A remarkable periodic solution of the three-body problem in the case of equal masses

Alain Chenciner and Richard Montgomery

Review from Zentralblatt MATH:

Many investigators have dreamed to find a new integrable case in problems of classical or celestial mechanics or, at least, some new classes of periodical solutions etc. From time to time such results were published in the scientific literature. And now we have an example of such solutions in one particular case of the famous three-body problem of celestial mechanics. Using a variational method, the authors has exibited simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising future is that the three bodis chase each other around a fixed eight-shaped curve. Additionally, the orbits visit in turns every Euler configuration in which one of the bodies sits at the midpoint of the segment defined by the other two.

Reviewed by Sergei Georgievich Zhuravlev

Keywords: tree-body problem; periodic solutions; eight-shaped orbits

Classification (MSC2000): 70-99

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