Need help time stepping this system

I have attatched my code and thte function that it calls. I am trying to get it to timestep through the steps but it tells me the array is too large and I have hit a barrier in trying to figure it out so any assistance would be appreciated.

[Jan]

Please post a copy of the complete error message. This is much better than a rough rephrasing, which let the readers guess, in which line the error occurs.

[Devon Romine]

Index exceeds array bounds.

Error in hard_sphere (line 22) x(i+1)=x(i)+velocities_fun(x)*dt; Sorry about that

Answer 1

[Jan]

I guess, the problem is that you overwrite x, y and z in each iteration:

x = zeros(length(t),1);
y = zeros(length(t),1);
z = zeros(length(t),1);
for i=1:length(t)-1
   x=r.*sin(theta).*cos(phi);   % Here x is overwritten by a 20x1 vector!
   y=r.*sin(theta).*sin(phi);
   z=r.*cos(theta);
   x(i+1)=x(i)+velocities_fun(x)*dt;  % This fails for i=21
   y(i+1)=y(i)+velocities_fun(y)*dt;
   z(i+1)=y(i)+velocities_fun(z)*dt;
end

Use another variable:

x = zeros(length(t),1);
y = zeros(length(t),1);
z = zeros(length(t),1);

% This does not depend on the loop counter, so move it before the loop:
xc = r .* sin(theta) .* cos(phi);
yc = r .* sin(theta) .* sin(phi);
zc = r .* cos(theta);
for i = 1:length(t)-1
   x(i+1) = x(i) + velocities_fun(xc) * dt;
   y(i+1) = y(i) + velocities_fun(yc) * dt;
   z(i+1) = y(i) + velocities_fun(zc) * dt;
end

Do you see, that some spaces around the operators improve the readability?

By the way: You use the first output of velocities_fun only, and no inputs. So you can simplify it to:

function V = velocities_fun()
V = normrnd(1,1);
end

But then creating xc, yc, zc is not useful at all.

[Devon Romine]

And this will create random velocities for each of the 20 points for (x,y,z)? Because I am trying to give 20 random points random velocities.

[Jan]

Please explain, which 20 points you mean. The purpose of the code is not clear.

[Devon Romine]

Before the time step there are 20 points generated by the random r, phi, and theta that are distributed throughout the sphere. What I am trying to do is have 20 separate points inside the sphere move at random velocities so I can simulate collisions with them, sorry I am not very good at explaining it.