Angular acceleration

If $\omega$ is allowed to vary over time, then we must consider angular acceleration. In the 2D case, this is defined as

$$\alpha = { d\omega(t) \over dt } .$$ (8.16)

For the 3D case, there are three components, which results in

$$(\alpha_x,\alpha_y,\alpha_z) .$$ (8.17)

These can be interpreted as accelerations of pitch, yaw, and roll angles, respectively.