# Euler Integration Step Size Change

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Hamish Brown on 6 Oct 2022
Commented: Hamish Brown on 6 Oct 2022
I'm currently performing a Euler integration to solve the equations of motion for a rocket launch. I'm using a timestep of 1 at the moment, just for simplicity. When i try and change this to say, 0.1, the code breaks. Anyone know how to fix this?
for i = 1:0.1:500
%density calculator
if y<=11000
Temp(i+1) = 15.04-0.00649*y(i);
p(i+1) = 101.29*((Temp(i)+273.1)/288.08)^5.258;
elseif 11000 < y <=25000
Temp(i+1) = -56.46;
p(i+1) = 22.65*exp(1.73-0.000157*y(i));
else
Temp(i+1) = -131.21 + 0.00299*y(i);
p(i+1) = 2.488*((Temp(i)+273.1)/216.6)^-11.388;
end
rho(i+1) = p(i)/(0.2869*(Temp(i)+273.1));
% gravity model
g(i+1) = 9.81*(R_E/(R_E + y(i)))^2;
%drag force D
D(i+1) = 0.5*rho(i)*v(i)^2*Area*cd;
%speed magnitude v
v(i+1) = v(i) + (T/m0(i) - D(i)/m0(i) - g(i)*sin(gam(i)));
%path angle gam (from 90 to 0 degrees)
if i <= 25
gam(i+1) = gam(i); %vertical flight
elseif 25 < i <= 40
gam(i+1) = gam(i) - 0.008*gam(i); %kickover manouvre
else
gam(i+1) = gam(i) - ((g(i)/v(i) - v(i)/(R_E+y(i)))*cos(gam(i))); %gravity turn equation
end
%x distance downrange
x(i+1) = x(i) + (R_E/(R_E+y(i))*v(i)*cos(gam(i)));
%altitude y
y(i+1) = y(i) + (v(i)*sin(gam(i)));
VG(i) = g(i)*sin(gam(i));
VD(i) = D(i)/m0(i);
if i <= burntime
m0(i+1) = m0(i) - mdot;
else
m0(i+1) = m0(burntime);
T = 0;
end
q(i+1) = (rho(i) * v(i)^2)/2;
%Vertical Velocity
Vy(i+1) = v(i)*sin(gam(i));
%Horizontal Velocity
Vx(i+1) = v(i)*cos(gam(i));
end
It produces the error message:
Array indices must be positive integers or logical values.
Error in newtry (line 51)
Temp(i+1) = 15.04-0.00649*y(i);
Any help is appreciated.

Torsten on 6 Oct 2022
Only integer values can be used for array indexing. The loop must run from i=1 to i=5000 instead.
Hamish Brown on 6 Oct 2022
right, I get it now. Thank you for the help, Torsten.

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