Why am I getting Complex number results?

I am doing an assignment for a course and I'm trying to map the position, velocity and acceleration of an object moving in a 2D fashion. Here is my code:

clear; clc;

rho_i=1.2;

c=6.5*10^-3;

T=300;

alpha=2.5;

theta=(45*pi)/180;

Area=pi*(.406/2)^2;

m=1225;

vi=762;

vxi=vi*cos(theta);

vyi=vi*sin(theta);

D=0.5;

g=9.81;

n=100000;

t=zeros(n,1);

x=zeros(n,1);

y=zeros(n,1);

vx=zeros(n,1);

vy=zeros(n,1);

v=zeros(n,1);

ax=zeros(n,1);

ay=zeros(n,1);

rho=zeros(n,1);

PError=zeros(8,1);

VError=zeros(8,1);

AError=zeros(8,1);

t(1)=0;

vx(1)=vxi;

vy(1)=vyi;

x(1)=0;

y(1)=0;

ax(1)=0;

ay(1)=0;

rho(1)=rho_i;

for j=1:7;

dt=10^(1-j);

for i=2:n;

t(i)=t(i-1)+dt;

vx(i)=vx(i-1)+ax(i)*t(i);

vy(i)=vy(i-1)+ay(i)*t(i);

v(i)=sqrt(vx(i)^2+vy(i)^2);

y(i)=y(i-1)+vy(i)*t(i);

x(i)=x(i-1)+vx(i)*t(i);

ax(i)=((-D*rho(i)*Area)/(2*m))*(v(i)*vx(i));

ay(i)=((-D*rho(i)*Area)/(2*m))*(v(i)*vy(i))-g;

a(i)=sqrt(ax(i)^2+ay(i)^2);

rho(i)=rho_i*(1-(c*y(i)/T)).^alpha;

end

end

I am completely confused as to why I am obtaining complex numbers for values in my arrays. Any ideas?

Answer 1

[David Goodmanson]

Hello Ethan,

The reason for this is that at step i = 14, the quantity on the third to last line, (1-(c*y(i)/T)) becomes negative, and since it is being taken to the alpha = 2.5 power which is not an integer power, the results are complex.

The y variables are growing far faster than they should because in several places you are using expressions such as

vx(i)=vx(i-1)+ax(i)*t(i);

rather than the correct

vx(i)=vx(i-1)+ax(i)*dt;

It's doable and not causing problems in this case, but I tend not to use i as an index variable due to possible confusion with i = sqrt(-1).

[Ethan Fritz]

Thank you very much sir. It worked out very well. Thank you again?