If you are given two randomly oriented pairs of 3D orthogonal coordinate axes and asked to align them ,what would you do? Is aligning one pair of axes enough? No! The other two pairs could still be rotated in their plane about this axis. So, what if you align another pair? That’s it! They are perfectly matched now. So, intuitively, we could say that to align two 3D frames we would need a minimum of two pairs of vectors in these frames. The same holds true for the body and reference frames of a satellite. <br \>

Mathematically too, it turns out that the rotation matrix (which represents this process of alignment) has nine elements with six constraints imposed on them to qualify as a valid rotation matrix. The other three constraints to uniquely determine this matrix are to come from the vector pairs compared in both frames. Each of these pairs, you might think, provides three additional constraints. After all, we are to match three coordinates of both the vectors in the two frames. Remember, however, that these two vectors depict the same physical quantity in two different frames. So if two of their coordinates are matched, so is their third. This is because their magnitude (and we know this value from what quantity they represent) has to be the same in both frames. In fact, the vector pairs are all normalised to make things less complicated. <br \>

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