that
(3.65)
3.5.2 Distinction Between the Rotation and Transformation Matrices
Here, it has been shown that the transformation matrix between two reference frames
3.6 Relationship Between the Matrix Representations of a Rotation Operator in Different Reference Frames
Consider the following rotation.
(3.66)
This rotation can be described by the following matrix equations expressed in two different reference frames
In the above equations,
(3.69)
(3.70)
As for the vectors
When Eqs. (3.71) and (3.72) are substituted, Eq. (3.68) becomes
When Eqs. (3.67) and (3.73) are compared, it is seen that the matrices
3.7 Expression of a Transformation Matrix in a Case of Several Successive Rotations
Suppose a reference frame
In such a rotational sequence, the overall transformation matrix can be obtained as follows:
The matrix
3.7.1 Rotated Frame Based (RFB) Formulation
In this case, rot(p, q) is expressed as a rotation matrix in one of the two relevant reference frames, i.e. either in the pre‐rotation frame
(3.77)
