Terminal-Velocity-Based Lambert Algorithm
Gang Zhang
Abstract
This paper provides an alternative Lambert solution based on the terminal velocity vector. The chordal terminal velocity component is selected as the independent variable since it is the final required parameter in Lambert’s problem and it can be directly solved in the minimum-fuel free-time impulsive targeting problem. The transfer time for arbitrary conic transfer is written as a function only of the terminal velocity component. The admissible ranges of the new independent variable are analytically derived for different trajectory types. The 180 deg case and the multiple-revolution case are also considered. The analytical derivative of transfer time is provided to improve computational efficiency in numerical iterations. Compared with the existing Lambert methods, the proposed approach is direct from the viewpoint of problem and physically more intuitive, although it is not superior in numerical performance.