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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.

## Homework 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.

## The Attempt at a Solution

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