I need help with a MATLAB problem. The following code uses an ode45 function to integrate the Kinematic Differential Equations. What I want to do is C_ode * transpose(C_ode)? I can't do that because C_ode is composed of multiple 3x3 matrices. The function transpose dosen't support N-D arrays. So, how do I accomplish C_ode * transpose(C_ode)? I tried using CCT = sum(C_ode .* permute(C_ode, [2, 1, 3]), 1); but it gives me 3x1 matrices which is incorrect. C_ode * transpose(C_ode) should give the a 3x3 identity matrix.

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
icon
Related questions
Question

I need help with a MATLAB problem. The following code uses an ode45 function to integrate the Kinematic Differential Equations. What I want to do is C_ode * transpose(C_ode)? I can't do that because C_ode is composed of multiple 3x3 matrices. The function transpose dosen't support N-D arrays. So, how do I accomplish C_ode * transpose(C_ode)? I tried using CCT = sum(C_ode .* permute(C_ode, [2, 1, 3]), 1); but it gives me 3x1 matrices which is incorrect. C_ode * transpose(C_ode) should give the a 3x3 identity matrix.

 

% Initial Conditions
w = [2;-1;1];
T = 30;
I = [150; 400; 400];
EP = [0;0;0;1];
C = eye(3,3);
tspan = [0 20]; 

% Using ode45 to integrate w dot
options = odeset('RelTol',1e-10,'AbsTol',1e-10);
result = ode45(@K_DDE, tspan, [w; C(:)], options);

% Extracting information from ode solver
t = result.x;
w_ode = result.y(1:3,:);
C_ode = reshape(result.y(4:end,:), [3,3,length(t)]);
CCT = C_ode*transpose(C_ode)


function dwCdt = K_DDE(t, w_C)
    w = w_C(1:3); % corrected indexing for w
    C = reshape(w_C(4:end), [3,3]); % corrected indexing for C

    % Kinematic Differential Equations for DCM
%     dCdt = zeros(3, 3);
%     dCdt(1,1) = C(1,2)*w(3) - C(1,3)*w(2);
%     dCdt(1,2) = C(1,3)*w(1) - C(1,1)*w(3);
%     dCdt(1,3) = C(1,1)*w(2) - C(1,2)*w(1);
%     dCdt(2,1) = C(2,2)*w(3) - C(2,3)*w(2);
%     dCdt(2,2) = C(2,3)*w(1) - C(2,1)*w(2);
%     dCdt(2,3) = C(2,1)*w(2) - C(2,2)*w(1);
%     dCdt(3,1) = C(3,2)*w(3) - C(3,3)*w(2);
%     dCdt(3,2) = C(3,3)*w(1) - C(3,1)*w(3);
%     dCdt(3,3) = C(3,1)*w(2) - C(3,2)*w(1);

    w_skew = [0 -w(3) w(2);
              w(3) 0 -w(1);
              -w(2) w(1) 0];
    dCdt = C*w_skew;

    dwCdt = [zeros(3,1); dCdt(:)];
end

Expert Solution
steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Knowledge Booster
Fundamentals of Boolean Algebra and Digital Logics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education