I'm having trouble visualizing Euler's Rotation Theorem.
I will give a simple example.
Consider an arbitrary sphere and 3 orthogonal vectors that start from the center of the sphere and extend to the sphere's surface.
Here the blue vector is pointing AWAY from the viewer.
Then rotate this sphere so the vectors now look like this:
The red vector is pointing TOWARDS the viewer.
Then rotate the sphere again:
Euler's rotation theorem:
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point.
However if we consider the first and last image, the only way I can imagine that the red vector displaces in that way, is for a rotation about the Green axis in the first image. However, a rotation in the Green axis guarantees the Green vector won't displace.
What would a single rotation axis look like (intuitively)?