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December 18th, 2012, 07:17 AM   #1
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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?

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December 18th, 2012, 03:35 PM   #2
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Re: Equations of motion of the classical 3 body problem

You should post a link - the label itself leads nowhere.
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December 18th, 2012, 04:42 PM   #3
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Re: Equations of motion of the classical 3 body problem

Sorry:

http://3bproblem.blogspot.com/
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December 19th, 2012, 01:08 PM   #4
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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.
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December 19th, 2012, 02:29 PM   #5
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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'..
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December 20th, 2012, 12:23 PM   #6
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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.
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December 20th, 2012, 02:41 PM   #7
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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.
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December 21st, 2012, 12:40 PM   #8
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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.
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December 22nd, 2012, 08:26 AM   #9
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Re: Equations of motion of the classical 3 body problem

I'm looking for the demonstration of those.
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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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