Quaternion frames and fractal surface as tools to control orientation of a spacecraft

Reorientation of an object's (spacecraft) problem is formulated in details in the SO(3,R) and SU(2) groups matrix terms using the most optional math tool of exceptional algebra of quaternion numbers. A thorough analysis of the two approaches is made resulting in original formulas linking parameters of the assigned object's consequent 3D rotations with a single rotation about a unit vector pointing the instant rotation axis, respective operational technology described with relevant examples. It is also demonstrated that an axial quaternion frame admits fractalization so that the reorientation problem is reduced to deformations of the sub-geometric fractal surface.