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The toy top, an integrable system of rigid body dynamics

Boris A. Springborn
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Abstract

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. Euler-Poisson equations are derived. Following Felix Klein, the special unitary group $\rm SU(2)$ is used as configuration space and the solution is given in terms of hyperelliptic integrals. The curve traced by the point moving in the horizontal plane is analyzed, and a qualitative classification is achieved. The cases in which the hyperelliptic integrals degenerate to elliptic ones are found and the corresponding solutions are given in terms of Weierstrass elliptic functions.

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Boris A. Springborn. 2000-07-01. The toy top, an integrable system of rigid body dynamics. https://doi.org/10.2991/jnmp.2000.7.3.6

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