Definition of the Euler Transformation Matrices
To transform motions about the Mir body axes into the inertial reference frame, define three Euler angles , , and as arguments of three rotation matrices. These matrices will be combined into one matrix to provide for a general multiaxis rotation. The Euler matrices , and rotate from the inertial unprimed frame to the primed frame use the form where is a vector in inertial space. First rotate about the inertial space axis z to get to the first primed frame.
At this point . Now we rotate about the primed frame y axis, by .
At this point . Now rotate the double primed frame axis about the primed frame z axis (note, not x, since this is the Euler system).
Finally . Define to be the combined solid body rotation matrix and be its inverse such that
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