Analysis on the Coning Motion Stability of Spinning Missiles Considering Elastic Effect

With the increase in the slenderness ratio of spinning missile, the elastic deformation of spinning missile has gradually become a non-negligible factor during flight operation. The interaction between the elastic effects and the missile's rigid-body motion may further affect the motion stability of the missile. Therefore, it is very necessary to analyze the motion stability of spinning missile considering the rigid-elastic coupling effects. Based on the rigid-elastic coupled dynamic model of spinning missiles, the linear perturbed motion equations incorporating the elastic deformation are established through the reasonable assumptions, a small-disturbance linearization and the frozen coefficient method. The influence of elastic effect on the coning motion of spinning missiles is systematically investigated by solving the roots of the characteristic equation at the critical points and deriving the analytical solutions for free perturbed motion. Furthermore, the characteristic root method is employed to determine the stable rotational speed boundary for elastic spinning missiles. The accuracy of the proposed analytical method is validated through numerical simulation. Through the comparative analysis of the stability criteria of the rigid-body model and the coupled rigid-elastic model, it is found that the stability boundary of rotational speed of spinning missile decreases from 26.7 r/s to 22.3 r/s. The elastic effects of projectile body are shown to reduce the operational range of stable rotational speeds, potentially leading to the destabilization of originally stable flight trajectories.