[[File:Equation67.png|frame|center]]

Euler angles, however, entails some limitations. Firstly, these values are not obvious. One cannot guess them by merely looking at the final orientation. Think of it, when you are restricted by convention to use a particular sequence of axis rotations, you have to in some sense have some ‘foresight’ to understand the consequence of each rotation on the following one(s) and correctly predict the right combination of values. In the case of our amateur astronomer who had to point to an airplane, if we were to ask him to make a rotation to account for its orientation first before pointing to it he would’ve had a hard time. He wouldn’t know how his action of pointing to it (i.e the subsequent rotations) affect this initial adjustment he has made for its orientation. <br \>

[[File:Equation1.gif|frame|center]]

In the rotation we have made above, Ф and ψ have lost their unique identities. There are multiple values we could use to obtain the same result (as long as Ф +ψ is the same). Here, we have lost a degree of freedom, only two independent parameters are required to represent this rotation. In a mathematical sense, this is a problem, because we don’t have unique Ф and ψ values at hand. <br \>