Abstract
J. A. Burns and V. S. Safronov (Mon. Not. R. Astron. Soc. 165, 403-411, 1973) estimated the damping time scale of rotational wobble for asteroids, and concluded that all asteroid rotations then known should be damped to a state of principal-axis rotation about the axis of maximum moment of inertia. I have reexamined this question in the light of some more recently determined cases of very slow rotation rates and find that for several asteroids, the damping time scale is expected to be considerably longer than the age of the Solar System, implying that these objects may very well exhibit non-principal-axis rotation, which in an extreme case of a large amplitude wobble of a very irregularly shaped body may lead to the appearance of nearly irregular "tumbling" in space. Perhaps most notable in this group is the asteroid 4179 Toutatis. Both radar observations (Ostro et al., Bul. Amer. Astron. Soc. 25, 1126, 1993) and lightcurve observations (M. A. Barucci, J. R. Spencer, personal communications 1993) suggest that Toutatis may indeed be in a more complex state of rotational motion than simple principal-axis rotation. I mention several other examples of objects which might be expected to be in similar states and a couple of examples of lightcurve observations of such objects that appear to support that conclusion.
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