Friday, March 21, 2008

restricted four-body problem

The Albouy-Chenciner equations for the restricted four-body problem seem to generally have 191 solutions. For masses m1=17/20, m2 = 19/20, and m3 = 1, there are 160 complex solutions in 6 variables (the mutual distances between the particles). Plotting each sextuplet as a polygon gives the following plot, followed by the configurations formed by the positive real solutions. Computed with Sage and phcpack.

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