3.4 Rotation Vector

The rotation vector, introduced in the previous chapter, is defined by an axis of rotation and an angular rotation about this axis. If u is a unit vector along the rotation axis and is the angular rotation then the rotation vector is given by

The rotation matrix (i.e. the DCM that describes this rotation), which was given by Eq. (2.23) is

Conversely, one can deduce the rotation vector from a given DCM. However it should be noted that the deduced rotation angle would be in terms of its sine and cosine rather than the explicit rotation angle.