# Understanding Euler's Rotation equation for rigid bodies (Frames Of Reference)

$$\tau_b=I_n\dot\omega_b+\omega_b\times I_b\omega_b$$

Now in the above is Euler's famous rigid body rotation equation, in the body frame of reference ..... this does not make sense to me. How can a body have a rotation in its own frame of reference? For example:

The earth rotates right, we all know it does, and from my understanding of frame of reference, when you pick the earth's frame of reference, you adopt its rotational and translational motion, hence from your point of view, the earth is not rotating or moving (if not for the star's moon and sun, we won't know that we are rotating), so how is it that an object can have a rotation in its own frame of reference?

I think an objects rotation in its own frame of reference is zero.

• the rotation is relatively to inertial frame . – Eli Mar 31 at 7:13