
The compelling mathematical challenge of the three-body problem - based2
https://news.ucsc.edu/2019/08/three-body-problem.html
======
scottlocklin
The 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.

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asoplata
Do you mind posting a link to your dissertation? That chapter sounds
interesting!

~~~
selimthegrim
Seconding. Is it on ProQuest?

~~~
scottlocklin
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.

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eraserj
I 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)

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coldcode
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.

~~~
fishmaster
What do you mean by original math?

~~~
TheGallopedHigh
Not OP but meaning inventing/discovering new theories in math. Basically
research in math that’s theoretical as opposed to applied.

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WalterBright
I wonder if the choreographies are stable or not.

~~~
lisper
That'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.

~~~
RBerenguel
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_.

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benrawk
I took linear algebra with him at UCSC! Super nice guy

