General 3-D Motion
Let us say that axes xyz rotate with angular velocity 
, which is different from the angular velocity 
of the body.
We can easily prove that
where dot indicates time derivative.
The expression for the velocity and acceleration of point P, become
where 
and 
If the axes are rigidly attached to the body, 
and Vrel and arel both are zero. In that case the equation reduces to previous equations.