function aufgabe5


tspan = [0 12];
y0 = [0.36; 
      -8.1*pi/180; 
      4/(20910^5*0.3048); 
      0.36*cos(-8.1*pi/180)/(1+4/(20910^5*0.3048))];


figure;
[t,y]=ode45(@f,tspan,y0);



% solve the problem using ODE45

% --------------------------------------------------------------------------



function dydt = f(t,y)

Sm=53200;
beta=4.26;
rota0=2.70410^(-3);
g=3.217210^(-4);
ft=03048;
R=20910^5*ft;

u=1;

Cw=1.174-0.9*cos(u);
Ca=0.6*sin(u);

dydt = [    -Sm*rota0*exp(-beta*R*y(3))*power(y(1),2)*Cw/2-g*sin(y(2))/(1+y(3))^2; 
            Sm*rota0*exp(-beta*R*y(3))*y(1)*Ca/2-g*cos(y(2))/(y(1)*(1+y(3))^2)+y(1)*cos(y(2))/R/(1+y(3));
            y(1)*sin(y(2))/R;
            y(1)*cos(y(2))/(1+y(3))                                                 ];