Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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I need help with my MATLAB code. This code produces an angular velocity plot. I want the x-axis of the plot to go from 0 to 12 hours instead of 0 to 43200 seconds. But I still want the input to be t = 0:43200. I just want to change what it says when the code produces the plot. Also, on the y-axis, I need it to go from -0.05 to 0.1. Can you help me with that?

 

 

% Initial conditions
mu = 398600;            % km^3/s^2
R = 6800;               % km
I = [400; 600; 800] * 10^-6;    % kg*km^2

% Initial PRP and velocity vectors
lambda = [1/sqrt(3); 1/sqrt(3); 1/sqrt(3)];
theta = 3;              % deg
w = [0; 0; sqrt(mu/R^3)];
t = 0:43200;            % sec

% Finding MRP
MRP = PRP2MRP(lambda, theta)

% Problem 1 (e.2)
% Integrate the Euler equations using ode45
options = odeset('RelTol',1e-10,'AbsTol',1e-10);
[t, y] = ode45(@KDE_MRP, t, [MRP; w; I], options);

% Extract the Euler parameters and angular velocities
MRP2 = y(:, 1:3);
w2 = y(:, 4:6);

 

plot(t,w2, '-')
xlabel('time (s)')
ylabel('angular velocity (rad/s)')
legend('w1', 'w2', 'w3')

 

 

 

function MRP = PRP2MRP(lambda, theta)
    
    % Finding EP from PRP
    EP1 = lambda(1)*sind(theta/2);
    EP2 = lambda(2)*sind(theta/2);
    EP3 = lambda(3)*sind(theta/2);
    EP4 = cosd(theta/2);

    EP = [EP1; EP2; EP3; EP4];

    % Finding MRP from EP
    sigma1 = EP(1)/(1+EP(4));
    sigma2 = EP(2)/(1+EP(4));
    sigma3 = EP(3)/(1+EP(4));
    MRP = [sigma1; sigma2; sigma3];


end

 

function dMRPwdt = KDE_MRP(~,MRPwI)

    MRP = MRPwI(1:3);
    w = MRPwI(4:6);
    I = MRPwI(7:9);

    dMRPdt = zeros(3,1);
    dwdt = zeros(3,1);

    C11 = 1 - dot(MRP,MRP) + 2*MRP(1)^2;
    C12 = 2*(MRP(1)*MRP(2) - MRP(3));
    C13 = 2*(MRP(1)*MRP(3) + MRP(2));
    C21 = 2*(MRP(2)*MRP(1) + MRP(3));
    C22 = 1 - dot(MRP,MRP) + 2*MRP(2)^2;
    C23 = 2*(MRP(2)*MRP(3) - MRP(1));
    C31 = 2*(MRP(3)*MRP(1) - MRP(2));
    C32 = 2*(MRP(3)*MRP(2) + MRP(1));
    C33 = 1 - dot(MRP,MRP) + 2*MRP(3)^2;
    
    C = [C11 C12 C13;
         C21 C22 C23;
         C31 C32 C33];

    dMRPdt = 0.25 * C * w;

    K1 = (I(2) - I(3)) / I(1);
    K2 = (I(3) - I(1)) / I(2);
    K3 = (I(1) - I(2)) / I(3);
    R_mag = 6800;
    R1 = (R_mag/(1+dot(MRP, MRP))^2) * (4*(MRP(1)^2 - MRP(2)^2 - MRP(3)^2) + (1 - dot(MRP, MRP)));
    R2 = (R_mag/(1+dot(MRP, MRP))^2) * (8*MRP(2)*MRP(1) - 4*MRP(3)*(1 - dot(MRP, MRP)));
    R3 = (R_mag/(1+dot(MRP, MRP))^2) * (8*MRP(3)*MRP(1) - 4*MRP(2)*(1 - dot(MRP, MRP)));
    dwdt(1) = K1*w(2)*w(3) - ((3*w(3)^2*K1*R3*R2)/R_mag^2);
    dwdt(2) = K2*w(1)*w(3) - ((3*w(3)^2*K2*R1*R3)/R_mag^2);
    dwdt(3) = K3*w(1)*w(2) - ((3*w(3)^2*K3*R2*R1)/R_mag^2);


    % Combine the time derivatives into a single vector
    dMRPwdt = [dMRPdt; dwdt; 0;0;0];
end

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