Libration vs. rotation for mass on rotating disc

Hello I have a question about the difference between rotation and libration. In some textbook it is stated that for libration $$\begin{equation} q (t+\tau) = q(t) \\ p (t + \tau) = p(t) \end{equation}$$ with the coordinates $$q$$, the momentum $$p$$, time $$t$$ and period $$\tau$$. Rotation is given by $$\begin{equation} p (q + q_0) = p(q) \end{equation}$$
Now I am wondering if a mass is fixed on a rotating disc, rotating with a constant angular velocity, then this would be a libration, but I would expect it to be a rotation, since I had the feeling that libration and oscillation should be similar, but this example is not an oscillation.

• I believe rotation is required for libration. For instance, the Moon rotates, librates, and nutates - and probable has other small oscillations. – Cinaed Simson Jul 14 at 0:05
• And I think of the libration, nutation, etc. as being a result of the mathematical description of the motion being imprecise. For instance, the case of the Moon, Cassin's Laws being imprecise. – Cinaed Simson Jul 14 at 0:08