TITLE: Find rotation axis in 3D space with quaternions
QUESTION [0 upvotes]: Rotation of $u_1$ around $q_1$(unknown) axis is $u_2$, and rotation of $u_2$ around $q_2$(unknown) axis is $u_3$.
What is the value of axis $q$,in case $q$=$q_1$=$q_2$?
Note that possible values of $q_1$ makes a circle,$c_1$, in 3d space,and $q_2$ another circle,$c_2$, in 3d space.
Question is to find the intersection($q$,unit vector) of these circles, $c_1$ and $c_2$.
related to question in find quaternion scalar from end points of the rotation

REPLY [0 votes]: Axis of rotation of $q_1$ is $c_{1} = u_1 \times u_2$.
Axis of rotation of $q_2$ is $c_{2} = u_2 \times u_3$.
The two circles intersect at $\pm (c_{1} \times c_{2})$ normalized to unit length.
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