New Solutions to Impulsive Correction for Argument of Perigee Using Gauss's Variational Equations

This paper provides two new solutions to the energy-optimal impulsive correction for argument of perigee using Gauss's variational equations (GVEs). A linear analytical approximation was derived by solving a cubic polynomial based on the classical linear GVEs. Compared with the existing analytical methods (e.g., special-point-based maneuver, circumferential impulse), the proposed linear analytical method can save energy cost and it is also valid for the large-eccentricity case. Moreover, a second-order numerical method was proposed based on the second-order GVEs and optimization technique. The proposed second-order method requires solving a three-dimensional equation, whereas the classical Lawden's method solves a six-dimensional equation. Numerical examples with different eccentricities and different changes of argument of perigee were provided to verify the proposed linear analytical method and the second-order numerical method. The results showed that the proposed second-order method needs less computational time while ensuring enough accuracy.