In Orientation Representations: Part 1, we explored the use of
rotation matrices and Euler angles. At the end of that
discussion, I alluded to the fact that there might be more
efficient ways of describing rotations. Let’s start with the
rotation of a simple rigid body (in this case a cylinder) as
shown in Figure 1. Here, the cylinder is rotated such that a
point on its surface originally at “A” is rotated to point “B”
in space. Figure 1: Rotation of a rigid body such that a
reference point moves from “A” to “B” For this simple case, I’ve
kept the axis of rotation along the vertical axis of the
cylinder as shown in Figure 2. But that is not a requirement for
the underlying mathematics to work. So long as we have a rigid
body, we can always describe the rotation in the manner that
follows. Figure 2: Overlay of Cartesian Coordinates onto System
of Figure 1 Figure 3 deals with the same rotation, but focuses
on the fact that we have a rotation plane that is perpendicular
with the axis of rotation. The movement of