Choreographic Three Bodies on the Lemniscate: GIF animation

Potential U_{12}(t)+U_{13}(t)+U_{01}(t)
with x_{1}(t) (red circle),
where U_{ij} = 1/2*log r_{ij}
and U_{01} = -sqrt{3}/8*r_{1}^2.

Potential V_{12}(t)+V_{13}(t)
with x_{1}(t) (red circle),
where
V_{ij}=1/2*log r_{ij} -sqrt{3}/24*r_{ij}^2.


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