4 ms·
The compelling mathematical challenge of the three-body problem
- WalterBright 7y agoI wonder if the choreographies are stable or not.
- lisper 7y agoThat's a great question, and mostly an open problem except in some special cases: http://scholarpedia.org/article/N-body_choreographies http://scholarpedia.org/article/N-body_choreographies But basically: some are, some aren't, and we can't generally tell (yet) which is which.
- LoSboccacc 7y ago> Motivations: Theoretical. Astronomical. Aesthetics. there are also important applications, like figuring out the right orbit and starting points for kerbin bodies in the principia n-body mod
- RBerenguel 7y agoChecking this page brings back memories. Carles Simó was the principal researcher at my research group (is now retired as a professor, but AFAIK is still a researcher), so I'm familiar with the work and people mentioned there, even if it was outside of my own research interests. I took his celestial mechanics course, and it was… _not easy_.
- benrawk 7y agoI took linear algebra with him at UCSC! Super nice guy
- The_mboga_real 7y agoStop what you're doing and have a look at this here math challenge, A 3-body problem.
- eraserj 7y agoI found a 2015 post on HN listing some stable n-body choreographies[0]. [0] https://news.ycombinator.com/item?id=8867741 https://news.ycombinator.com/item?id=8867741
- coldcode 7y agoI often wish I had considered studying math back when I was considering getting a PhD in chemistry, but wound up as a programmer instead. But it's hard to make a living doing math research, you either wind up teaching or working in some practical field like programming or AI. I know two PhDs in math who each do one of those and neither can do any original math.
- fishmaster 7y agoWhat do you mean by original math?
- TheGallopedHigh 7y agoNot OP but meaning inventing/discovering new theories in math. Basically research in math that’s theoretical as opposed to applied.
- scottlocklin 7y agoThe history of this problem is even more interesting than they let on. Because I'm a self-indulgent twat I put a chapter on this in my dissertation; it dates back to Eudoxus of Cnidae's work on the motions of the Moon; he developed a sort of "ancient Greek Fourier transform" to deal with it, with guys like Hipparchus of Rhodes, Ptolemy taking the idea farther. The figures in classical physics that were mentioned; Newton, Lagrange. It was also crucial in development of quantum mechanics -there was no way at the time of applying Bohr's semiclassical picture to the helium atom, so they had to develop matrix mechanics and the Schroedinger picture. Eventually (in the 90s) we got the semiclassical quantization by the great Dieter Wintgen, using the tools developed by Gutzwiller, and well, I guess this guy was probably the last important contributor to the problem (I, alas, didn't do anything good). In physics, folks like to refer to simple models which inform other models: the harmonic oscillator, the hydrogen atom, two body scattering and so on. The three body problem is one of the simplest commonly encountered physical problems for which there is no general solution on the torus (Montgomery found a particular solution on the torus). As such, it has driven forward a lot of research and innovation in theoretical physics tools. You could write a pretty good and beefy physics book where you only talk about the three body problem with central potentials.
- asoplata 7y agoDo you mind posting a link to your dissertation? That chapter sounds interesting!
- selimthegrim 7y agoSeconding. Is it on ProQuest?
- scottlocklin 7y agoI don't even know what that is. I graduated in 2004! Not even sure where the PDF is at this point; if I dig it up I'll put it on my blog.