3 ms·
Isn't there some theorem stating that all 3 coordinate reps of rotations in R^3 have a singularity? But bumping up to 4 coordinates (or 9 if you like rotation m
by santaclaus 10y ago
Isn't there some theorem stating that all 3 coordinate reps of rotations in R^3 have a singularity? But bumping up to 4 coordinates (or 9 if you like rotation mats) eliminates the singularity.
Edit: seems kind of like latitude and longitude. At latitude + or - 90, all longitudes map to the same point so that coordinate has no information.
- chombier 10y agoYes, R^3 and the rotation group SO(3) are not homeomorphic (they have different topologies), meaning you can not cover SO(3) with a single chart. So any representation of rotations by 3 numbers is singular somewhere.