Assessment of application of the steep-lifting entry trajectory solution to real-time entry guidance

Closed-form analytical guidance algorithms are highly desirable in the context of real-time aerospace guidance applications. The steep-lifting entry trajectory solution is a set of closed-form analytical approximate solutions to the planar equations of motion, which includes expressions for range, flight-path angle, and altitude as functions of velocity. This thesis assesses the applicability and performance of the steep-lifting entry trajectory solution in the context of a root-solving guidance algorithm for direct entry applications with bank angle modulation. A root-solving guidance algorithm is developed for direct entry applications: the steep-lifting root-solving guidance algorithm. The use of the steep-lifting entry trajectory solution in the context of direct entry applications is inherently limited by the assumptions in the solution, and the conditions for which it is valid. It was observed that the steep-lifting guidance algorithm has comparable performance to the other guidance algorithms (i.e. Apollo final phase, and analytic and numeric predictor-correctors), where the steep-lifting entry trajectory solution assumptions and conditions were valid; however, due to the assumptions in the steep-lifting entry trajectory solution, the Apollo final phase and numeric predictor-corrector guidance algorithms offer better performance over a larger range of initial and terminal states. Within its region of applicability, the steep-lifting guidance algorithm has comparable performance to the Apollo final phase and numeric predictor-corrector guidance algorithms in the context of robustness to dispersions in initial flight conditions, vehicle/aerodynamic properties, and atmospheric conditions. The steep-lifting entry trajectory solution provides a rapid, first-order capability for nominal guidance purposes. However, the utility of the steep-lifting entry trajectory solution, in the context of entry guidance algorithms, is limited due to the assumptions and mathematical structure of the solution