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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 366
The Toy Top, and Integrable System of Rigid Body Dynamics Boris A. Springborn
A toy top is defined as a rotationally symmetric body moving in a constant gravitational field while one point on the symmetry axis is constrained to stay in a horizontal plane. It is an integrable system similar to the Lagrange top. Paralleling work of Felix Klein, a solution in terms of hyperelliptic integrals is given. The special unitary group SU(2) is used as configuration space. The curve traced by the tip of the top is analyzed and the cases in which the hyperelliptic integrals degenerate to elliptic ones are solved in terms of Weierstrass elliptic functions
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