Aren't asteroids contradicting Euler's rotation theorem? I am totally confused about Euler's rotation theorem.
Normally I would think that an asteroid could rotate around two axes simultaneously. But Euler's rotation theorem states that:

In geometry, Euler's rotation theorem
  states that, in three-dimensional
  space, any displacement of a rigid
  body such that a point on the rigid
  body remains fixed, is equivalent to a
  single rotation about a fixed axis
  that runs through the fixed point. It
  also means that the composition of two
  rotations is also a rotation.

But asteroids do rotate around two axes. Look at the videos from this website:
http://csep10.phys.utk.edu/astr161/lect/asteroids/features.html

The Spin of Asteroid Toutatis
By making a series of observations, it
  is possible to study the rotation of
  some asteroids. Most have simple
  rotations around a fixed axis, with
  periods typically between one hour and
  one day. For example, here is a movie
  (83 kB MPEG) made by the Hubble Space
  Telescope of the asteroid Vesta in
  rotation (Ref). However, the asteroid
  4179 Toutatis (which crosses Earth's
  orbit) has been found through radio
  telescope observations to have an
  irregular shape and a complex tumbling
  rotation---both thought to arise from
  a history of violent collisions. Here
  is a short animation (47 kB MPEG) of
  the spin of Toutatis; here is a longer
  animation (288 kB MPEG).

Here are the movies:
http://csep10.phys.utk.edu/astr161/lect/asteroids/toutspin.mpg
and
http://csep10.phys.utk.edu/astr161/lect/asteroids/toutspin2.mpg
You can clearly see that those rotations are not possible around one axis. But then isn't it contradicting Euler's rotation theorem?
 A: I think you are confusing a single rotation (as a fixed displacement) with a  rotational motion.
Euler theorem says that the composition of two individual rotations (say, I rotate a body 15 degrees around a vertical axis, then I rotate it 10 degrees around some horizontal axis) is equivalent to a single rotation around some axis. 
But suppose I do the same double rotation, with the same axes but, say, double angles ( 30 and 20 degrees): they would be, again, equivalent to a single rotation, but the equivalent axis would be different.
Hence, the composition of two rotation (motions) with fixed axis is not equivalent to some other rotation (motion) with another (fixed) axis. Then, to speak of the superposition of two rotational motions (that cannot be reduced to a single rotational motion) makes perfect sense.
Example: Take a long cilinder, make it rotate quicky along its longitudinal axis. Superpose to that a slow rotation along a transversal axis. If both axis passes through the center of the cylinder, there is a fixed point. However, the resulting rotational motion cannot be expressed as a single rotational motion (with a fixed axis).
A: Hmm well actually for any rigid body, it does rotate along an axis. (at least for a infinitesimal amount of time) and this rotation will stay around the same axis over time as long as no torque is applied. It may just be difficult to see that axis. 
