一类旋转弹在高空中的锥形运动稳定性

为揭示弹箭在高空飞行过程中由于重力持续作用产生大攻角的物理本质,建立了弹道平面内时变参数的弹体运动数学模型,并推导了弹体在高空飞行段的攻角响应方程.同时,为了分析弹道顶点附近锥形运动的稳定性,综合考虑弹体姿态运动和位移运动建立了旋转弹锥形运动的动力学模型.针对大攻角引起显著气动非线性效应的情况,采用李雅普诺夫一级近似方法,给出了弹道顶点附近弹体锥形运动的稳定判据,并通过数值仿真验证了其正确性.

Stability of coning motion of spinning bocket projectiles at high altitude

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.