clear;

vB = 1;
l = 1;

function dx = boat(t,x)
  // dx/dt = vx = - vB * x / ��(x^2 + y^2)
  dx(1) = - vB * x(1) / sqrt(x(1) ^ 2 + x(2) ^ 2)
  // dy/dt = vy = vB * y / ��(x^2 + y^2) + vR
  dx(2) = - vB * x(2) / sqrt(x(1) ^ 2 + x(2) ^ 2) + b * vB
endfunction

T = linspace(0,4,50);
X0 = [l; 0];

b = 0.1;
X = ode(X0, 0, T, boat);
plot(X(1,:),X(2,:),'-or');

b = 0.5;
X = ode(X0, 0, T, boat);
plot(X(1,:),X(2,:),'-og');

b = 0.8;
X = ode(X0, 0, T, boat);
plot(X(1,:),X(2,:),'-ob');

b = 1.0;
X = ode(X0, 0, T, boat);
plot(X(1,:),X(2,:),'-om');

b = 1.5;
X = ode(X0, 0, T, boat);
plot(X(1,:),X(2,:),'-oc');

b = 2;
X = ode(X0, 0, T, boat);
plot(X(1,:),X(2,:),'-oy');

zoom_rect([0, 0, l, 2]);
xlabel("x");
ylabel("y");
legend("b = 0.1","b = 0.5","b = 0.8","b = 1.0","b = 1.5","b = 2.0",1);