Symmetry groups of the planar 3-body problem and action--minimizing trajectories
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Abstract
G-equivariant minimizers for the action functional (given a symmetry group G) can be thought as the natural generalization of relative equilibrium motions. The purpose of the paper is to apply systematically the G-equivariant calculus of variations to the planar 3-body problem -- with homogeneous interaction potential. We develop a theory and describe all the main aspects involved in the G-equivariant minimization: in particular, the classification of all possible symmetry groups, the description of the main properties of their minimizers and the proof of the fact that 3-body minimizers are always collisionless.Keywords
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