High-Fidelity Low-Thrust Trajectory Determination Research and Analysis

This document discusses a numerical analysis method for low thrust trajectory propagation known as the proximity quotient or Q-Law. The process uses a Lyapunov feedback control law developed by Petropoulos [1] to propagate trajectories of spacecraft by minimizing the user defined function at the target orbit. A simplified propagator is created from the core mechanics of this method in MATLAB and tested in several user defined cases to demonstrate its capabilities. Several anomalies arose in test cases where variations in eccentricity, inclination, right ascension of the ascending node, and argument of perigee were specified. Solutions to these anomalies are discussed and include development of a coasting mechanic and a new method for thruster angle selection. Nomenclature α = azimuthal angle (rad) β = elevation angle (rad) θ = true anomaly (rad) ω = argument of perigee (rad) ߱ሶ = rate of change of argument of perigee (rad/s) Ω = right ascension of the ascending node (rad) ߗ ሶ = rate of change of right ascension of the ascending node (rad/s) a = semi-major axis (km) ܽሶ = rate of change of semi-major axis (km/s) e = eccentricity ݁ሶ = rate of change of eccentricity (sec-1) inc = inclination (rad) ଓ݊ܿ ሶ = rate of change of inclination (rad/s) Q = proximity quotient ܳ ሶ = time rate of change of proximity quotient W = weight oe = orbital element ‫݁݋‬ ሶ = time rate of change of orbital element Subscripts h = direction of angular momentum i = current time step i+1 = next time step p = periapse pmin = minimum periapse r = radial direction T = target θ = circumferential direction