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)? % 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)]); 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
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)?
% 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)]);
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
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