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The Poisson structure in the quaternion variables was proposed for asymmetrictop in the external axially symmetric magnetic field. For that model ofinteraction the motion equation were got. The model was simulated in theneighbourhood of a relative equilibrium of the symmetric top -- Orbitron byMonte Carlo method. For small deviations with respect to the symmetry weobserve the persistence of the stability.

Quaternions in Hamiltonian dynamics of a rigid body -- Part III. Asymmetric Top in the Orbitron