# ode45 goes busy endlessly when using the sign of a state variable

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Diaa on 23 Apr 2021
Answered: Diaa on 23 Apr 2021
This term "- fr*Mass*9.8*sign(y(2))" makes ode45 busy forever specifically when using 'sign(y(2))'
I just need to make -fr*Mass*9.8=0 only when y(2)=0
Any explanations are highly welcomed.
clearvars
clc
close all
[t,y] = myexercise;
plot(t,y(:,2))
function [t,y] = myexercise
tspan = [0 , 10];
y0 = [ 0 ; 5 ];
Mass = 1300;
CD = 0.3;
fr = 0.015;
Af = 1.6;
traction = @(t) (t>3&t<5)*5*t;
[t,y] = ode45(@(t,y) deceleration(t,y) , tspan , y0);
function yp = deceleration(t,y)
yp = [ ...
y(2) ;...
( -0.5*1.23*CD*Af*y(2)^2 + traction(t) - fr*Mass*9.8*sign(y(2)) )/Mass ...
];
end
end
James Tursa on 23 Apr 2021
Please explain the physical problem and post the differential equation you are trying to solve so we can understand why you think you need the sign function.
Diaa on 23 Apr 2021
It is a moving vehicle subjected to traction force and resistive aerodynamic drag and rolling resistance. Your comment made me realize that I forgot dividing the whole second equation by Mass. After fixing it, fr*Mass*9.8)*(y(2)>0) was enough to make it work.

Diaa on 23 Apr 2021
Thanks to the explanation of Star Strider, the use of sign() can be replaced by fr*Mass*9.8)*(y(2)>0) to make it work.

Walter Roberson on 23 Apr 2021
You really should read ballode to see how to use event functions. https://www.mathworks.com/help/matlab/math/ode-event-location.html