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Convexity in the Figure Eight Solution to the Three-Body Problem

Toshiaki Fujiwara·Richard Montgomery
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Abstract

The figure eight is a remarkable solution to the Newtonian three-body problem in which the three equal masses chase each around a planar curve having the qualitative shape and symmetries of a figure eight. Here we prove that each lobe of this eight is convex.

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Toshiaki Fujiwara, Richard Montgomery. 2003-09-02. Convexity in the Figure Eight Solution to the Three-Body Problem. https://arxiv.org/abs/math/0308252

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