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Variational methods for the choreography solution to the three-body problem. (English) Zbl 1145.70314
Summary: In this paper, we give a short proof for the existence of nontrivial choreography solution to the equal-mass three-body problem, which is discovered by A. Chenciner and R. Montgomery [Ann. Math. (2) 152, No. 3, 881–901 (2000; Zbl 0987.70009)] recently.
MSC:
70F07Three-body problems
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
70H12Periodic and almost periodic solutions (mechanics of particles and systems)