Changes

[[File:Euler2.png|frame|center|Image reproduced from [http://keywordsuggest.org/gallery/427706.html here]]]

Shown above is a rotation following a particular convention of (Ф,Ө,ψ), the angles being rotation about (z,x,z) axes respectively. The rotation matrix A then is,

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 \>

Another major problem with euler angles is that of gimbal lock. If Ө=π/2 above, then final rotation matrix A would be: