Composition of rotational transformations

seyma

Show that when basic rotations are combined to find composite rota-
tional transformations, if the rotation is about one of the principal axes of
OXYZ (the fixed frame) the previous resultant rotation matrix is premulti-
pled by the new rotational transformation, and if the rotation is about one
of the principal axes of OUVW (the moving frame) the previous resultant
rotation matrix is postmultipled by the new rotational transformation.


2. Relevant equations

I know that I can write fixed frame coordinates in terms of moving frame that is the transition matrix which is composed of unit vectors of two coordinates. I call this R. Then I
call fixed frame rotation A and moving frame rotation B. then this becomes A = RB. also for any rotation matrix call R' I can write AR' = R'B.



3. The attempt at a solution

Also I know all transformation matrix is orthonormal. However I cannot know how to prove.