# 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
##### 2 CommentsShowHide 1 older comment
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