function r = planar3rhsOctave(z,t)
%
% Defines the righthandside vector of the system of first-order
%   differential equations for the planar 3-body problem.
% As the time t is second argument, this script is suitable for
% the lsode command of Octave.
% 
% ON INPUT :
%   z        a vector with 12 entries, ordered in blocks of 4:
%            x[k](t), x'[k](t),y[k](t),y'[k](t), k = 1,2,3;
%   t        value for the time parameter.
%
% ON RETURN :
%   r        12 values of the righthandside for the ODE.
%
% defining the three masses
m = [1 0.5 0.2];
% m = [1 1 1];
r = zeros(1,12);
% relabel input vector z
x1 = z(1); u1 = z(2);  y1 = z(3);  v1 = z(4);
x2 = z(5); u2 = z(6);  y2 = z(7);  v2 = z(8);
x3 = z(9); u3 = z(10); y3 = z(11); v3 = z(12);
% u and v are first derivatives of x and y
r(1) = u1; r(3) = v1; 
r(5) = u2; r(7) = v2;
r(9) = u3; r(11) = v3;
% compute squared distances
dx12 = x1 - x2; sdx12 = dx12^2;
dx13 = x1 - x3; sdx13 = dx13^2;
dx23 = x2 - x3; sdx23 = dx23^2;
dy12 = y1 - y2; sdy12 = dy12^2;
dy13 = y1 - y3; sdy13 = dy13^2;
dy23 = y2 - y3; sdy23 = dy23^2;
% denominators 
d12 = (sdx12 + sdy12)^(3/2); 
d13 = (sdx13 + sdy13)^(3/2);
d23 = (sdx23 + sdy23)^(3/2); 
% righthandside for second order
r(2) = - m(2)*dx12/d12 - m(3)*dx13/d13;
r(4) = - m(2)*dy12/d12 - m(3)*dy13/d13;
r(6) = - m(1)*(-dx12)/d12 - m(3)*dx23/d23;
r(8) = - m(1)*(-dy12)/d12 - m(3)*dy23/d23;
r(10) = - m(1)*(-dx13)/d13 - m(2)*(-dx23)/d23;
r(12) = - m(1)*(-dy13)/d13 - m(2)*(-dy23)/d23;