how to code simple pendulum motion using ode45
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how to code simple pendulum motion (displacement vs time) using ode45
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Ameer Hamza
2020-10-4
The equation of simple pendulum is 
, which can be converted to two first order ODEs
, which can be converted to two first order ODEs
and then using ode45 like this
theta_ic = [0.5; 0]; % initial conditions: theta(t=0)=0.5; dtheta(t=0)=0.
tspan = [0 10];
[t, theta] = ode45(@odeFun, tspan, theta_ic);
plot(t, theta);
legend({'$\theta$', '$\dot{\theta}$'}, ...
'Location', 'best', ...
'Interpreter', 'latex', ...
'FontSize', 16)
function dtheta = odeFun(t, theta)
g = 9.8;
l = 1;
% theta(1) = theta, theta(2) = dtheta
dtheta = zeros(2, 1);
dtheta(1) = theta(2);
dtheta(2) = -g/l*theta(1);
end
4 个评论
Ashan Cooray
2020-10-4
Ameer Hamza
2020-10-5
I am glad to be of help!
Raphaël Candelier
2022-6-14
Isn't there a sin() function missing in the solution ?
Sam Chak
2022-6-14
Yes, @Raphaël Candelier, you're right. However, at 0.5 rad or 28.65°, the difference is generally not noticeable at the beginning.
0.5 - sin(0.5)
ans =
0.020574461395797
fv1 = @(t, x, y) y;
fv2 = @(t, x, y) - (9.8/1)*sin(x);
opt = odeset('RelTol', 1e-4, 'AbsTol', 1e-6);
[t, v] = ode45(@(t, x) ([fv1(t, x(1), x(2)); fv2(t, x(1), x(2))]), [0 10], [0.5 0], opt);
plot(t, v, 'linewidth', 1.5)
At 10 seconds, you should be able notice the slight difference in phase.
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