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The three-body problem and equivariant Riemannian geometry
M. Alvarez-Ramírez, A. García, J. Meléndez, J. G. Reyes-Victoria
Source abstract
We study the planar three-body problem with 1/r2 potential using the Jacobi-Maupertuis metric, making appropriate reductions by Riemannian submersions. We give a different proof of the Gaussian curvature’s sign and the completeness of the space reported by Montgomery [Ergodic Theory Dyn. Syst. 25, 921–947 (2005)]. Moreover, we characterize the geodesics contained in great circles.
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