This paper focuses on the analysis and control of some mathematical models representing the dynamics of a quadrotor. By using a normal form approach, the highly coupled parts in the quadrotor system are eliminated, while all possible properties of the original system are not changed. The bifurcations of the system are then analyzed. A two dimensional system is deduced at the origin which can determine the stability and possible local bifurcations of the system. Based on the normal form and indirect method of Lyapunov, we propose a state feedback control method with computational simplicity as well as practical implementation facility. Comparing to a standard PID control, the proposed method has faster response time and less tracking errors especially with wind disturbance.