弹道式飞行器再入段状态变量的解析预测

Analytical Estimation of State Variables for Reentry Ballistic Vehicle

摘要

弹道式飞行器再入段因其飞行速度快和防御拦截难的特点,在现代军事冲突中得到了广泛应用。为提高弹道式飞行器状态变量的解析预测精度,并揭示各状态变量间的内在关系,对弹道式飞行器再入段状态变量的解析预测问题展开研究。利用再入动力学的变量代换方法,推导出地心距、飞行速度与飞行路径角之间的全微分关系,并结合相关假设条件,推导出飞行速度与地心距之间新的近似解析关系。与传统忽略重力得到的近似解析关系相比,新的飞行速度-地心距公式具有更高的精度和更广泛的适用性。在此基础上,根据再入动力学微分方程组,利用级数展开方法推导出新的地心距-飞行时间、飞行路径角-地心距和飞行速度-飞行时间的解析关系,并与传统的解析公式和四阶龙格-库塔数值方法进行仿真对比。结果表明,在相同的再入初始条件下,新解析公式所得结果与数值解更为接近。此外,该解析模型还可以预测弹道式飞行器再入段末端的打击速度以及再入的大致时间。研究结果可为弹道式飞行器再入段的初步设计和空天防御等领域提供理论参考。

Abstract

Ballistic reentry vehicle(BRV)has been widely utilized in modern military conflicts due to its high velocity and difficulty of interception.To improve the analytical prediction accuracy of state variables for BRV and to reveal the intrinsic relationships among these state variables,analytical prediction problem of their state variables was addressed in this paper.Firstly,by applying variable substitution to the reentry dynamics equations,a total differential relation among geocentric radius,flight velocity and flight path angle was derived.Under appropriate assumptions,a new approximate analytical relation between flight velocity and geocentric radius was established.Comparing with the traditional methods of neglecting the gravity effect,the proposed formula features higher accuracy and greater generality.Then,based on the new formula and the fundamental reentry dynamics differential equations,new analytical relations for geocentric radius versus flight time,flight path angle versus geocentric radius,and flight velocity versus flight time were derived using series expansion.The proposed formulas were compared with traditional analytical methods and the fourth-order Runge-Kutta(RK4)numerical method.The results demonstrate that under identical initial reentry conditions,the results obtained from the new analytical formulas are in closer agree with the RK4 numerical solution.Furthermore,the new analytical solutions can also predict the terminal impact velocity and approximate reentry duration of BRV.The results can provide theoretical reference for the preliminary design of BRV and related fields such as aerospace defense.

关键词

弹道式飞行器 / 再入段 / 地心距 / 飞行速度 / 飞行路径角 / 解析公式

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基金资助

深圳市孔雀团队项目(KQTD20190929172704911)