I think you might have some mathematical gaps, they are not overspecified. It is impossible to fully specify 3d rotations as 3 variables.. if you want a nice al

I think you might have some mathematical gaps, they are not overspecified. It is impossible to fully specify 3d rotations as 3 variables.. if you want a nice algebraic structure. R^3 is not isomorphic to SO(3). All the representations have tradeoffs, quarterions are the simplest algebraically.