T_u_inv(T) = [   0 1/T  0;
              -1/T   0  0;
                 0   0 -1]
T_u_inv_dot(T, Ṫ) = [    0 -Ṫ/T^2 0;
                     Ṫ/T^2      0 0;
                         0      0 0]
T_ω(T) = [0 -T  0;
          T  0  0;
          0  0  0]
skew(x) = [    0  -x[3]   x[2];
            x[3]      0  -x[1];
           -x[2]   x[1]     0]
