弹丸的随机动态稳定性研究

项目名称： 弹丸的随机动态稳定性研究

项目编号： No.11302106

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 黄勇

作者单位： 南京理工大学

项目金额： 26万元

中文摘要： 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。

中文关键词： 弹箭运动系统；随机噪声；Lyapunov指数；Monte Carlo仿真；随机中心流形

英文摘要： 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,

英文关键词： projectile system；random noise；Lyapunov exponent；Monte Carlo simulation；stochastic center manifold theory