The dynamical rotatory motion of a rigid, symmetrical body about a dynamically symmetric axis is addressed in this study. It is considered that this body has a single-rotor and a filled spherical hollow with highly viscous fluid exhibits spherical motions around its center of mass under the influence of one component of a gyrostatic moment vector. The controlling system of motion is obtained, stationary movements are identified, and analyses of their stabilities are performed. The numerical method of Runge-Kutta from fourth-order (RK-4) is used to calculate the numerical results of this system and they are displayed graphically. Based on the feedback principle, numerous controls that stabilize both stable and unstable stationary motions of the body to asymptotically stable have been identified. The astonishing applications in the industries of gyroscopes and submarines are where this work's significance lies. This paper focuses on the dynamical rotational motion of a symmetric RB about a dynamically symmetric axis. This body is thought to have a single rotor, and it exhibits spherical motions around its centre of mass when one component of a gyrostatic moment (GM) vector acts on it. The motion's governing system is found, stationary motions are determined, and investigations of their stabilities are carried out.