My Math Forum Equations of motion of the classical 3 body problem

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 December 18th, 2012, 07:17 AM #1 Newbie   Joined: Dec 2012 Posts: 9 Thanks: 0 Equations of motion of the classical 3 body problem I've come across this blog/website, 3bproblem.blogspot.com, when running a search on the subject. If this is a formulation of the problem in six equations one can expect it to have a solution, since only six constants are needed instead of nine. Or this fact doesn't necessarily mean that it has a solution, even with only six equations? Thank you!
 December 18th, 2012, 03:35 PM #2 Global Moderator   Joined: May 2007 Posts: 6,528 Thanks: 589 Re: Equations of motion of the classical 3 body problem You should post a link - the label itself leads nowhere.
 December 18th, 2012, 04:42 PM #3 Newbie   Joined: Dec 2012 Posts: 9 Thanks: 0 Re: Equations of motion of the classical 3 body problem
 December 19th, 2012, 01:08 PM #4 Global Moderator   Joined: May 2007 Posts: 6,528 Thanks: 589 Re: Equations of motion of the classical 3 body problem You need only six equations, since the problem has m_0 fixed, so you will be getting the relative trajectories of m_1 and m_2.
 December 19th, 2012, 02:29 PM #5 Newbie   Joined: Dec 2012 Posts: 9 Thanks: 0 Re: Equations of motion of the classical 3 body problem Precisely and that's the problem. I'm not a guru on the subject but I can't find a formulation of this problem in 6 equations anywhere else, and the demonstration links to a page 'coming soon'..
 December 20th, 2012, 12:23 PM #6 Global Moderator   Joined: May 2007 Posts: 6,528 Thanks: 589 Re: Equations of motion of the classical 3 body problem I don't understand your objection. The only thought I have is that problems are usually based on a fixed center of mass, rather than fixing one body.
 December 20th, 2012, 02:41 PM #7 Newbie   Joined: Dec 2012 Posts: 9 Thanks: 0 Re: Equations of motion of the classical 3 body problem I'm not objecting the equations in any way because I don't know how to get them. I know the center of mass formulation of the problem in 9 equations. My question is how do you get this one in 6 equations. Any source? Thanks.
 December 21st, 2012, 12:40 PM #8 Global Moderator   Joined: May 2007 Posts: 6,528 Thanks: 589 Re: Equations of motion of the classical 3 body problem I am not sure what you are looking for. The link you supplied gives the six equations.
 December 22nd, 2012, 08:26 AM #9 Newbie   Joined: Dec 2012 Posts: 9 Thanks: 0 Re: Equations of motion of the classical 3 body problem I'm looking for the demonstration of those.
December 22nd, 2012, 12:08 PM   #10
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Re: Equations of motion of the classical 3 body problem

Quote:
 Originally Posted by spacey I'm looking for the demonstration of those.
The expressions in the link come directly from Newton's law of gravity.

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