Hamiltonian structure, equilibria, and stability for an axisymmetric gyrostat motion in the presence of gravity and magnetic fields

Abstract

This work is interested in studying the motion of a rigid body carrying a rotor that rotates with a constant angular velocity about an axis parallel to the axis of dynamical symmetry. This motion is assumed to take place due to the effect of a combination of both uniform fields of gravity and magnetism that do not possess an axis of common symmetry. The equations of motion are constructed, and they are rewritten by means of the Hamiltonian function in the framework of the Lie–Poisson system. The equilibrium positions are inserted. The necessary conditions for the stability are introduced by applying the linear approximation method, while the sufficient conditions for stability are determined by utilizing the energy-Casimir method.