  Bodies with the nonspherical tensor of inertia exhibit a variety of
rotational motion patterns, including chaotic motion, stable periodic
(quasi-periodic) rotation, unstable rotation around the direction close to the
body's second principal axis, featuring a well-known tennis-racket (also known
as Garriott-Dzhanibekov) effect -- series of seemingly spontaneous 180 degrees
flips. These patterns are even more complex if the body's tensor of inertia
(TOI) is changing with time. Changing a body's TOI has been discussed recently
as a tool to perform controllable Garriott-Dzhanibekov flips and similar
maneuvers. In this work, the optimal control of the TOI of the body
(spacecraft, or any other device that admits free rotation in three dimensions)
is used as a means to perform desirable re-orientations of a body with respect
to its angular velocity. Using the spherical TOI as the initial and final point
of the maneuver, we optimize the parameters of the maneuver to achieve and
stabilize the desired orientation of the body's principal axes with respect to
spin angular velocity. It appears that such a procedure allows for finding
arbitrarily complex maneuver trajectories of a spinning body. In particular,
intermediate axis instability can be used to break the alignment of the body's
principal axis and the axis of rotation. Such maneuvers do not require
utilization of propellants and could be straightforwardly used for attitude
control of a spin-stabilized spacecraft. The capabilities of such a method of
angular maneuvering are demonstrated in numerical simulations.
