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

2015/02/13 by Stanislav S. Zub, Zub, Stanislav S., Sergiy I. Zub +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1502.04674

arxiv created 2015/02/13 · arxiv updated 2015/02/17

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 S¹ 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)/S¹. 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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