Analytic solutions of optimal angularly constrained guidance for first-order lag system

Closed-form solutions of an optimal impact-angle-control guidance for a first-order lag system are derived. Under the assumptions of a stationary target and a first-order missile with constant speed and small flight path angle, they are obtained by solving a third-order linear time-varying ordinary differential equation. It is shown that the solutions are expressed by combinations of polynomial, logarithmic, and hypergeometric functions. Moreover, terminal misses due to the system lag and homing geometries for zero miss-distance have been studied. Linear and non-linear simulations are performed to verify the proposed results.