ODE45: IF/loop function

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Komal Rajana
Komal Rajana 2020-1-9
回答： Jyothis Gireesh 2020-2-12
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
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Meg Noah
Meg Noah 2020-1-10
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
Aquatris 2020-1-10
There are a lot of examples online, here is on of them.

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Jyothis Gireesh
Jyothis Gireesh 2020-2-12
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

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