The Three-body problem and the shape sphere
arXiv:1402.0841
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
27 pages, 8 figures, submitted to American Math Monthly
Cited by in corpus (5)
- Specific PDEs for Preserved Quantities in Geometry. I. Similarities and Subgroups
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- Specific PDEs for Preserved Quantities in Geometry. II. Affine Transformations and Subgroups
- Quadrilaterals in Shape Theory. II. Alternative Derivations of Shape Space: Successes and Limitations
- Isotropy Groups and Kinematic Orbits for 1 and 2- -Body Problems