The Toy Top, an Integrable System of Rigid Body Dynamics

DOI

10.2991/jnmp.2000.7.3.6How to use a DOI?

Abstract

A toy top is defined as a rotationally symmetric body moving in a constant gravittional 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 equtions are derived. Following Felix Klein, the special unitary group 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 Weiestrass elliptic functions.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Boris A. Springborn
PY  - 2000
DA  - 2000/08/01
TI  - The Toy Top, an Integrable System of Rigid Body Dynamics
JO  - Journal of Nonlinear Mathematical Physics
SP  - 387
EP  - 410
VL  - 7
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2000.7.3.6
DO  - 10.2991/jnmp.2000.7.3.6
ID  - Springborn2000
ER  -