> #L=target length, t0=angle for the tip of the arrow
> iter :=proc(t)
> global l; local x0,y0,x,y,X,Y;
> x0:=a*cos(t0);y0:=b*sin(t0);
>  x:=a*cos(t); y:=b*sin(t);
>  l:=sqrt((x-x0)^2+(y-y0)^2);
>  X:=x0+(x-x0)*L/l; Y:=y0+(y-y0)*L/l;
>  RETURN(arctan((Y/b),(X/a)));
> end;
> 

  iter := proc(t)
local x0, y0, x, y, X, Y;
global l;
    x0 := a*cos(t0);
    y0 := b*sin(t0);
    x := a*cos(t);
    y := b*sin(t);
    l := sqrt((x - x0)^2 + (y - y0)^2);
    X := x0 + ((x - x0)*L)/l;
    Y := y0 + ((y - y0)*L)/l;
    RETURN(arctan(Y/b, X/a))
end

> iter := proc (t) local x0, y0, x, y, X, Y; global l; x0 := a*cos(t0); y0 := b*sin(t0); x := a*cos(t); y := b*sin(t); l := sqrt((x-x0)^2+(y-y0)^2); X := x0+(x-x0)*L/l; Y := y0+(y-y0)*L/l; RETURN(arctan(Y/b,X/a)) end;

  iter := proc(t)
local x0, y0, x, y, X, Y;
global l;
    x0 := a*cos(t0);
    y0 := b*sin(t0);
    x := a*cos(t);
    y := b*sin(t);
    l := sqrt((x - x0)^2 + (y - y0)^2);
    X := x0 + ((x - x0)*L)/l;
    Y := y0 + ((y - y0)*L)/l;
    RETURN(arctan(Y/b, X/a))
end

> a:=3; b:=0.5; L:=0.1;t0:=0;# small value of L: fast convergence...

                                a := 3


                               b := .5


                               L := .1


                               t0 := 0

> #initialisation of angle
> t:=t0+L/sqrt((a*sin(t0))^2+(b*cos(t0)^2));
> if (t > evalf(Pi/2)) then t:= evalf(Pi/2); fi;

                           t := .1414213562

> #iteration
> for i from 1 to 30 do t:=iter(t): print(i,l,l-L); if abs(l-L)<1e-5 then break; fi; od: 

                    1, .07657519119, -.02342480881


                     2, .1048283676, .0048283676


                    3, .09900886367, -.00099113633


                     4, .1002041853, .0002041853


                    5, .09995796284, -.00004203716


                                              -5
                     6, .1000086554, .86554 10


> a:=3; b:=0.5; L:=0.5;t0:=0;#larger value of L, slow convergence...

                                a := 3


                               b := .5


                               L := .5


                               t0 := 0

> #initialisation of angle
> t:=t0+L/sqrt((a*sin(t0))^2+(b*cos(t0)^2));
> if (t > evalf(Pi/2)) then t:= evalf(Pi/2); fi;

                           t := .7071067812

> #iteration
> for i from 1 to 30 do t:=iter(t): print(i,l,l-L); if abs(l-L)<1e-5 then break; fi; od: 

                     1, .7892090456, .2892090456


                     2, .3718449450, -.1281550550


                     3, .5888779655, .0888779655


                     4, .4523038305, -.0476961695


                     5, .5298679218, .0298679218


                     6, .4829125443, -.0170874557


                     7, .5103161893, .0103161893


                     8, .4939663391, -.0060336609


                     9, .5035959667, .0035959667


                    10, .4978805683, -.0021194317


                     11, .5012574327, .0012574327


                    12, .4992568831, -.0007431169


                     13, .5004401811, .0004401811


                    14, .4997396175, -.0002603825


                     15, .5001541498, .0001541498


                    16, .4999087853, -.0000912147


                     17, .5000539895, .0000539895


                    18, .4999680494, -.0000319506


                     19, .5000189104, .0000189104


                    20, .4999888084, -.0000111916


                                               -5
                     21, .5000066236, .66236 10

>