弹丸的随机动态稳定性研究

With the further study of ballistics, the random phenomena in the projectile(refers to artillery shells, rockets, missiles and other aircraft) flying get much more attention and urgently need to be studied systematically. Based on the random dynamical system theory, the dynamical stability of the projectile will be investigated. With Khasminskii transform, the stochastic averaging method, the perturbation method and a spectrum representation of the FPK operator, the moment Lyapunov exponent,the largest Lyapunov exponent and the stability boundary of the projectile random dynamical system can be obtained. Then we can analyze the random dynamic stability of projectiles qualitatively, describe the random bifurcation behavior(dynamic bifurcation and phenomenological bifurcation)of the system, get the stochastic stability criterion(sample stability and the moment stability)of projectiles and guide the design of projectiles. In addition, via the establishment of the stochastic differential equations of the projectile flight under various random disturbances, the simulation of the movement processes and the analysis of the dynamic stability of projectiles, the mechanism of the stochastic dynamic instability of projectiles can be revealed. This project is of great significance on improving exterior ballistics research, exploring new projectile design, getting high hit rate and promoting the application of stochastic dynamics in the field of aviation, aerospace, military and so on.

随着弹道学研究的逐步深入，弹丸（泛指炮弹、火箭、导弹等飞行器）飞行过程中普遍存在的随机现象越来越被人们所重视，迫切需要进行深入系统地研究。本项目基于随机动力系统理论开展弹丸的动态稳定性研究，采用Khasminskii变换、随机平均法、Arnold摄动法以及FPK算子的特征谱展开式等方法，求解相关随机动力系统的矩Lyapunov指数、最大Lyapunov指数和稳定边界，定性分析弹丸的随机动态稳定性，全面刻画系统的随机分岔（动态分岔和唯象分岔）行为，给出弹丸随机稳定性（样本稳定性和矩稳定性）判据，指导弹丸的优化设计。此外通过建立不同噪声作用下弹丸飞行的随机微分方程，模拟弹丸在不同随机扰动下的运动过程，分析各类随机因素对弹丸动态稳定性的影响，揭示弹丸的随机动态失稳机理。本项目对于丰富外弹道理论的研究，探索新型弹丸设计，满足高命中率的要求，推动随机动力学在航空、航天、军事等领域的应用具有重要意义。

在所有外弹道问题中弹箭的飞行稳定性无疑是在科学和工程上最受关注的问题之一。随着弹箭飞行稳定性研究的深入，弹箭飞行过程中普遍存在的随机现象越来越被人们所重视，迫切需要进行系统深入地研究。本项目基于随机动力系统理论对弹箭的动态稳定性进行了系列研究，通过在弹箭运动系统中引入随机噪声，探讨了弹箭在随机扰动下的飞行稳定性。项目组计算了白噪声作用下弹箭运动系统的p阶矩Lyapunov指数以及稳定指数的渐近解析式，给出了白噪声作用下弹箭运动的随机稳定性判据。在此基础上对阵风环境中弹箭的随机稳定性进行研究，采用通用的Press模型模拟阵风环境，推导系统的p阶矩Lyapunov指数以及稳定指数的渐近式，确定系统的随机分岔点，给出了系统在阵风环境中的稳定性判据。通过对阵风环境中弹丸的随机动力学行为进行数值仿真，给出了分岔点前后平稳概率密度函数的变化情况。通过本项目的研究，明确了系统各参数对弹箭运动稳定性的影响，掌握了随机扰动下弹箭失稳的机理，对于丰富外弹道理论的研究，探索新型弹丸设计，满足高命中率的要求，推动随机动力学在航空、航天、军事等领域的应用具有重要意义。