private function checkCollision(ball0:animation_ch11_Ball, ball1:animation_ch11_Ball):void
    {
     var dx:Number = ball1.x - ball0.x;
     var dy:Number = ball1.y - ball0.y;
     var dist:Number = Math.sqrt(dx*dx + dy*dy);
     if(dist < ball0.radius + ball1.radius)
     {
      // calculate angle, sine and cosine
      var angle:Number = Math.atan2(dy, dx);
      var sin:Number = Math.sin(angle);
      var cos:Number = Math.cos(angle);
      
      // rotate ball0's position
      var pos0:Point = new Point(0, 0);
      
      // rotate ball1's position
      var pos1:Point = rotate(dx, dy, sin, cos, true);
      
      // rotate ball0's velocity
      var vel0:Point = rotate(ball0.vx,
            ball0.vy,
            sin,
            cos,
            true);
      
      // rotate ball1's velocity
      var vel1:Point = rotate(ball1.vx,
            ball1.vy,
            sin,
            cos,
            true);
      
      // collision reaction
      var vxTotal:Number = vel0.x - vel1.x;
      vel0.x = ((ball0.mass - ball1.mass) * vel0.x + 
                2 * ball1.mass * vel1.x) / 
                (ball0.mass + ball1.mass);
      vel1.x = vxTotal + vel0.x;
  
      // update position
      var absV:Number = Math.abs(vel0.x) + Math.abs(vel1.x);
      var overlap:Number = (ball0.radius + ball1.radius) 
                            - Math.abs(pos0.x - pos1.x);
      pos0.x += vel0.x / absV * overlap;
      pos1.x += vel1.x / absV * overlap;
      
      // rotate positions back
      var pos0F:Object = rotate(pos0.x,
              pos0.y,
              sin,
              cos,
              false);
              
      var pos1F:Object = rotate(pos1.x,
              pos1.y,
              sin,
              cos,
              false);
  
      // adjust positions to actual screen positions
      ball1.x = ball0.x + pos1F.x;
      ball1.y = ball0.y + pos1F.y;
      ball0.x = ball0.x + pos0F.x;
      ball0.y = ball0.y + pos0F.y;
      
      // rotate velocities back
      var vel0F:Object = rotate(vel0.x,
              vel0.y,
              sin,
              cos,
              false);
      var vel1F:Object = rotate(vel1.x,
              vel1.y,
              sin,
              cos,
              false);
      ball0.vx = vel0F.x;
      ball0.vy = vel0F.y;
      ball1.vx = vel1F.x;
      ball1.vy = vel1F.y;
     }
    }
    
    private function rotate(x:Number,
          y:Number,
          sin:Number,
          cos:Number,
          reverse:Boolean):Point
    {
     var result:Point = new Point();
     if(reverse)
     {
      result.x = x * cos + y * sin;
      result.y = y * cos - x * sin;
     }
     else
     {
      result.x = x * cos - y * sin;
      result.y = y * cos + x * sin;
     }
     return result;
    }  
   }
  }