To see a physical example of non-commuting rotations, do the following experiment. Put a book on your desk and imagine a set of rectangular axes with the x and y axes in the plane of the desk with the z axis vertical. Place the book in the first quadrant with the and y axes along the edges of the book. Rotate the book 900 about the x axis and then 900 about the z axis; note its position. Now repeat the experiment, this time rotating 900 about the z axis first, and then 900 about the x axis; note the different result. Write the matrices representing the 900 rotations and multiply them in both orders. In each case, find the axis and angle of rotation.
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Mathematical Methods in the Physical Sciences
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