Chapter 11. Looking at Elementary Quaternion Frames
The quaternion framework allows us to analyze the relationships among coordinate frames in a variety of ways. In preparation for the more complex situations that will soon arise in subsequent chapters, we pause for a moment to review a few very simple cases that exploit quaternion visualization. In the following we will look at single frames, the relationships between two or more discrete frames, and smoothly changing sequences of frames.
A Single Quaternion Frame
The simplest possible frame is the identity frame. If we take coordinate labels for points on S3 to be (w, x, y, z)—standing for the Euler-eigenvector rotation parameterization q = (cos(θ/2), sin(θ/2))—the 3D identity frame can be represented ...
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