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arXiv · 1502.04674

Hamiltonian dynamics of a symmetric top in external fields having axial symmetry. Levitating Orbitron

Stanislav S. Zub·Sergiy I. Zub
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Abstract

The symmetric top is a special case of the general top, and canonical Poisson structure on $T^*SE(3)$ is the common method of its description. This structure is invariant under the right action of $SO(3)$, but the Hamiltonian of the symmetric top is invariant only under the right action of subgroup $S^1$ that corresponds to the rotation around the symmetry axis of the symmetric top. So, its Poisson structure was obtained as the reduction $T^*SE(3)/S^1$. Next we propose the Hamiltonian that describes the wide class of the interaction models of symmetric top and axially-symmetric external field. The stability of the levitating Orbitron in relative equilibrium was proved.

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Stanislav S. Zub, Sergiy I. Zub. 2015-02-13. Hamiltonian dynamics of a symmetric top in external fields having axial symmetry. Levitating Orbitron. https://arxiv.org/abs/1502.04674

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