Orbit dynamics and kinematics with full quaternions

Full quaternions constitute a compact notation for describing the generic motion of a body in the space. One of the most important results about full quaternions is that they can be partitioned into a unit quaternion (which describes the orientation with respect to a suitable reference), and a modulus (which represents the translational motion along the direction indicated by the unit quaternion). Since vectors and scalars are also full quaternions, the equations of motion of the body can be rewritten in quaternion form. In this paper the orbit dynamics and kinematics of a point mass moving in the space are transformed in quaternion form. Simple application examples are also presented.