Constructing the Hyperbolic Plane as the reduction of a three-body\n problem

2016/09/16 by Richard Montgomery, Montgomery, Richard
Engineering · Physics and Astronomy · #37N05 #70F10 #70G45 #Astro and Planetary Science #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Space Satellite Systems and Control #Spacecraft Dynamics and Control #Stellar, planetary, and galactic studies

paper · pdf · doi:10.48550/arxiv.1609.05220

openalex publication_date 2016/09/16 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We construct the hyperbolic plane with its geodesic flow as the scale plus\nsymmetry reduction of a three-body problem in the Euclidean plane. The\npotential is -I/\Δ² where I is the triangle's moment of inertia and\n\Δ its area. The reduction method uses the Jacobi-Maupertuis metric,\nfollowing the author's earlier paper "Putting Hyperbolic Pants on a Three-body\nProblem".\n

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