Software matematic

6.5. Tratarea evenimentelor 149
y
1
0.8
0.6
0.4
0.2
0
Corp in cadere
tfinal = 1.6575
0 0.2 0.4 0.6 0.8
t
1 1.2 1.4 1.6
Figura 6.10: Traiectoria unui corp în cădere
Sursa MATLAB 6.3 Problema celor două corpuri
function orbit(reltol)
y0 = [1; 0; 0; 0.3];
opts = odeset(’events’, @gstop,’RelTol’,reltol);
[t,y,te,ye] = ode45(@twobody,[0,2*pi], y0, opts, y0);
tfinal = te(end)
yfinal = ye(end,1:2)
plot(y(:,1),y(:,2),’-’,0,0,’ro’)
axis([-0.1 1.05 -0.35 0.35])
%---------function
ydot = twobody(t,y,y0)
r = sqrt(y(1)ˆ2 + y(2)ˆ2);
ydot = [y(3); y(4); -y(1)/rˆ3; -y(2)/rˆ3];
%-------function
[val,isterm,dir] = gstop(t,y,y0)
d = y(1:2)-y0(1:2);
v = y(3:4);
val = d’*v;
isterm = 1;
dir = 1;