ODE45: IF/loop function

Hello,

I would like to know if its correct to write my differential equations as follow in the 'if' command in the function file. If not, please advice. I am trying to model a simple damper.

Thanks.

function [dy] = SDOF2(t, u);
dy = zeros(2,1);
m=1000; %Mass (lb.sec^2/in.)
k =100000; %Stiffness (lb/in.)
omega = sqrt(k/m); %Natural Frequency 
c=2000;%Damping coefficient (lb.sec/in.)
g =386;%Acceleration of gravity (in./sec^2)
c_cr=2*m*omega; %Critical damping coefficient
xi = c/c_cr;%Damping ratio
%%Define the forcing function 
% if t<=0.5
%     F = sin(4*pi*t);
% else
%     F =0;
F = 0;

% b=1*m*(((-omega*omega*u(1)-2*xi*omega*u(2)+F))/u(2)>0);

% end %%%%-ESTIMATION-%%%% 
if ((((-omega*omega*u(1))-(2*xi*omega*u(2))+F/m)/u(2))>0)
dy(1) = u(2); 
dy(2)= -omega*omega*u(1)-2*xi*omega*u(2)+F/m-0.5*m*((-omega*omega*u(1))-(2*xi*omega*u(2))+F/m);
else
   dy(1) = u(2); 
dy(2)= -omega*omega*u(1)-2*xi*omega*u(2)+F/m;
end 
% dy(2)= -omega*omega*u(1)-2*xi*omega*u(2)+F/m;

end

[Walter Roberson]

You need to switch to using event functions to terminate the ode45 call and then restart it.

ode45 requires that the function be differentiable. When you have an if in the function it is rarely differentiable. You need to stop at the discontinuity and restart.

[Komal Rajana]

HI Walter,

But is it possible to specify the 'value' as >0 in the event and not '='?

thanks

[Walter Roberson]

Strictly speaking, no. However you can subtract eps(realmin) from the value as the result will be negative if the value was exactly 0.

[Aquatris]

It might be easier to write your own RK method for this problem.

[Komal Rajana]

Hi Aquatris,

Can you provide an example...I am having a horrible time with this.

thanks,

Komal

[Meg Noah]

There's a solution here on the web:

https://www.matlab-monkey.com/ODE/resonance/resonance.html

Also, I've implemented a Runge-Kutta to solve baseball motion under atmosphere drag and lift:

https://www.mathworks.com/matlabcentral/fileexchange/73825-baseball-flight

It's a 3-D version.

[Aquatris]

There are a lot of examples online, here is on of them.

Answer 1

[Jyothis Gireesh]

It is my understanding that the differential equation is a function of “u(1)” and “u(2)”. So it is safe to assume that “u(1)” and “u(2)” are symbolic variables (or can be defined as symbolic). In this case, it may be better to use the “piecewise” function which allows conditionally defined expressions or functions.

Please refer to the following documentation link to get information on “piecewise” function

https://www.mathworks.com/matlabcentral/answers/499674-ode45-if-loop-function