# Homework Help: Matlab Problem Motion Object

1. Nov 14, 2013

### eltrinco

1. The problem statement, all variables and given/known data

I have created random mass and try to make them go around each other . somehow i couldnt find where all the code goes wrong. how do i fix this

3. The attempt at a solution

I have coded this. but still the file cant be run. i dont know where to fix this .

% Creating initial positions/velocities (Randomly)
clear all
close all
clc
n_masses=10;
m=rand(1,n_masses) %RANDOM masses fore each body IF YOU WANT
% the same mass for all use instead :
%m=k*ones(1,n_masses) where k is the mass

x=randn(1,n_masses); %X position
y=randn(1,n_masses); %Y position
vx(1,:)=randn(1,n_masses); %X component velocity (initial)
vy(1,:)=randn(1,n_masses) %Y component velocity (initial)
scatter(x,y,round(100.*m),'filled','blue') % different masses, different sizes
title('Initial configuration')
figure

% Calculating force matrix (F{i,j} means Force exterted by the i-th
% particle on the j-th.
%when j=i -> force is zero
[F,F_totalx,F_totaly]=calculating_F_matrix(x,y,m);

%Evolution
dt=0.05; %interval
n_steps=40; %number of timesteps
%starting positions for the simulation
xx{1}=x; %Will contain the succession of the X positions
yy{1}=y; %Will contain the succession of the Y positions

for s=1:n_steps+1
disp(['Simulating at time t=' num2str(dt*(s-1))]);
for i=1:n_masses
[F,F_totalx,F_totaly]=calculating_F_matrix(xx{s},yy{s},m);
%initial accelerations (fixed)
ax(s,:)=F_totalx;
ay(s,:)=F_totaly;

%Updating velocities
vx(s+1,i)=vx(s,i)+dt*ax(s,i);
vy(s+1,i)=vy(s,i)+dt*ay(s,i);

%Updating positions
xx{s+1}(i)=xx{s}(i)+dt*xx{s}(i);
yy{s+1}(i)=yy{s}(i)+dt*yy{s}(i);

end
end

% Graphics (plot the evolution of the particles)
%find max x and y to correctly set the reference for the plot
for i=1:length(xx)
xm(i)=max((abs(xx{i})));
ym(i)=max(abs(yy{i}) );
end

axis (1.1.*[-max(xm) max(xm) -max(ym) max(ym) ]); % set axis to see all particles
for s=1:n_steps
scatter(xx{s},yy{s},round(100.*m),'filled','red')
axis (1.2.*[-max(xm) max(xm) -max(ym) max(ym) ]); % set axis to see all particles
title(['Time t=' num2str(dt*(s-1))])
pause(0.15)
end

function [F,F_totalx,F_totaly]=calculating_F_matrix(2,3,5)
n_masses=length(m);
G=6.67*10^(-11); % Universal gravity constant
for i=1:n_masses %influenced index
for j=1:n_masses %index generating field
if j~=i % excluding j=i
Xdistance=abs(x(i)-x(j));
Ydistance=abs(y(i)-y(j));
%distance=sqrt((x(i)-x(j)).^2 )%+(y(i)-y(j)).^2); %distance i-j
% dij=(x(i)-x(j)) %unitary vector dij
F{i,j}(1)=G*m(i)*m(j)/(Xdistance);
F{i,j}(2)=G*m(i)*m(j)/(Ydistance);
else
F{i,j}(1)=0;
F{i,j}(2)=0;
end
end
end

% Calculating the total force (per unit of mass m_i) acting on i-th particle (by components)
F_totalx(1)=0;
F_totaly(1)=0;
for i=1:n_masses
Z=cell2mat(F(i,:)'); %vector of all forces acting on the i-th particle
F_totalx(i)=sum(Z(:,1))./m(i);
F_totaly(i)=sum(Z(:,2))./m(i);
end