Mathematical Model of Interaction of a Symmetric Top with an Axially Symmetric External Field
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A symmetric top is considered, which is a particular case of a mechanical top that is usually described by the canonical Poisson structure on T*SE (3). This structure is invariant under the right action of the rotation group SO(3), but the Hamiltonian of the symmetric top is invariant only under the right action of the subgroup S 1, which corresponds to the rotation of the symmetric top around its axis of symmetry. This Poisson structure is obtained as the reduction T* SE (3) / S 1. A Hamiltonian and motion equations are proposed that describe a wide class of interaction models of the symmetric top with an axially symmetric external field.
Keywordsmathematical model of a symmetric top Poisson reduction symplectic leaf Kirillov–Kostant–Souriau 2-form relative equilibrium energy-momentum method
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