I am a part time computer engineering student which works in the field of computer graphics. I am forcing myself to get to know deeper tha math I work with and I am a bit stuck on the concept of gimbal lock from a topological point of view.
Could someone try to explain both formally and more intuitevely why euler angles are SO(3)/toroidal and not simply connected while quaternions are? and why quaternions have a covering map to the real projective space?
Thanks!