using ODE45 when parameters in my function change in time?

Hi,

I am using ode45 to simulate a model of a mass linked to a pivot through a spring. Radial force and torque are applied and can change in time.

I used previously ode45 with equations that do not change in time, by creating a function eg dtheta= fn (t, theta) as suggested on Mathworks. I am not sure how to do with variable parameters though.

This is my code:

function [ dtheta ] = leg( t,theta)
% theta (1) is theta, Theta (2) is angular velocty
m=1;
g=9.8;
tau=0;
f=0;
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

which I will call with

close all

t0=0;
tf=10;
theta0=pi/2;
angvel0=0;

[T,THETA] = ode45(@leg,[t0 tf],[theta0 angvel0]);
plot(T,THETA(:,1))
xlabel('time')
ylabel('theta (radians)');

Right now I am simulating the model with 0 torque and 0 radial force. As well I could simulate it with constant torque and force. But I need them to change in time (eg being vectors in time). How do I do that?

Thanks!!! Cristina

Answer 1

[Ced]

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?