Jmol Quaternion Illustrator

Left-drag to rotate q1 or q2. You can also rotate the reference frame in the top left to get a better look at q1 q2, dq, and Dq. "dq" (q2 / q1) is the quaternion taking q1 to q2 in the stationary reference frame; "Dq" (q1 \ q2) is the quaternion taking q1 to q2 from the perspective of the q1 frame. Mathematically:
Dq = q1-1 * dq * q1 = q1 \ dq * q1.
q1  spin
q2  spin
dq = q2 / q1
Dq = q1 \ q2
trace