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Question: Motion of airplane

Question:Motion of airplane

SandorSzabo 607 Maple
coordinates
October 05 2007
0
I have found a very interesting physics problem which describes the motion of an airplane, it is a very simple math model. We use only two coordinates, x(t) and y(t), t is the time. The airplane starts at the point (0,a), a>0 and airport located at the origin (0,0). It leads to the differential system ( v0, w>0 are given ): 
sys_ode:=diff(x(t),t)=-v[0]*x(t)/sqrt(x(t)^2+y(t)^2), diff(y(t),t)=-v[0]*y(t)/sqrt(x(t)^2+y(t)^2)+w;

   d                v[0] x(t)         d                v[0] y(t)          
  --- x(t) = - --------------------, --- y(t) = - -------------------- + w
   dt                         (1/2)   dt                         (1/2)    
               /    2       2\                    /    2       2\         
               \x(t)  + y(t) /                    \x(t)  + y(t) /         
ics:=x(0)=a,y(0)=0;

                             x(0) = a, y(0) = 0
assume(a>0);
assume(w>0);
assume(v0>0);
dsolve([sys_ode, ics]);

Error, (in tools/eval) numeric exception: division by zero
Is it possible somehow to obtain, maybe implicitly, x(t),y(t)? Sandor
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