Heydi ho everyone,
I was doing some differentiation of quaternions, and am trying to find the differentiation of a position wrt change in quaternion exponential.

That is, if I have a quaternion, I can translate a point using:

pos = q t q*

where t = q(0,x,y,z)

simple, yes?

If I have the exponent of the quaternion, the axis-angle (w) - which is the axis multiplied by the angle, which we call 'w'. So my quaternions are q(w) and q(w)* - since they are from the axis-angle exponent w.

What would be the change in position with change in axis-angle (i.e., the exponential).

d( q(w) t q(w)* ) / dw = ??

If that makes sense?