Controllability of a rotating body with a single rotor under conservation of angular momentum

This paper discusses the controllability of three dimensional orientation of a rotating body with non-zero angular momentum. Unlike conventional reorientation problem, the body will not have a stationary orientation due to conserved angular momentum. The control problem here is to achieve a specific orientation at a given time using only one reaction wheel. This is clearly impossible if the body is initially stationary. With the help of non-zero angular momentum, however, the vector fields satisfy the strong accessibility rank condition almost everywhere, but with singularities. Behavior on the singular points is also discussed.