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I've also used an analogy of a bowling ball on a spring inside a box as a simplified mechanical explaination for some internally powered movement.
I can't explain what dantian is and I'm pretty sure even if I could it would not matter - the phenomenology is what matters. What does dantian driven movement look like? Look closely at the Mexican jumping bean and notice that there is nothing on the exterior of the bean which can be used to make the bean jump -no legs, arms, or appendages of any kind. Yet the bean moves and even 'jumps' and can fly through the air ( in smallish bean sized flights).
The phenomenom of the jumping bean is exactly what internally powered movement looks like. What happens inside the bean is responsible for the observed external movement. The twitchy worm inside is what makes the bean move. No, gentle reader, dantian is not a worm inside you - well, actually, yes it is ... sort of. The point is movement with no movement - stillness in motion and motion in stillness. We now know what to look for -movement like a Mexican jumping bean.
A bit of a diversion ... everyone is familiar with gravity, Newton and apples and all that. If you're like me you even know certain equations that describe the phenomenom of gravity (classically like Newton or 'modern' using general relativity) and can even write the equations describing a black hole, neutron star and an electron in 'orbit' . Let's presume one can even solve such equations even only approximately (no one can) ... you still can't make gravity. We all know the label 'gravity' and a great many can manipulate said equations and even use then to assit in landing people on the distant moon but nobody can simply make gravity. There is a great body of work about gravity but nobody can really say exactly what gravity is (silly boy, gravity is just space-time bent by energy density) - at least not in any way that does anything beyond describing the phenomenom. What gravity does we know a lot but exactly what is gravity is pure philosophy (a.k.a. waste of time trying to figure).
Dantian is kind of the same ... does it matter what it is compared to how to use it to do 'stuff' like internally powered movement? I don't think so but others do.
Let's observe that a person can stand in a natural posture and suddenly with no discernable movement of their appendages launch into the air (in a modest person sized flight plan) just like our little Mexican jumping bean. Same thing when sitting in seiza and suddenly launching forward ~ 2 feet with no pressure on the ground, no flapping of arms and no twitching of legs - pure internally powered movement. Attempt to describe the phenomenom and one must conclude there is a large worm inside twitching. Let's call our friendly worm dantian.
Before we launch into why there is no worm and of course there are better descriptions of dantian we must first come to agree that there is such a thing as internally powered movement that defys explaination except for our friend the worm dantian. Pretty simple - take someone able to utilize dantian and put them on a force plate and have then launch themselves upward using pure internally powered movement (twitch their dantian) - note that the force plate does not show downward pressure. Scientific evidence than cries out for explaination ... twitchy worms, you say? We need to do the force plate experiment because 20 experienced martial artists in a room watching a person launch themselves using internally powered movement will only devolve into bickering and fighting (they are martial artists after all - they fight more than hockey players). Even our force plate equipped science friends will not believe it so they will now insist on encasing our 'test subject' in acrylic resin so they actually cannot move externally ... so dehumanizing this pursuit of knowledge can be. Please note the Mexican jumping bean can jump and is encased in a very rigid hard bean. If a worm can do it why not a person?
Once we get past the stage of arguing the existence of internally powered movement driven primarily by dantian we can progress to interesting uses of dantian. For example doing the Mexican jumping bean but instead of jumping direct the force through ours arms and hands into the person we are touching and watch them be slammed as if punched (the infamous no inch punch). The list of such things is endless.
If you can't do pure internally powered movement then find someone who can (you now have a test for them) and listen to them - they may explain how to develop dantian and how to use it and probably a whole bunch of other stuff you have no idea about.
Don't care about pure internally powered movement? Sorry I wasted your time. Want to help me solve some squirrely field equations - even approximately?
Frankly, I can't really see that clearly if Ueshiba Morihei is using pure internally powered movement in the referenced clip. I've seen better examples of the Mexican jumping bean and that person is not dead and he does teach 'how to'.