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Rodrigues Parameters from Rotation Matrix

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

 

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