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Jagrut Alpeshbhai
Jagrut Alpeshbhai am 20 Feb. 2023
y0 = [r0 Vn0];
t0 = 0;
nrevs = 100;
tmax = nrevs*Period;
h0 = 0;
x0 = [r0; h0; V0];
r= @(x) [sqrt(x(1)^2 + x(2)^2 + x(3)^2)];
f = @(t,x) [x(3); x(2)*x(3)^2/x(1) -mu/x(1)^2; -x(2)*x(3)/x(1)];
settings1=odeset('RelTol',1e-4,'AbsTol',1e-4);
settings2=odeset('RelTol',1e-8,'AbsTol',1e-8);
settings3=odeset('RelTol',1e-11,'AbsTol',1e-11);
[T1,x1]=ode45(f,[0 tmax],x0,settings1)
[T2,x2]=ode45(f,[0 tmax],x0,settings2)
[T3,x3]=ode45(f,[0 tmax],x0,settings3)
% Plot the trajectories for each tolerance
% Plot the trajectories for each tolerance
figure;
plot(x1(:,1).*cos(x1(:,2)), x1(:,1).*sin(y1(:,2)), '-', ...
x2(:,1).*cos(x2(:,2)), x2(:,1).*sin(x2(:,2)), '-', ...
x3(:,1).*cos(x3(:,2)), x3(:,1).*sin(x3(:,2)), '-');
legend('tol=1e-4', 'tol=1e-8', 'tol=1e-11');
title('Orbit Trajectories');

Antworten (1)

Sulaymon Eshkabilov
Sulaymon Eshkabilov am 20 Feb. 2023
Here is the corrected code (Note that the Initial Conditions were missing and some arbitrary values are taken. Therefore they need to be changed. Also, note that in figure 1 three solution sets overlap each other. Hence, they are plotted in separate) :
t0 = 0;
nrevs = 100;
Period = 2;
tmax = nrevs*Period;
mu = 2.5;
h0 = 0; %
r0 = 1; % use the given value
V0 = 0.5; % use the given value
x0 = [r0; h0; V0];
f = @(t,x) ([x(3); x(2).*x(3).^2./x(1)-mu./x(1).^2; -x(2).*x(3)./x(1)]);
settings1=odeset('RelTol',1e-4,'AbsTol',1e-4);
settings2=odeset('RelTol',1e-8,'AbsTol',1e-8);
settings3=odeset('RelTol',1e-11,'AbsTol',1e-11);
[T1,y1]=ode45(f,[0 tmax],x0,settings1);
Warning: Failure at t=2.004057e+00. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (7.105427e-15) at time t.
[T2,y2]=ode45(f,[0 tmax],x0,settings2);
Warning: Failure at t=2.003988e+00. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (7.105427e-15) at time t.
[T3,y3]=ode45(f,[0 tmax],x0,settings3);
Warning: Failure at t=2.003988e+00. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (7.105427e-15) at time t.
% Plot the trajectories for each tolerance
figure;
plot(y1(:,1).*cos(y1(:,2)), y1(:,1).*sin(y1(:,2)), 'r-', ...
y2(:,1).*cos(y2(:,2)), y2(:,1).*sin(y2(:,2)), 'b--', ...
y3(:,1).*cos(y3(:,2)), y3(:,1).*sin(y3(:,2)), 'g-.');
legend('tol=1e-4', 'tol=1e-8', 'tol=1e-11');
title('Orbit Trajectories');
axis equal
figure
plot(y1(:,1).*cos(y1(:,2)), y1(:,1).*sin(y1(:,2)), 'r-')
legend('tol=1e-4');
title('Orbit Trajectories');
axis equal
figure;
plot(y2(:,1).*cos(y2(:,2)), y2(:,1).*sin(y2(:,2)), 'b--');
legend('tol=1e-8');
title('Orbit Trajectories');
axis equal
figure;
plot(y3(:,1).*cos(y3(:,2)), y3(:,1).*sin(y3(:,2)), 'g-.');
legend('tol=1e-11');
title('Orbit Trajectories');
axis equal

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