ode45 fail with pendulum

2 views (last 30 days)
Bobby Fischer
Bobby Fischer on 13 Jan 2021
Edited: Mischa Kim on 13 Jan 2021
Hello. I have proof that in my machine the pendulum goes all the way around, contradicting reality. Any thoughts?
-----------------------------------------------------------------------------------------------------
MATLAB Version: 9.8.0.1323502 (R2020a)
MATLAB License Number: 40875211
Operating System: Microsoft Windows 8.1 Version 6.3 (Build 9600)
Java Version: Java 1.8.0_202-b08 with Oracle Corporation Java HotSpot(TM) 64-Bit Server VM mixed mode
-----------------------------------------------------------------------------------------------------
MATLAB Version 9.8 (R2020a)
Simulink Version 10.1 (R2020a)
Optimization Toolbox Version 8.5 (R2020a)
Statistics and Machine Learning Toolbox Version 11.7 (R2020a)
Symbolic Math Toolbox
function pendule2
[~,y]=ode45(@fun,0:0.05:40,[pi-0.1,0]);
figure(1)
close(1)
figure(1)
[n,~]=size(y);
t1=0:0.05:2*pi;
x1=cos(t1);
y1=1+sin(t1);
for k=1:n
hold on
axis equal
axis([-1 1 0 2])
plot(x1,y1,'k--')
plot(sin(y(k,1)),1-cos(y(k,1)),...
'bo','MarkerSize',5,'MarkerFaceColor','b')
plot([0 sin(y(k,1))], [1 1-cos(y(k,1))],'b')
pause(0.01)
clf
end
hold on
axis equal
axis([-1 1 0 2])
plot(x1,y1,'k--')
plot(sin(y(n,1)),1-cos(y(n,1)),...
'bo','MarkerSize',5,'MarkerFaceColor','b')
plot([0 sin(y(n,1))], [1 1-cos(y(n,1))],'b')
text(0.85,0.1,'end')
function [dydt]=fun(~,y)
dydt=[y(2); -sin(y(1))];
end
end

Accepted Answer

Mischa Kim
Mischa Kim on 13 Jan 2021
Edited: Mischa Kim on 13 Jan 2021
Hi Bobby, this is the wonderful world of numerical (vs symbolic) computation. ode45 is a numerical integrator that approximates the actual solution. In essence this mean that with every integration step there will be a small error that adds up over time. You can fine-tune how well you would like to approximate the solution by setting tolerance levels. Try, e.g.
options = odeset('RelTol',1e-10);
[~,y] = ode45(@fun,0:0.05:40,[pi-0.1,0],options);

More Answers (0)

Categories

Find more on Numerical Integration and Differential Equations in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!