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	Mathematik-Online-Aufgabensammlung: Lösung zu
	Aufgabe 1589: Shuttle-Flug

Schreiben Sie ein MATLAB-Programm shuttle, das die durch

function shuttle(r,time_factor)
% shuttle flight 
% r [= 20000]: distance of stationary orbit 
% time_factor [= 1/500]: ratio to real time
% control flight using arrow keys:
% left/right, up = accelerate, down = brake
% force ~ number of consecutive key strokes  

global A Amin GAMMA;

if nargin < 2; 
   time_factor = 1/500;
   if nargin < 1;
      r = 20000; 
   end;
end;

% parameters
GAMMA = 398690;  
r_earth = 6378; 
pts_orbit = 100;
Amin = GAMMA/(r_earth.^2*10);

mode = {'slower', 'right', 'off', 'left', ...  
   'faster'};
u = [r; 0; 0; sqrt(GAMMA/r)];
A = [0; 0];
dt = 2*pi*sqrt(r_earth.^3/GAMMA)/pts_orbit;

figure;
% identify key-function
set(gcf,'KeyPressFcn','key_action');
axis equal; hold on; 

% draw earth
theta = 2*pi*linspace(0,1);
fill(r_earth*cos(theta),r_earth*sin(theta),'b');


while length(A)>0;
   % time step
   [t, udt] = ode45(@fct,[0 dt],u);
   plot([u(1) udt(end,1)],[u(2) udt(end,2)],'r');
   u = udt(end,:)';
   % show current parameter values
   f = num2str(round(norm(A)/Amin)); 
   v = num2str(round(1000*norm(u(3:4))));
   xlabel(['velocity: ' v '          ' ... 
      mode{3+[2,1]*sign(A)} ' ' f]);
   % check distance to planet
   if norm(u(1:2)) < r_earth; 
      return; 
   end;
   pause(dt*time_factor);
end;

hold off;

%%%%%

function key_action()
% changes thrust value and direction 
% according to keys pressed

global A Amin;

key = double(get(gcf,'CurrentCharacter'));
switch key
   case 28   % left 
      if A(2) >= 0 & A(1) == 0  
         A = A+[0; Amin]; 
      else 
         A = 0*A;
      end;
   case 29   % right
      if A(2) <= 0 & A(1) == 0
         A = A-[0; Amin]; 
      else 
         A = 0*A;
      end;
   case 30   % up
      if A(1) >= 0 & A(2) == 0 
         A = A+[Amin; 0]; 
      else 
         A = 0*A;
      end;
   case 31   % down
      if A(1) <= 0 & A(2) == 0 
         A = A-[Amin; 0]; 
      else 
         A = 0*A;
      end;
   otherwise
      A = [];
end;

%%%%%

function du = fct(t,u) 
% equations of motion for shuttle flight

global A GAMMA;

p = u(1:2); 
v = u(3:4); 
w = [-v(2); v(1)];  
du = [v; -GAMMA*p/norm(p).^3];
du(3:4) = du(3:4) + [v, w]*A/(1/10+norm(v));