Talk:Charts on SO(3)
|WikiProject Mathematics||(Rated Start-class, Low-importance)|
Euler angles are z-y-z. Tait-Bryan (aka Cardan aka nautical) angles are x-y-z. These latter are often called "Euler angles", and somewhere mention of this confusion should be made, but it should not be presented as anything "correct" or "official".
Cayley rational parameters are in Weyl The Classical Groups. The reference should go in the C.r.p., not here.
The skew-symmetric matrices themselves form a chart near the identity. Their exponentials are the orthogonal matrices, so the previous version was just a complicated way of saying SO(3) parameterizes SO(3).