# Euler rotations and acceleration

I have a system determined by 3 Euler angles that describe the orientation with respect to a fixed coordinate system XYZ.

The angular velocities are: $$\omega_2$$ (precession), $$\omega_1$$ (nutation) and $$\omega_z$$ (spin). The angular acceleration of $$\omega_z$$ is $$\alpha_z$$. The other angular accelerations are 0.

How can I find the acceleration of a point (e.g. A on the spinning reference frame xyz)? I am looking for the procedure to follow.

$$\vec{v}_P =\vec{v}_O + \vec{\omega}\times \vec{r}_P$$ $$\vec{a}_P =\vec{a}_O + \dot{\vec{\omega}}\times \vec{r}_P + \vec{\omega}\times \left( \vec{\omega}\times \vec{r}_P\right)$$