I'm reading a book on 3D game math where the author points out that when using Euler angles the same orientation can be reached by doing two different operations; say rotating a cube 90 degrees around Y-axis is the same as rotating 90 degrees around X, Y and Z-axis successively.
While I have experimentally verified that aliasing is persent when using Euler angles to represent orientation (since the mapping is many-to-one), I'm unable to understand why this singularity leads to the loss of a degree of freedom (Gimbal Lock).
Can someone mathematically explain the reason? I see no loss here, I'll still be able to orient the cube whichever way I want it to be oriented, then where's the lock?
Many people pointed me to videos in YouTube, which explains gimbal lock using 3D animations where a gimbal gets aligned to another and rotation is arrested; while this is a visual display of gimbal lock, I don't understand why something which is a mechanical/physical limitation also applies to the mathematical model of assoicating orientation with 3 (Euler) angles.