Stability Conditions for Permanent Rotations of a Heavy Gyrostat with Two Constant Rotors

In this paper, we consider the motion of an asymmetric heavy gyrostat, when its center mass lies along one principal axes inertia. We determine possible permanent rotations and, by means Energy-Casimir method, give sufficient stability conditions. prove that there exist stable gyrostat is oriented in any direction space, action two spinning rotors, them aligned axis, where lies. also derive necessary conditions that, some cases, are same as ones.