homework and exercises - Determining the torque needed to rotate a spacecraft to a given rotation/quaternion

Which is the correct algorithm to determine the torque needed to rotate a spacecraft to a given quaternion ? I have a set of quaternions of a spacecraft and the time difference (delta T) between the quaternions.

I've tried estimating the angular velocity and angular acceleration as: 1. Find quaternion q so q = q1/q0

2. Convert quaternion q to axis and angle:

len=sqrt(q.xq.x+q.yq.y+q.z*q.z); angle=2*atan2(len, q.w); axis = q.xyz()/len;

3. angular velocity w = axis * angle / dt.


4. angular acceleration a = w/dt.

Using this algorithm, the computed angular acceleration (a) is not correct.

What I'm doing wrong? Is this the correct way to obtain the angular acceleration and torque from a sequence of two quaternions?