The compelling mathematical challenge of the three-body problem(news.ucsc.edu)
news.ucsc.edu
The compelling mathematical challenge of the three-body problem
https://news.ucsc.edu/2019/08/three-body-problem.html
6 comments
Do you mind posting a link to your dissertation? That chapter sounds interesting!
Seconding. Is it on ProQuest?
I 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.
Not even sure where the PDF is at this point; if I dig it up I'll put it on my blog.
I found a 2015 post on HN listing some stable n-body choreographies[0].
[0] https://news.ycombinator.com/item?id=8867741
[0] https://news.ycombinator.com/item?id=8867741
I 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.
What do you mean by original math?
Not OP but meaning inventing/discovering new theories in math. Basically research in math that’s theoretical as opposed to applied.
I wonder if the choreographies are stable or not.
That's a great question, and mostly an open problem except in some special cases:
http://scholarpedia.org/article/N-body_choreographies
But basically: some are, some aren't, and we can't generally tell (yet) which is which.
http://scholarpedia.org/article/N-body_choreographies
But basically: some are, some aren't, and we can't generally tell (yet) which is which.
Checking 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_.
> 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
there are also important applications, like figuring out the right orbit and starting points for kerbin bodies in the principia n-body mod
I took linear algebra with him at UCSC! Super nice guy
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.