5 ms·
Ah, I see, so they've basically found a nice way to express the easy stuff (finding the constraints) but the devil's in the optimisation, of course. Thanks for
by bubblyworld 2y ago
Ah, I see, so they've basically found a nice way to express the easy stuff (finding the constraints) but the devil's in the optimisation, of course.
Thanks for taking the time to reply. Coincidentally, I'm doing a project with Arnold's book on CM at the moment, so that all makes perfect sense to me.
- catgary 2y agoRight, basically the generalization goes: Lie groups -> Lie group actions -> Lie groupoids. This is not a new observation (in fact Arnold’s fluid mechanics can be rephrased using lie groupoids https://tspace.library.utoronto.ca/bitstream/1807/91859/1/Fusca_Daniel_201811_PhD_thesis.pdf https://tspace.library.utoronto.ca/bitstream/1807/91859/1/Fu..., and big names like Alan Weinstein have worked in that area). I don’t think the authors actually understand that story, so they very naively went groups -> group actions -> monads. If it went that way someone in mathematical physics or optimization would have stumbled onto other concrete examples. But they haven’t, because it doesn’t.