Capturability of a Geometric Guidance Law in Relative Velocity Space

In this paper, capturability of a recently proposed geometric guidance law is analyzed in the plane defined by the relative velocity vector. The kinematic equations for planar engagements are derived in the relative velocity space. The analysis is done completely in the time domain. The capturability analysis of the guidance law is carried out for the entire relative velocity space as compared with the existing work where classical geometric curve theory is used to obtain and analyze the guidance law. The entire relative velocity space is partitioned into subsets corresponding to different missile and target engagement geometries. Sufficient conditions for capture are then obtained by analyzing the differential equations governing the motion of the trajectories in the relative velocity space. A comparison of the capture conditions obtained in this paper and previous work is presented. It is seen that analysis in the relative velocity space relaxes the condition on the navigation gain in the guidance law. From the analysis of both nonmaneuvering and maneuvering targets, it is also seen that a combination of these sufficient conditions can be used to obtain a more general capturability analysis of the guidance law. Numerical simulation results are given to validate the analytical results.