I have alot of confusion with Eulerian angle so first of all I would like to address something I don't understand from the book and maybe that would shed some light on the intuition of eulerian angles.
Here is the book Explanation for Eulerian angles:
The coordinate system labeled O-123 is defined by the three principal axes fixed to the rigid body and rotates with it. The coordinate system fixed in space is labeled Oxyz. A third,rotating system, O$x'y'z'$ providing a connection between the principal axes attached to the body and axes fixed in space, is also defined as follows: The $z'$-axis coincides with the 3-axis of the body --- its symmetry axis The $x'$-axis is defined by the intersection of the body 1-2 plane with the fixed xy plane ? This is called the line of nodes.
So I don't understand is the plane O-x
yz` changing always with time or is it fixed?