Chapter 06. Fundamentals of Rotations
Quaternions are related in a fundamental way to 3D rotations, which can represent orientation frames and can act to produce changes in orientation frames. In this chapter, we begin by presenting the relationships among 2D rotation operations, 2D rotation matrices, and complex numbers. We then move on to 3D rotation matrices, examine an interesting idea that looks like the square root of a rotation, and finally relate all of this to 3D rotations and quaternions.
2D Rotations
Rotations of 2D vectors are implemented by the action of 2D orthogonal matrices R2 with determinant one, and thus
Equation 6.1.
The 2 × 2 matrix ...
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