if you'd find a way to express your ideas in the prevailing model, so that I (and others) can wrap my head around it.
It's also possible that you've overlooked something, trivialized the fundamentals, and gotten lost down the rabbit hole of technique exploration. That, to me, is jujutsu in today's world. No martial art advocates force against force (at an advanced level), and to say that evasion and leading are what makes aikido unique misses the point.
If only there were some kind of forum, where people could meet and talk about these things, in a common language that most people undestand. Oh wait, there is! Welcome (back) to aikiweb. If you agree to talk about these things in the terms others have, there can be a meaningful exchange of information. As a bonus, you might find your frustration level decreases.
I guess this is a good place to apologize for sounding smug, or appointing myself some kind of ambassador for the discussions here. Worse, I admit to not having any skill! Still, it's my opinion that the first step to talking about this stuff is agreeing to a framework. No one says the prevailing model is perfect, but at this point I don't think it can be disputed that it allows effective communication about these skills to take place. Of course, it's only an opinion and it's offered with the best of intentions (and one selfish motive, to not see pages of people talking past each other in the middle of productive threads).