I created a DCM from Euler angle sequence 1-2-3. Then I found the Principal Rotation Parameters from the DCM. Then I used the Principal Rotation Parameters to find the DCM again. But I produced a different DCM both times. Can you help me fix the MATLAB code, so I produce the same DCM both times?

 

 

EA = [pi/3; -pi/4; -pi/6];
EA123toDCM = EA123DCM(EA)

[theta, lambda] = DCMtoPRP(EA123toDCM)

PRPtoDCM = PRP2DCM(theta, lambda)

 

function [R] = EA123DCM(EA)

    theta1 = EA(1,1);
    theta2 = EA(2,1);
    theta3 = EA(3,1);
   
   
    R1 = @(a)[1    0      0    ;
              0  cos(a) sin(a);
              0  -sin(a) cos(a)];
         
    R2 = @(a)[cos(a)  0 -sin(a) ;
                0     1   0    ;
              sin(a) 0 cos(a)];
         
    R3 = @(a)[ cos(a) sin(a) 0;
               -sin(a) cos(a)  0;
                 0      0     1];
     
    R = R3(theta1)*R2(theta2)*R1(theta3);

 

end

 

function [theta, lambda] = DCMtoPRP(EA123toDCM)

    theta = acos((1/2)*(trace(EA123toDCM)) - 1);
    lambda = (1/(2*sin(theta))) * [EA123toDCM(2,3) - EA123toDCM(3,2);
                                   EA123toDCM(3,1) - EA123toDCM(1,3);
                                   EA123toDCM(1,2) - EA123toDCM(2,1)];

end

 

function [PRPtoDCM] = PRP2DCM(theta, lambda)
    C11 = lambda(1,1)^2*(1-cos(theta))+cos(theta);
    C12 = lambda(1,1)*lambda(2,1)*(1-cos(theta))+lambda(3,1)*sin(theta);
    C13 = lambda(1,1)*lambda(3,1)*(1-cos(theta))-lambda(2,1)*sin(theta);
    C21 = lambda(1,1)*lambda(2,1)*(1-cos(theta))-lambda(3,1)*sin(theta);
    C22 = lambda(2,1)^2*(1-cos(theta))+cos(theta);
    C23 = lambda(3,1)*lambda(2,1)*(1-cos(theta))+lambda(1,1)*sin(theta);
    C31 = lambda(1,1)*lambda(3,1)*(1-cos(theta))+lambda(2,1)*sin(theta);
    C32 = lambda(3,1)*lambda(2,1)*(1-cos(theta))-lambda(1,1)*sin(theta);
    C33 = lambda(3,1)^2*(1-cos(theta))+cos(theta);

    PRPtoDCM = [C11 C12 C13;
                           C21 C22 C23;
                           C31 C32 C33];

end