3-body solution in two dimensions

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SUMMARY

The discussion centers on the quest for exact solutions to two-dimensional projections of three-body problems. Participants explore the concept of deriving a three-dimensional trajectory R(t) = by solving for trajectories in two separate planes: the z = 0 plane (R(t) = ) and the y = 0 plane (R(t) = ). The consensus is that while this approach seems logical, it does not yield an exact solution for the three-dimensional problem, which remains unsolved in classical mechanics.

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Physicists, mathematicians, and students studying dynamical systems, particularly those interested in the complexities of the three-body problem and trajectory analysis.

Loren Booda
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Are there any exact solutions for two-dimensional projections of 3-body problems?
 
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I really don't know anything about 3-body problems so I should probably just keep quiet, but...

If you have an unknown trajectory R(t) = <x(t),y(t),z(t)> it seems to me that if we could exactly solve for the trajectory in each of two planes we could solve the original trajectory exactly. In the z = 0 plane you would have R(t) = <x(t),y(t)> and in the y = 0 plane you would know R(t) = <x(t),z(t)> with perhaps a different parameterization. I would think having those two you could build the 3D version exactly, which, apparently, you can't do.

Disclaimer: The above may be worthless speculation.
 

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