The three-body problem and equivariant Riemannian geometry

We study the planar three-body problem with 1/r 2 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,...

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Bibliographic Details
Published in:Journal of mathematical physics 2017-08, Vol.58 (8), p.1
Main Authors: Alvarez-Ramírez, M., García, A., Meléndez, J., Reyes-Victoria, J. G.
Format: Article
Language:English
Subjects:
Curvature
Geodesy
Geometry
Great circles
Mathematical problems
Normal distribution
Physics
Three body problem
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Summary:We study the planar three-body problem with 1/r 2 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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5000075