Lyapunov stability of a heavy charged gyrostat in a central attractive potential

This study investigated the stability of certain motions of a heavy, electrically charged gyrostat moving in a central attractive field. The Euler–Poisson equations were derived and then reformulated within the Lie–Poisson framework. We identified and analyzed the system's permanent rotations, presenting a mechanical interpretation of these motions. To assess stability, the Energy–Casimir method is employed to establish sufficient stability criteria. Moreover, the necessary conditions for the stability of the corresponding equilibrium configurations were also presented.