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相对于直接在笛卡尔坐标系内对质点运动进行分解而言,使用微分几何原理对质点的运动进行分析是一种较为巧妙的方法。本文基于古典微分几何原理,对拦截弹的制导进行了建模研究。首先,分析了弹目相对视线的运动规律,建立了视线旋转坐标系提出了视线曲率与挠率的概念,得到了视线运动方程.并将视线运动方程与弹目相对运动相结合,构造了新的弹目相对运动方程。其次,通过研究发现,在视线旋转坐标系内存在视线瞬时旋转平面,可以在该平面内构造具有三维拦截能力的二维制导律。空间真比例导引律(TPN)可以不加近似地直接引入视线瞬时旋转平面,成为降维TPN。同时通过研究在视线瞬时旋转平面内对目标机动加速度进行补偿的方法,可以得到新的修正比例导引律(APN)系列和视线角加速度制导律(AAG)系列。再次,提出了视线瞬时旋转平面内制导律的微分几何制导指令,与Chiou和Kuo所提出的微分几何制导律进行对比分析,可以发现该制导律是本文的一种特例,并且微分几何制导指令将降低视线瞬时旋转平面内制导律的性能。最后,以拦截大气层外高速机动目标为算例进行仿真分析,验证了拦截弹微分几何制导模型的有效性。
Compared with the direct analysis of particle motion in Cartesian coordinate system, it is a clever way to use the principle of differential geometry to analyze particle motion. Based on the principle of classical differential geometry, this paper studies the guidance of the interceptor. Firstly, the law of motion of the relative line of sight of the projectile is analyzed, and the concept of line-of-sight curvature and torsion is put forward by establishing the line-of-sight rotation coordinate system, and the equation of line of sight motion is obtained. Combining the line of sight motion equation with the relative movement of projectile, The projectile relative motion equation. Secondly, the study found that there is a line of sight instantaneous rotation plane in the line-of-sight rotating coordinate system, and a two-dimensional guidance law with three-dimensional interception capability can be constructed in this plane. The true proportional guidance law (TPN) of space can be directly introduced into the line of sight instantaneous rotation plane and become dimensionality reduction TPN. At the same time, a series of APN series and AAG series can be obtained by studying the method of compensating the target maneuvering acceleration in the instantaneous rotation plane of sight. Thirdly, the differential geometry guidance order of instantaneous rotating plane guidance is proposed. Compared with the differential geometry guidance law proposed by Chiou and Kuo, it can be found that the guidance law is a special case of this paper, and the differential geometry guidance instruction Reduce the performance of the guidance law in the instantaneous rotation plane of the line of sight. Finally, the simulation of the intercepting maneuvering target of the extra-high-speed atmosphere is carried out to verify the validity of the interceptor differential geometry guidance model.