When I first read the title of this article, I thought it was referring to a different (though related) problem: computing the course of a satellite (one body) through a two-body system (such as the Earth and the Moon). When I was a kid first learning about space travel, this was a notoriously unsolved problem. Instead of the usual sort of mathematical solution to this problem, navigators at NASA resorted to finite state models to solve the problem. Later on (in the '70s, if memory serves me right), mathematicians did develop equations that solved that particular three-body problem, but systems with more bodies (like Jupiter and Saturn) remained challenging, and were still normally solved with finite state modeling.
But this article is about a different sort of three-body problem – stable orbits of three-body systems. Similar, and still interesting, though...
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