Euler, Jacobi, and Missions to Comets and Asteroids

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.