MATLAB: How to code simple pendulum motion using ode45

ode45simple pendulum

how to code simple pendulum motion (displacement vs time) using ode45

Best Answer

The equation of simple pendulum is

, 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

Related Solutions

MATLAB: Using ODE45 when parameters in the function change in time

Hi Cristina

It depends a bit on how your torque and force trajectories are defined, but the easiest way in my opinion: If torque and force are functions of (t,theta) as well, then simply write two functions, e.g. tau = compute_torque(t,theta) and f = compute_force(t,theta), and replace the expressions in your leg function, i.e.

function tau = compute_torque(t,theta)
   tau = (1-exp(-t^2); % here comes your tau function
end
function f = compute_force(t,theta)
   f = sin(t)*theta(2); % here comes your force function
end
function [ dtheta ] = leg( t,theta)
% theta (1) is theta, Theta (2) is angular velocty
m=1;
g=9.8;
tau=compute_torque(t,theta);
f=compute_force(t,theta);
k=500;
r0=0.01;
dtheta=zeros(2,1);
dtheta(1)=theta(2);
dtheta(2)=tau/m+g*sin(theta(1))*( (f - m*g*cos(theta(1)))/k +r0 );
end

All clear?

MATLAB: How do we plot differential Equation

Use ode45() for estimating a numerical solution

IC = [0.1, 0.3, 0.2];
tspan = [0 1];
[t, thetas] = ode45(@odeFun, tspan, IC);
plot(t, thetas);
legend({'\theta_1', '\theta_2', '\theta_3'}, 'FontSize', 16, 'Location', 'best');
function dthetas = odeFun(t, thetas)
    theta1 = thetas(1);
    theta2 = thetas(2);
    theta3 = thetas(3);
    
    dtheta1 = 1+sin(theta2-theta1);
    dtheta2 = 1+sin(theta1-theta2)+sin(theta3-theta2);
    dtheta3 = 1+sin(theta2-theta3);
    
    dthetas = [dtheta1; dtheta2; dtheta3];
end

Best Answer

Related Solutions

MATLAB: Using ODE45 when parameters in the function change in time

MATLAB: How do we plot differential Equation

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