基于章动运动理论的火箭弹锥形运动稳定性分析

Analysis of Stability for Coning Motion of Rockets Based on Theory of Nutation Movement

基于自旋弹体短周期力矩投影的动力学方程,建立了以弹体摆动章动角和进动角为变量的弹体锥形运动的非线性数学模型,通过引入广义章动角及进动角速率,使难以用解析手段处理的非线性模型转换成可解析的一般模型。根据线性化模型分析了弹体章动及进动运动的相互关系,给出了自旋弹体章动运动稳定性条件。对非线性模型,研究了章进动运动对弹体锥形运动极限环的作用,给出了弹体锥形运动稳定时自旋弹体章动角度及进动角速度应满足的解析关系。

A nonlinear mathematic model of coning motion taking nutation and precession as variable was established by the dynamic equation based on short period moment projection of the spin projectile, which is transformed into an analytical model by introducing generalized nutation and precession angular rate into the model. The relation of nut.ation and precession was analyzed, critical condition was obtained for a stable rocket based on linear model. Effects of nutation and precession on limit cycle of coning motion of the projectile were investigated, and satisfied analytical relations between nutation, precession angular rate vs. time at steady coning motion were given for the nonlinear model.