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:
You can clearly see that those rotations are not possible around one axis. But then isn't it contradicting Euler's rotation theorem?