Same as the chicken's ability... only with a small bird I accidently injured :(
Birds have a great ability to keep their heads stable. Our bodies use a gyro-like mechanism in our ears which has 3 mutually orthogonal inertial measurement devices. Modern motion processors use something called an Inertial Measurment Unit (IMU). These devices provide movement data which can be used to compensate for the movement.
I called a licensed wildlife rehabilitator who said birds with broken wings have a very small chance for survival. After the first day, it looked like he was getting healthier. Unfortunately he died shortly after. :(