Time varying force with ode23

Hi there

I have the following code:

tf = 1;
t = linspace(0,3);
Ft = zeros(length(t),1);

% Here I generate the force values at different time intervals.
for i = 1:length(t)
    if t(i) <= tf
        Ft(i) = Fo*sin(2*pi*t(i)/tf);
    elseif t(i) > tf
        Ft(i) = 0;
    end
end

ic = [0, 0]; % Initial conditions

dXdt = @(t, x)     [x(2);
                            Ft * 1/(m1+m2)];
        
[t, x] = ode23(dXdt, [0, 3], ic);

I'm struggling to incorportate this time varying force F(t) into the ode23 function.

Any help as to how I can maybe get this done?

Thanks in advance!

Answer 1

[darova]

Use function handle

Ft = @(t) (t<=tf)*Fo*sin(2*pi*t/tf);
dXdt = @(t, x)     [x(2);
                        Ft(t) * 1/(m1+m2)];

[Walter Roberson]

That would work if the driving force was not discontinuous.

[Christo van Rensburg]

It seems to work though.

Walter I'll try your method now, because what you're saying makes sense.

Thanks for the help!

Answer 2

[Walter Roberson]

You cannot do that the way you want. The ode* routines cannot handle discontinuities in the driving functions. You need to break it up into two time periods, one with the force and one without the force.

tf = 1;

dXdt_F = @(t, x) [x(2);  Fo*sin(2*pi*t/tf) / (m1+m2)];
dXdt_NF = @(t, x) [x(2); 0];

ic = [0, 0]; % Initial conditions
[t1, x1] = ode23(dXdt_F, [0, tf], ic);
ic2 = x1(end,:);
[t2, x2] = ode23(dXdt_NF, [tf, 3], ic2);

t = [t1; t2(2:end)];
x = [x1; x2(2:end,:)];

[Christo van Rensburg]

Both methods seem to work fine.

Thanks guys.