The basis of determining time derivatives of a vector using a rotating frame
is illustrated in Figure 1.3.17.

FIGURE 1.3.17 Time derivative of a  vector using a rotating reference frame.

Analysis of Velocities and Accelerations Using Rotating and Translating Frames

With the concept of general motion understood, an advantageous method
of determining velocities and accelerations is available by the method of
rotating reference frames. There are two cases in which this method
can be used. For a common origin of XYZ and xyz, with r being
a position vector to a point P,

For the origin A of xyz translating with respect XYZ:

where ? is the angular velocity of the xyz frame with respect to XYZ.
2? ? vxyz is the Coriolis acceleration.
Read more…