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An asteroid generally has an irregular shape, therefore, one would expect its rotation is quite erratic in some sense. Are there any observational examples?

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    $\begingroup$ Actually no, any body would rotate about its center of mass in a predictable way in the absence of external forces. $\endgroup$ – ja72 Jul 20 '15 at 19:42
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Rigid bodies with three distinct moments of inertia have two stable rotation axes, the axes with the greatest and least moments of inertia (typically the shortest and longest axes). Non-rigid bodies have but one stable rotation axis, the axis with the greatest moment of inertia. The axis with the least moment of inertia becomes unstable thanks to entropy.

Assuming no external torques act on the body, the body's angular momentum will be conserved. It's rotational energy, however, is not conserved. The tumbling of a non-rigid body causes the object to heat up a bit. That heat gets radiated into space. The object loses energy to the universe as a whole (thereby maximizing entropy). The axis with the smallest moment of inertia represents the largest rotational energy configuration for a fixed angular momentum. That axis gets locked out as the body radiates away energy. The axis with the largest moment of inertia represents the smallest rotational energy configuration for a fixed angular momentum. This is the configuration toward which non-rigid rotators eventually migrate.

As a consequence, most asteroids rotate about their shortest axis (the axis with the greatest moment of inertia). There are a few that don't. Toutatis exhibits a complex rotational motion.

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