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Annals of Mathematics, II. Series Vol. 152, No. 3, pp. 881901 (2000) 

A remarkable periodic solution of the threebody problem in the case of equal massesAlain Chenciner and Richard MontgomeryReview 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 threebody 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 eightshaped 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: treebody problem; periodic solutions; eightshaped orbits Classification (MSC2000): 7099 Full text of the article:
Electronic fulltext finalized on: 9 Sep 2001. This page was last modified: 17 Jul 2002.
© 2001 Johns Hopkins University Press
