Discrete quaternion time derivative

Hi everybody!

I would like to ask you an opinion. I have a file with time variable quaternions and I would like to numerically evaluate the time derivative, that is given q(i), q(i-1) t(i) and t(i-1) I express the quaternion time derivative as

q_dot = (q(i) - q(i-1)) / (t(i) - t(i-1))

where q denotes a quaternion and t is the time.

Now my question is: do I have to express the time in a quaternion form [t(i) 0 0 0] and use the quaternion division or can I divide a quaternion by a scalar?

I know there is a formula linking the angular velocity to the time derivative of the quaternion, but I don't know the angular rate which has to be determined using this formula.

I hope some of you can help me or suggest me another way to cope with this problem. Many thanks for your help.

Phate