Let’s suppose we are given an Euler angle sequence ZYX with angles

as = {0.2, 0.25, 0.3}

**We have been asked to convert that to ZYZ.**

(You probably want to have read the previous quaternion posts.) I will remind us that the notation ZYX means the rotation

Rx Ry Rz,

with the Z-axis rotation first; and I write the angles in the same order, ZYX,, so the given rotation is

m0 = Rx(.3) Ry(.25) Rz(.2).

We do not need to compute it, but we might as well; if for no better reason than that we will be able to check our answer. The rotation matrix for the given Euler angle sequence works out to: