In this paper we study the human eye movement and the head movement system as a simple mechanical control system. Most of the time, eye movements obey Listing's constraint, which states that the allowed orientations of the eye are obtained by rotating a fixed 'primary gaze direction' by a subclass of rotation matrices. These rotation matrices have their axes of rotation restricted to a fixed plane perpendicular to the primary gaze direction. Likewise, a spontaneous head movement satisfy Donder's constraint which is similar to the Listing's constraint except that the axes of rotation of the head away from a primary head position is restricted to a fixed surface, which is not necessarily a plane. When head is restrained to remain fixed, eye movement satisfies the Listing's constraint throughout its entire trajectory. On the other hand, when the head is allowed to move (satisfying the Donder's constraint), the eye satisfies the Listing's constraint only at the beginning and at the end of a trajectory. Intermediate points of the trajectory, partially guided by the vestibulo-ocular reflex, do not apparently satisfy the Listing's constraint. In this paper we introduce control strategy that would regulate the eye from an initial to a final gaze position with or without satisfaction of the Listing's constraint during all the intermediate points of the eye movement trajectory. We study the head movement problem under the assumption that the head always satisfies the Donder's constraint. The control signals are generated by choosing a suitable potential function and adding to it a suitable damping term. The overall dynamical system is constructed using the well known Euler Lagrange's equation. The main result of this paper is to compare, using simulations, the total distance and the total time it takes to regulate the eye and the head between two orientations.