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Geometric characterizations for variational minimization solutions of the 3-body problem. (English) Zbl 0980.70009
Summary: We prove that, for any given positive masses, the variational minimization solutions of the three-body problem in 3 or 2 are precisely planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular restricted three-body problem in 3 or 2 are also planar equilateral triangle circular solutions.
MSC:
70F07Three-body problems
70G75Variational methods for dynamical systems
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