% Refer to 5-48,5-49,5-50, "Matlab, Mathematic. The language of Technical 
% Computing". The MathWorks. 2004. Matlab7.
% ORBITODE Restricted three-body problem
%
% The system is defined as follows:
% (1) y_1'=y_3
% (2) y_2'=y_4
% (3) y_3'=2(y_4)+(y_1)-[(µ*((y_1)+µ)/(r_1)^3]-[(µ(y_1)+µ*)/(r_2)^3]
% (4) y_4'=-2(y_3)+(y_2)-[µ*(y_2)/(r_1)^3]-[(µ(y_2)/(r_2)^3]
% with 
% µ=1/82.45
% µ*=1-µ
% r1=[(y_1)+µ)^2+(y_2)^2]^(1/2) 
% r2=[(y_1)-µ*)^2+(y_2)^2]^(1/2)

tspan = [0 7];
y0 = [1.2; 0; 0 ; -1.04935750983031990726];
options= odeset('RelTol',1e-5,'AbsTol',1e-4,...
                'OutputFcn',@odephas2,'Events',@events);

[t,y,te,ye,ie] = ode45(@fct_tbp,tspan,y0,options);

plot(y(:,1),y(:,2),ye(:,1),ye(:,2),'o');
title('Restricted three body problem')
xlabel('x(t)')
ylabel('y(t)')

% The MathWorks, Matlab7. Copyright (c).