Rigid-body rotation with a rotating axis of rotation?

Question

How does the conservation of angular momentum apply to complicated rotations where the actual axis of rotation is itself rotating about a different axis? Aren't the rotations of Hyperion and 4179 Toutatis like this? If no torque acts on the system, are even these complicated rotations preserved in space? Or do they gradually simplify into simple single-axis rotations over a billion years or so?

http://en.wikipedia.org/wiki/Hyperion_%28moon%29
http://en.wikipedia.org/wiki/4179_Toutatis

Answer 1

Revised (thought you were talking about starts)

The rotation of an asymmetric body is rather complicated. The important thing to understand is that angular velocity and angular momentum are vectors (with three components), and they do not always point in the same direction. Furthermore, the moment of inertial is a *tensor*. You need to treat the case in question in the context of a more general rigid body motion. I suggest a good text book on classical mechanics. The wiki ref is a good place to start.

As for decaying away over time, precessional motion is quite persistent, and there is little in the way of dissipative effects. The earth, for example, is quite happy with its equinox precession.

Answer 2

Yes you are right about that they do simplify single axis rotations but not of a billion years but of of a few thousand years.

Answer 3

So you did the summation of the linear kinetic energy of the wheel + the initial kinetic energy of rotation ( E1+E2), but I am kind of wandering where does the quantity of (1+0.8) that you multipied comes from?