Aren't asteroids contradicting Euler's rotation theorem?

geometry physics rotations euclidean-geometry

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).

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