The modern development of missiles and projectiles that have shown that nonlinearities, usually ignored in traditional ballistics, have a significant impact on the flight performance of projectiles. However, the complexity of the high order terms coupled in the angular equations and the lack of appropriate analytical tools have hampered the investigation of these effects. In this paper, the method of normal forms, featuring transformations that can simplify the dynamical system equations, is applied directly to the angular motion equation to obtain a simplified formulation for the nonlinear angular problem. Analytical solutions are obtained under quantic static moments. Numerical simulations are carried out to demonstrate the efficiency and accuracy of this method. Besides, a criteria identifying the stable region of initial angle of attack is derived and examined feasible and effective. The results of this research can contribute to the studies of more complicated problems related to nonlinear angular motion.
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