The reason this works is often skipped in computationally oriented writeups:
Rotations of 3-dimensional real space form the topological group SO(3). Naive parameterizations of that group do not form a cover [1], but the group of norm-1 quaterinons, Spin(3), does.
The failure of naive parameterizations, like the Euler angles, to be a cover manifests itself as gimbal lock.
Rotations of 3-dimensional real space form the topological group SO(3). Naive parameterizations of that group do not form a cover [1], but the group of norm-1 quaterinons, Spin(3), does.
The failure of naive parameterizations, like the Euler angles, to be a cover manifests itself as gimbal lock.
[1] https://en.wikipedia.org/wiki/Covering_space