To explore the reason for appearance of large angle of attack at the apogee of trajectory in mathematics, the kinematic equations of a representative spinning rocket in vertical plane is established, and the response of angle of attack with the time-variant coefficients is further obtained mathematically. Considering the motion of attitudes and mass of centre jointly, dynamics equations of coning motion of the rocket projectile with low rotation rate and large launch angle is established. Taking aerodynamic nonlinearities induced by the large angle of attack into account, stability limits of coning motion near the top of the trajectory is derived by the Lyapunov indirect method.