Abstract: An angle of attack equation of pneumatic eccentric projectile under the action of cubic nonlinear static moment and quadratic nonlinear equatorial damping moment is established for the structure design and aerodynamic design of pneumatic asymmetric projectiles, such as non-parachute terminal sensitive projectile, and the approximate analytical solution of the equation and linear variational equation are solved by using average method. On this basis, the asymptotic stability conditions of forced conical motion for pneumatic eccentric projectile is obtained according to Hurwitz criterion, and the physical meaning of the conditions is analyzed. The numerical calculation example is used to verify the conditions. Result shows that the projectile under the action of cubic nonlinear static moment and quadratic nonlinear equatorial damping moment can achieve steady forced conical motion at fixed angle of attack when spin velocity and pneumatic eccentric angle satisfy certain constraint conditions. Key

Key words: non-parachureterminalsensitive, projectile, pneumaticeccentricity, nonlinearaerodynamics, conicalmotion, kineticstability