Quaternion Differential

[BinaryBob]

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

[Enthalpy]

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".

[D H]

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).