In this example we derive Rodrigues parameters/Gibbs Vector from the rotation matrix elements. The Rodrigues parameters have a singularity at 180 deg and use is limited for principal rotations which are less than 180 deg.
clc; clear all; % Rotation matrix Rm = [0.36 0.48 -0.8; -0.8 0.6 0; 0.48 0.64 0.6 ]; g1 = (Rm(2,3)- Rm(3,2))/(1 + trace(Rm)); g2 = (Rm(3,1)- Rm(1,3))/(1 + trace(Rm)); g3 = (Rm(1,2)- Rm(2,1))/(1 + trace(Rm)); G = [g1 g2 g3]'
G =
-0.2500
0.5000
0.5000
Small Satellites 