https://github.com/achristmascarl/three_body

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achristmascarl / three_body Public

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 rudimentary simulation of the three-body problem

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achristmascarl/three_body

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Cargo.lock      Cargo.lock                          

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README.md       README.md                           

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paper_f10.png   paper_f10.png                       

three_body.gif  three_body.gif                      

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  * README

 three_body

 

a very rudimentary simulation of the three-body problem. i was
curious how far we could get with just euler's method and a small
time step, and it turns out we can get something pretty visually
interesting!

three body problem gif

three body problem image

i was also curious about what would happen if the polar coordinates
of the bodies over time were translated into rgb values and animated;
the results are below.

warning: some of the transitions from this orbit are pretty abrupt,
so there may be flashing colors.

three body problem color gif

sources

 

the starting positions for the graphics above are for periodic orbit
F[10] from this paper: https://arxiv.org/abs/1805.07980

This is what F[10] looks like when solved with ODE solver dop853
(according to the paper):

F10 from the paper

as you can see, although the overall shape is similar/recognizeable,
the error in the calculations above grow fairly noticeable after just
2 periods.

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 rudimentary simulation of the three-body problem

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