  Neutron stars, asteroids, comets, cosmic-dust granules, spacecraft, as well
as whatever other freely spinning body dissipate energy when they rotate about
any axis different from principal. We discuss the internal-dissipation-caused
relaxation of a freely precessing rotator towards its minimal-energy mode (mode
that corresponds to the spin about the maximal-inertia axis). While the body
nutates at some rate, the internal stresses and strains within the body
oscillate at frequencies both higher and lower than this rate. The internal
dissipation takes place mostly the second and higher harmonics. We discuss the
application of our findings to asteroids. Regarding the comets, estimates show
that the currently available angular resolution of spacecraft-based instruments
makes it possible to observe wobble damping within year- or maybe even
month-long spans of time. We also discuss cosmic-dust astrophysics; in
particular, the role played by precession damping in the dust alignment. We
show that this damping provides coupling of the grain's rotational and
vibrational degrees of freedom; this entails occasional flipping of dust grains
due to thermal fluctuations. During such a flip, grain preserves its angular
momentum, but the direction of torques arising from H2 formation reverses. As a
result, flipping grain will not rotate fast in spite of the action of
uncompensated H2 formation torques. The grains get ``thermally trapped,'' and
their alignment is marginal.
