As meindnoch points out, the connection needs to loop over the rotating object. That is no problem if the only affect of the rotation that interests you is the centrifugal force.
When you give plasma (not whole blood) the nurses use a centrifuge machine that seems impossible: one tube goes from you to it (carrying whole blood), another tube goes from it back to you (carrying plasma depleted blood). The mechanism of Dale. A. Adams keeps the tubes from twisting. Search “antitwister mechanism patent” for a drawing of the mechanism. As for the principle behind the mechanism, see http://Antitwister.ariwatch.com for a PC program where you can adjust every variable imaginable.
What a fascinating project. It looks a real labor of love, and I wish I understood it more deeply. I've been making my own visualization sandboxes like this to explore configuration spaces and groups - but for much simpler, more intuitive physical systems.
I went down a few rabbit holes on the site - is this program also written in Basic?
Yes, specifically the PowerBasic console compiler version 4 (later versions don’t do animation nearly as well). The PowerBasic compilers are no longer being sold and the company appears to be defunct. Anyway, you can do a lot with a good BASIC compiler.
A series of rotations – a discrete walk (or continuous path) in the manifold of the rotation group SO(3) or SU(2) – can of course be inverted (starting from the end, find a walk that returns to the beginning) by performing the steps in reverse. Eckmann et alshow that, for almost all walks, there is another way: starting at the end, perform the steps in the original order (1) twice, and (2) uniformly scaled by a factor.
Apparently – I haven’t read the article – the factor depends on the walk. (One would think the abstract would say if there were.) The theorem says there exists such a factor but not how to find it. As the factor varies from 0 on up, the end point of the twice traveled path, scaled by some factor, is dense in the rotation manifold. It isn’t surprising though the fact that the end of the once traveled path (scaled) is not dense, is.
If the authors cannot give a comparatively simple way to find the factor, or at least bounds on it, the theorem isn’t of much use. It looks like there is too much hype accompanying its announcement.
Sorry, but the existence of such an inversion still is interesting from a mathematical perspective. It isn't "of much use" practically without the inversion formula/calculation, but that's ok. "There exists" is still a fascinating fact.
Completely agree. Beyond being of interest in its own right, "There exists" is a prerequisite for further work in finding a practical approach to find the path.
When you give plasma (not whole blood) the nurses use a centrifuge machine that seems impossible: one tube goes from you to it (carrying whole blood), another tube goes from it back to you (carrying plasma depleted blood). The mechanism of Dale. A. Adams keeps the tubes from twisting. Search “antitwister mechanism patent” for a drawing of the mechanism. As for the principle behind the mechanism, see http://Antitwister.ariwatch.com for a PC program where you can adjust every variable imaginable.