  Whenever a freely spinning body is found in a complex rotational state, this
means that either the body is a recent victim of an impact or a tidal
interaction, or is a fragment of a recently disrupted progenitor. Another
factor (relevant for comets) is outgassing. Due to impacts, tidal forces and
outgassing, the asteroidal and cometary precession must be a generic
phenomenon: while some rotators are in the state of visible tumbling, a much
larger amount of objects must be performing narrow-cone precession not so
easily observable from the Earth. The internal dissipation in a freely
precessing top leads to relaxation (gradual damping of the precession) and
sometimes to spontaneous changes in the rotation axis. Recently developed
theory of dissipative precession of a rigid body reveals that this is a highly
nonlinear process: while the body is precessing at an angular rate $ \omega$,
the precession-caused stresses and strains in the body contain components
oscillating at other frequencies. Dependent upon the spin state, those
frequencies may be higher or, most remarkably, lower than the precession rate.
In many states dissipation at the harmonics is comparable to or even exceeds
that at the principal frequency. For this and other reasons, in many spin
states the damping of asteroidal and cometary wobble happens faster, by several
orders, than believed previously. This makes it possible to measure the
precession-damping rate. The narrowing of the precession cone through the
period of about a year can be registered by the currently available
spacecraft-based observational means. However, in the near-separatrix spin
states a precessing rotator can considerably slow down its relaxation.
