Question: What are principal rotations, and how can any spatial rotation be decomposed into them?

Answer: Principal rotations are rotations around the three axes of a coordinate system: the x, y, and z axes. Any rotation in three-dimensional space can be decomposed into a combination of these principal rotations. To perform a rotation around a point or axis in three-dimensional space, you can first rotate around the x axis, then rotate around the y axis, and finally rotate around the z axis. This is known as the "axis-angle" representation of a rotation. In two dimensions, the principal rotations are around the x and y axes, and a rotation can be decomposed into a combination of these two. Principal rotations form a group under the operation of composition, meaning that if you perform one rotation followed by another, the result is also a rotation.
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