基于摄动法考虑高度影响的二维末段解析解  

2-D terminal-phase analytical solution with height effect being considered based on perturbation method

作　　者：王楠翔 陈万春[1,2] 王鹏 WANG Nanxiang;CHEN Wanchun;WANG Peng(School of Astronautics,Beihang University,Beijing 100191,China;Key Laboratory of Spacecraft Design Optimization and Dynamic Simulation Technologies,Ministry of Education,Beijing 100191,China)

机构地区：[1]北京航空航天大学宇航学院,北京100191 [2]航天器设计优化与动态模拟技术教育部重点实验室,北京100191

出　　处：《飞行力学》2024年第6期71-76,82,共7页Flight Dynamics

摘　　要：针对末段打击任务,提出一种基于摄动法的解析解。在零控情况下,考虑重力加速度随高度变化和阻力的影响,利用摄动法建立了高度、速度和弹道倾角的解析表达式。将二维三自由度非线性动力学,分为考虑重力和阻力主要影响的零阶动力学和补偿其他影响的一阶动力学,利用经验引入一个中间变量,并用拉格朗日插值多项式拟合求解解析解。仿真结果表明:得到的高度、速度和弹道倾角的解析式与弹道积分精度相当,但计算效率远高于后者;相比未考虑重力加速度变化的解析解而言,对于弹道积分拟合程度更好,精度更高。Aiming at the end-of-range strike mission,an analytical solution based on the perturbation method is proposed.In the case of zero control,with the changing gravity due to height and drag effect taken into consideration,the terminal-phase analytical solution of height,velocity and flight-path angle is established by using the perturbation method.The two-dimensional three-degreeof-freedom nonlinear dynamics is divided into zero-order dynamics considering the main influence of gravity and drag and first-order dynamics compensating other relevant influence.An intermediate variable is introduced and the analytical solution is obtained by solving Lagrange interpolation polynomial.It is shown that the analytical solution of height,velocity and flight-path angle is almost as precise as the ballistic integral method and presents higher calculation efficiency than the latter.In comparison with the analytic solution with the gravity changes not considered,this terminal-phase analytical solution generates better and preciser ballistic integral fitting.

关 键 词：摄动法 末段解析解 非线性动力学 

分 类 号：TJ765[兵器科学与技术—武器系统与运用工程]