This paper addresses an impact angle control guidance problem for nose-dive missiles to achieve the maximum terminal speed against a fixed target in the same vertical plane. By modeling the aerodynamic drag as a drag polar, we set up the nonlinear system equations needed to pursue an analytic closed-form solution. This paper shows that maximizing the terminal speed is equivalent to minimizing a weighted quadratic cost of the curvature of trajectory, and can be used as an equivalent problem to the original problem. Applying Pontryagin’s maximum principle to the equivalent problem, we obtained a closed-form optimal guidance law, described in terms of air density parameters as well as heading error angle, flight path angle, range-to-go, and time-varying speed.

本文探讨了前俯式导弹的撞击角控制制导问题，以实现在同一垂直平面内针对固定目标的最大终端速度。通过将气动阻力建模为阻力极，我们建立了追求解析闭合形式解所需的非线性系统方程。本文表明，最大化终端速度等效于最小化轨迹曲率的加权二次方成本，并且可以用作原始问题的等效问题。将庞特里亚金的最大原理应用到等效问题上，我们获得了一种封闭形式的最优制导律，用空气密度参数以及航向误差角，飞行路径角，可到达范围和时变速度来描述。