An object is rotated about its X axis by an amount φ and then it is rotated about its new Y axis by an amount Ψ From our study of Euler angles, we know that the resulting orientation is given by
whereas, if the two rotations had occurred about axes of the fixed reference frame, the result would have been
It appears that the order of multiplication depends upon whether rotations are described relative to fixed axes or those of the frame being moved. It is more appropriate, however, to realize that, in the case of specifying a rotation about an axis of the frame being moved, we are specifying a rotation in the fixed system given by (for this example) rotation matrix that is equivalent to the result is given by (2.72).)
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