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arXiv · 1609.05220

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

Richard Montgomery
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Abstract

We construct the hyperbolic plane with its geodesic flow as the scale plus symmetry reduction of a three-body problem in the Euclidean plane. The potential is $-I/\Delta^2$ where $I$ is the triangle's moment of inertia and $\Delta$ its area. The reduction method uses the Jacobi-Maupertuis metric, following the author's earlier paper "Putting Hyperbolic Pants on a Three-body Problem".

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Richard Montgomery. 2016-09-16. Constructing the Hyperbolic Plane as the reduction of a three-body problem. https://arxiv.org/abs/1609.05220

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