I need help with my MATLAB code. I am trying to numerically integrate two sets of equations. I want the ode45 to output a column vector of size (12,1). I am getting an error that says unable to meet integration tolerances without reducing the step size, but my t = 0:30. I am only going from 0 s to 30 s. How can that be too much? Can you see if you can fix it? Please make sure it works. clc; clear all; Problem 2 % Problem 2 (e) % Initial conditions mu = 398600; % km^3/s^2 R = 7000; % km I = [500; 600; 800] * 10^-6; % kg*km^2 A = [0;0]; % 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 = 0:30; % sec % Finding EP EP = PRP2EP(lambda, theta); % Using ode45 to integrate KDE and EOM options = odeset('RelTol',1e-10,'AbsTol',1e-10); [t, y] = ode45(@KDE_C, t, [EP; w; I; A], options); C11 = y(:,1); C12 = y(:,2); C13 = y(:,3); C21 = y(:,4); C22 = y(:,5); C23 = y(:,6); C31 = y(:,7); C32 = y(:,8); C33 = y(:,9); w2 = y(:,10:12); % Plotting the angular velocities plot(t, w2, '-') xlabel('Time (sec)') ylabel('Angular Velocity (rad/s)') legend('w1', 'w2', 'w3') plot(t, C11, t, C22, t, C33, '-') function EP = PRP2EP(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]; end function dCwdt = KDE_C(~,EPwI) EP = EPwI(1:4); w = EPwI(5:7); I = EPwI(8:10); mu = 398600; % km^3/s^2 R = 7000; dwdt = zeros(3,1); C11 = 1-2*EP(2,1)^2-2*EP(3,1)^2; C12 = 2*(EP(1,1)*EP(2,1)+EP(3,1)*EP(4,1)); C13 = 2*(EP(1,1)*EP(3,1)-EP(2,1)*EP(4,1)); C21 = 2*(EP(1,1)*EP(2,1)-EP(3,1)*EP(4,1)); C22 = 1-2*EP(1,1)^2-2*EP(3,1)^2; C23 = 2*(EP(3,1)*EP(2,1)+EP(1,1)*EP(4,1)); C31 = 2*(EP(1,1)*EP(3,1)+EP(2,1)*EP(4,1)); C32 = 2*(EP(3,1)*EP(2,1)-EP(1,1)*EP(4,1)); C33 = 1-2*EP(1,1)^2-2*EP(2,1)^2; C11_dot = C12*w(3) - C13*w(2); C12_dot = C13*w(1) - C11*w(3); C13_dot = C11*w(2) - C12*w(1); C21_dot = C22*w(3) - C23*w(2); C22_dot = C23*w(1) - C21*w(3); C23_dot = C21*w(2) - C22*w(1); C31_dot = C32*w(3) - C33*w(2); C32_dot = C33*w(1) - C31*w(3); C33_dot = C31*w(2) - C32*w(1); dCdt1 = [C11_dot; C12_dot; C13_dot]; dCdt2 = [C21_dot; C22_dot; C23_dot]; dCdt3 = [C31_dot; C32_dot; C33_dot]; K1 = (I(2) - I(3)) / I(1); K2 = (I(3) - I(1)) / I(2); K3 = (I(1) - I(2)) / I(3); R_mag = 7000; R1 = R_mag*C11; R2 = R_mag*C21; R3 = R_mag*C31; dwdt(1) = K1*w(2)*w(3) - ((3*(sqrt(mu/R^3))^2*K1*R3*R2)/R_mag^2); dwdt(2) = K2*w(1)*w(3) - ((3*(sqrt(mu/R^3))^2*K2*R1*R3)/R_mag^2); dwdt(3) = K3*w(1)*w(2) - ((3*(sqrt(mu/R^3))^2*K3*R2*R1)/R_mag^2); % Combine the time derivatives into a single vector dCwdt = zeros(12,1); dCwdt = [dCdt1; dCdt2; dCdt3; dwdt]; end

I need help with my MATLAB code. I am trying to numerically integrate two sets of equations. I want the ode45 to output a column vector of size (12,1). I am getting an error that says unable to meet integration tolerances without reducing the step size, but my t = 0:30. I am only going from 0 s to 30 s. How can that be too much? Can you see if you can fix it? Please make sure it works. clc; clear all; Problem 2 % Problem 2 (e) % Initial conditions mu = 398600; % km^3/s^2 R = 7000; % km I = [500; 600; 800] * 10^-6; % kgkm^2 A = [0;0]; % 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 = 0:30; % sec % Finding EP EP = PRP2EP(lambda, theta); % Using ode45 to integrate KDE and EOM options = odeset('RelTol',1e-10,'AbsTol',1e-10); [t, y] = ode45(@KDE_C, t, [EP; w; I; A], options); C11 = y(:,1); C12 = y(:,2); C13 = y(:,3); C21 = y(:,4); C22 = y(:,5); C23 = y(:,6); C31 = y(:,7); C32 = y(:,8); C33 = y(:,9); w2 = y(:,10:12); % Plotting the angular velocities plot(t, w2, '-') xlabel('Time (sec)') ylabel('Angular Velocity (rad/s)') legend('w1', 'w2', 'w3') plot(t, C11, t, C22, t, C33, '-') function EP = PRP2EP(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]; end function dCwdt = KDE_C(~,EPwI) EP = EPwI(1:4); w = EPwI(5:7); I = EPwI(8:10); mu = 398600; % km^3/s^2 R = 7000; dwdt = zeros(3,1); C11 = 1-2EP(2,1)^2-2EP(3,1)^2; C12 = 2(EP(1,1)EP(2,1)+EP(3,1)EP(4,1)); C13 = 2(EP(1,1)EP(3,1)-EP(2,1)EP(4,1)); C21 = 2(EP(1,1)EP(2,1)-EP(3,1)EP(4,1)); C22 = 1-2EP(1,1)^2-2EP(3,1)^2; C23 = 2(EP(3,1)EP(2,1)+EP(1,1)EP(4,1)); C31 = 2(EP(1,1)EP(3,1)+EP(2,1)EP(4,1)); C32 = 2(EP(3,1)EP(2,1)-EP(1,1)EP(4,1)); C33 = 1-2EP(1,1)^2-2EP(2,1)^2; C11_dot = C12w(3) - C13w(2); C12_dot = C13w(1) - C11w(3); C13_dot = C11w(2) - C12w(1); C21_dot = C22w(3) - C23w(2); C22_dot = C23w(1) - C21w(3); C23_dot = C21w(2) - C22w(1); C31_dot = C32w(3) - C33w(2); C32_dot = C33w(1) - C31w(3); C33_dot = C31w(2) - C32w(1); dCdt1 = [C11_dot; C12_dot; C13_dot]; dCdt2 = [C21_dot; C22_dot; C23_dot]; dCdt3 = [C31_dot; C32_dot; C33_dot]; K1 = (I(2) - I(3)) / I(1); K2 = (I(3) - I(1)) / I(2); K3 = (I(1) - I(2)) / I(3); R_mag = 7000; R1 = R_magC11; R2 = R_magC21; R3 = R_magC31; dwdt(1) = K1w(2)w(3) - ((3(sqrt(mu/R^3))^2K1R3R2)/R_mag^2); dwdt(2) = K2w(1)w(3) - ((3(sqrt(mu/R^3))^2K2R1R3)/R_mag^2); dwdt(3) = K3w(1)w(2) - ((3(sqrt(mu/R^3))^2K3R2*R1)/R_mag^2); % Combine the time derivatives into a single vector dCwdt = zeros(12,1); dCwdt = [dCdt1; dCdt2; dCdt3; dwdt]; 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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clc;
clear all;

Problem 2
% Problem 2 (e)

% Initial conditions
mu = 398600; % km^3/s^2
R = 7000; % km
I = [500; 600; 800] * 10^-6; % kg*km^2
A = [0;0];

% 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 = 0:30; % sec

% Finding EP
EP = PRP2EP(lambda, theta);

% Using ode45 to integrate KDE and EOM
options = odeset('RelTol',1e-10,'AbsTol',1e-10);
[t, y] = ode45(@KDE_C, t, [EP; w; I; A], options);

C11 = y(:,1);
C12 = y(:,2);
C13 = y(:,3);
C21 = y(:,4);
C22 = y(:,5);
C23 = y(:,6);
C31 = y(:,7);
C32 = y(:,8);
C33 = y(:,9);
w2 = y(:,10:12);

% Plotting the angular velocities
plot(t, w2, '-')
xlabel('Time (sec)')
ylabel('Angular Velocity (rad/s)')
legend('w1', 'w2', 'w3')
plot(t, C11, t, C22, t, C33, '-')

function EP = PRP2EP(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];
end

function dCwdt = KDE_C(~,EPwI)

EP = EPwI(1:4);
w = EPwI(5:7);
I = EPwI(8:10);
mu = 398600; % km^3/s^2
R = 7000;

dwdt = zeros(3,1);

C11 = 1-2*EP(2,1)^2-2*EP(3,1)^2;
C12 = 2*(EP(1,1)*EP(2,1)+EP(3,1)*EP(4,1));
C13 = 2*(EP(1,1)*EP(3,1)-EP(2,1)*EP(4,1));
C21 = 2*(EP(1,1)*EP(2,1)-EP(3,1)*EP(4,1));
C22 = 1-2*EP(1,1)^2-2*EP(3,1)^2;
C23 = 2*(EP(3,1)*EP(2,1)+EP(1,1)*EP(4,1));
C31 = 2*(EP(1,1)*EP(3,1)+EP(2,1)*EP(4,1));
C32 = 2*(EP(3,1)*EP(2,1)-EP(1,1)*EP(4,1));
C33 = 1-2*EP(1,1)^2-2*EP(2,1)^2;

C11_dot = C12*w(3) - C13*w(2);
C12_dot = C13*w(1) - C11*w(3);
C13_dot = C11*w(2) - C12*w(1);
C21_dot = C22*w(3) - C23*w(2);
C22_dot = C23*w(1) - C21*w(3);
C23_dot = C21*w(2) - C22*w(1);
C31_dot = C32*w(3) - C33*w(2);
C32_dot = C33*w(1) - C31*w(3);
C33_dot = C31*w(2) - C32*w(1);

dCdt1 = [C11_dot; C12_dot; C13_dot];
dCdt2 = [C21_dot; C22_dot; C23_dot];
dCdt3 = [C31_dot; C32_dot; C33_dot];

K1 = (I(2) - I(3)) / I(1);
K2 = (I(3) - I(1)) / I(2);
K3 = (I(1) - I(2)) / I(3);
R_mag = 7000;
R1 = R_mag*C11;
R2 = R_mag*C21;
R3 = R_mag*C31;
dwdt(1) = K1*w(2)*w(3) - ((3*(sqrt(mu/R^3))^2*K1*R3*R2)/R_mag^2);
dwdt(2) = K2*w(1)*w(3) - ((3*(sqrt(mu/R^3))^2*K2*R1*R3)/R_mag^2);
dwdt(3) = K3*w(1)*w(2) - ((3*(sqrt(mu/R^3))^2*K3*R2*R1)/R_mag^2);

% Combine the time derivatives into a single vector
dCwdt = zeros(12,1);
dCwdt = [dCdt1; dCdt2; dCdt3; dwdt];
end

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