# 3-body problem

1. Nov 28, 2012

### fvicaria

Hello,
I am currently studying the 3-body problem and I am struggling to find some examples of exercises or resolved examples.

Can anyone point me to a good book or resource I can download?

I found a few good ones for the two-body problem when I was studying it and they were very useful for me to consolidate the fundamentals.

Thank you very much.

2. Nov 28, 2012

### HomogenousCow

Three body problems are difficult because you have three interaction terms..they're comminly not taught and hence few exercises can be found

3. Nov 28, 2012

### fvicaria

I am more interested in the Restricted Circular Three-Body Problem case. Which is a little easier. I am looking for exercises involving the Jacobi constant, Zero Velocity Curves, Lagrange Points, etc. This is a major part of my course on Solar System Dynamics.

Any help will be much welcome.

4. Nov 28, 2012

### mikeph

determine where the stationary points are and find which ones are stable under small perturbations

5. Nov 28, 2012

### fvicaria

I have done that.
I am interested in general resolved questions to help me prepare for the exam.

6. Nov 28, 2012

### nlieb

The closest I've ever come to making actual calculations involving Newtonian Gravity with more than two bodies was proving that there always existed a solution to the N-Body problem. That took three days and a lot of caffeine and I don't think I could do it twice. Something about it being decomposable into an infinite dimensional linear partial differential equation (it had an infinite number of variables). Unfortunately I've lost the proof. I looked at the proof that already existed afterwards and it was similar, but not the same. Somehow, this infinite dimensional linear partial differential equation had solutions, at least in theory, although I never found a general solution and I don't think the differential equation I came up with would be very useful because it didn't show singularities and likely wouldn't unless you inputted an infinite number of coefficients (or perhaps the right coefficient), due to the nature of singularities in linear differential equations.

My recollection is that there has been quite a lot of work done on the three-body problem, particularly by a French mathematician whose name is escaping me now (I really should know his name, because he's quite well known). In general, you'll find more work done by mathematicians than by physicists, excepting, of course, mathematical physicists.

Good luck!

7. Nov 29, 2012

### andrien

An old one is 'A treatise on the analytical dynamics of particles and rigid bodies:
with an introduction to the problem of three bodies' by E.T. Whittaker.

8. Dec 18, 2012