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M. Efroimsky (Harvard-Smithonian Center for Astrophysics and the Department of Physics, Harvard University)
Whenever a freely spinning body is found in a complex rotational state, this means that either the body experienced some interaction within its relaxation-time span, or that it was recently ``prepared'' in a non-principal state. Both options are encountered in astronomy where a wobbling rotator is either a recent victim of an impact or a tidal interaction, or is a fragment of a disrupted progenitor. Another factor (relevant only for comets) is outgassing. By now, the optical and radar observational programmes have disclosed that complex rotation is hardly a rare phenomenon among the small bodies. 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 observable tumbling, a much larger amount of objects must be performing narrow-cone precession not so easily visible 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 (as it happened in 1958 to satellite Explorer). 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 dissipation processes in the body are taking place also at other frequencies. Dependent upon the spin state, those frequencies may be higher or lower than the precession rate. In many states dissipation at the harmonics exceeds that at the principal frequency \omega.
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. We propose an appropriate observational scheme that could be accomplished by comet and asteroid-aimed missions. Improved understanding of the damping of excited rotation will directly enhance understanding of the current distribution of small-body spin states. It also will constrain the structure and composition of excited rotators.
There exist, however, spin states in which the precessing rotator can considerably slow down its relaxation. (These are the near-separatrix states.) This lingering effect is similar to the one discovered in 1968 by Russian spacecraft engineers who studied free precession of a tank with viscous fuel.
The author(s) of this abstract have provided an email address for comments about the abstract: efroimsk@fas.harvard.edu