# Finding quaternion $q_x$ in the following equation: $q_x q_1 q_x' = q_2$

Given that $$q_1$$ and $$q_2$$ are known quaternions.

• It looks like you're trying to find the quaternion that performs a particular spatial rotation. Is that correct? – Adrian Keister Jan 25 at 21:38
• The rotation about unit vector $u_x\mathbf{i}+u_y\mathbf{j}+u_z\mathbf{k}$ through an angle $\theta$ corresponds to the quaternion $\mathbf{q}=\cos(\theta/2)+(u_x\mathbf{i}+u_y\mathbf{j}+u_z\mathbf{k})\,\sin(\theta/2)$. – Adrian Keister Jan 25 at 21:42
• I'd like to find a quaternion that rotates q1 so it matches q2. The actual problem I was trying to solve is in this thread: math.stackexchange.com/questions/3087370/… – Övünç Tüzel Jan 25 at 23:35
• Possible duplicate of Finding the Quaternion that rotates a coordinate system to match another. You didn't really have to make a new contextless question. – rschwieb Jan 26 at 13:50