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

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/(2sin(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

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

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

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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?

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