时域下空间曲线曲率及挠率问题的研究  

Research on Curvature and Torsion of Space Curve in Time Domain

作　　者：许飞 刘翠香 闵祥娟 单彩虹 曹贻鹏 XU Fei;LIU Cui-xiang;MIN Xiang-juan;SHAN Cai-hong;CAO Yi-peng(Basic Education Department,Army Academy of Armored Force,Beijing 100072,China)

机构地区：[1]陆军装甲兵学院基础部,北京100072

出　　处：《火力与指挥控制》2021年第1期108-111,共4页Fire Control & Command Control

摘　　要：空间域下拦截弹制导问题可转化为空间曲线进行研究,由空间曲线论的基本定理可知该曲线的曲率和挠率能够完全确定曲线的性态,由此可通过曲率和挠率的调整来确定拦截弹的制导路径,从而实现对目标弹的有效拦截,基于此思想,将几何中弧长域下的Frenet公式转化为时域下的Frenet公式,并建立了视线运动方程和弹目相对运动方程,在此基础上推导了曲率和挠率的指令公式,相对于比例导引律及大量的现代制导律,采用几何的方法更加直接,为拦截弹制导及相关问题的进一步研究提供了思路。The guidance problem of interceptor missile in space domain can be transformed into the study of space curve.According to the basic theorem of space curve theory,the curvature and torsion of the curve can completely determine the properties of the curve.Thus,the guidance path of interceptor missile can be determined by adjusting curvature and torsion,so as to achieve effective interception of target missile.In this paper,the Frenet formula in the arc-length domain of geometry is transformed into the Frenet formula in the time domain,and the sight motion equation and the relative motion equation of missile and target are established.On this basis,the directive formulas of curvature and torsion are derived.Compared with proportional guidance law and a large number of modern guidance laws,the geometric method is more direct.It provides a way of thinking for the further study of interceptor missile guidance and related issues.

关 键 词：曲率 挠率 FRENET公式 制导律 

分 类 号：TJ013[兵器科学与技术—兵器发射理论与技术] O186.1[理学—数学]