微分几何制导律捕获条件分析

基于Frenet坐标系的传统微分几何制导律推导过程较为复杂，工程应用中存在很大的局限性。首先在时域中推导了微分几何制导指令，其次为方便对导弹捕获目标条件的研究，建立了相对速度坐标系。基于此坐标系将弹目相对运动轨迹区域进行了分割，根据分割的不同区域给出导弹捕获目标的充分条件，并对其进行了证明推导。最后仿真结果表明，当弹目相对运动初始信息位于不同的区域时，根据给定的充分条件，导弹能够捕获目标，并且具有较高的制导精度。

Capture condition analysis of differential geometric guidance laws

Based on the Frenet coordinate system, it is complicated to derive the differentric geometric guidance law, which has heavier limitation in employing the project. The differential geometric guidance law is firstly derived and the relative velocity coordinate system is built to analyze the capture condition for convenience. The relative motion area between missile and target is partioned into subsets, then the sufficient condition for capture is obtained, also the course is derived and proved. Simulation results show that the missile can capture the target and has a higher guidance precision when the initional information satisfies the sufficient condition for capture in different subsets of the relative velocity space.