In this paper ive consider the problem of maneuvering an axisymmetric space
craft in the case that no torques about the symmetry axis can be exerted, f
or example due to a thruster failure. Explicit control laws are derived whi
ch steer such a spacecraft between states of pure spin between prescribed a
ttitudes. These laws are found by minimizing a Cost junctional measuring th
e suitably weighted overall angular velocities during the maneuver. In arri
ving at the solution, differential geometric techniques in the theory of op
timal control are used.