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arXiv · 1402.0841

The Three-body problem and the shape sphere

Richard Montgomery
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Abstract

[This is an expository article. I have submitted it to the American Mathematical Monthly.] The three-body problem defines a dynamics on the space of triangles in the plane. The shape sphere is the moduli space of oriented similarity classes of planar triangles and lies inside shape space, a Euclidean 3-space parametrizing oriented congruence classes of triangles. We derive and investigate the geometry and dynamics induced on these spaces by the three-body problem. We present two theorems concerning the three-body problem whose discovery was made through the shape space perspective

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Richard Montgomery. 2014-02-04. The Three-body problem and the shape sphere. https://arxiv.org/abs/1402.0841

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