Heydi ho everyone,

I was doing some differentiation of quaternions, and if I have a quaternion, I can translate a point, e.g.

 

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). so my quaternions are q(w) and q(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?

 

Thanx,

 

Bob

Because quaternion multiplication doesn't commute, you have to distinguish between differentiation to the right and to the left.

 

Which my old book on that topic briefly commented with: "this must be one reason why differential calculations on quaternions are little developed".

Which my old book on that topic briefly commented with: "this must be one reason why differential calculations on quaternions are little developed".

Which old book? I suggest a newer one such as Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality by J. B. Kuipers. Chapter 11 discusses "quaternion calculus for kinematics and dynamics" (that's the title of the chapter).