A study on the nonlinear angular motion characteristics has been conducted with the goal of addressing the stability issue of a controlled projectile with self-rotating wraparound fins under the influence of nonlinear aerodynamic force and duck rudder control force. According to the ballistic and structural characteristics of this type of sling and arrows, a seven-degree-of-freedom rigid-body motion model is established, according to which the nonlinear angular equations of motion in the state-space form are deduced. The characteristic points of the ballistic trajectory are selected, and the corresponding nonlinear aerodynamic coefficients are obtained by using the numerical simulation and polynomial fitting methods, and the estimation of the domain of attraction based on the sum-of-squares planning is adopted to analyse the effects of the duck rudder control and nonlinear aerodynamic coefficients on the stability domain of this type of slings and arrows in a quantitative manner. Based on the results of the simulation and theoretical analysis, the size of the duck rudder control force has a significant impact on the stable attraction domain of the angular motion of the projectile and arrow. For example, in the paper, the attraction domain boundary decreases by approximately 16.9% when the rudder deflection angle δ_c is 20° compared to the uncontrolled state, while the control force azimuth has barely any effect. The lift coefficient derivative, the static moment coefficient derivative, and the nonlinear terms of the forebody and aft body Magnus moment coefficient derivative are the main factors affecting the stable attraction domain of the projectile and arrow in this type of motion. The nonlinear Magnus moment of the rear body has a significantly larger effect on the region of attraction of the angular motion of the projectile than that of the front body.