Lambert’s problem involves solving the orbits connecting two position vectors with a given flight time. When introducing variations to the input of this problem (that is, terminal positions and the flight time), the output terminal velocities vary in response. The higher-order Lambert problem pursues a higher-order Taylor approximation of the output with respect to the input. Instead of finding a real number root, Householder methods are adapted to find a Taylor series solution of the transfer-time equation. By using explicit derivatives of the transfer-time equation, the newly implemented Householder methods converge faster than the general partial inversion method. In applications such as pork-chop plots and orbital admittance maps that require solving a large number of Lambert’s problems, a higher-order Lambert solution can reduce the running time by more than 80% when compared to solving the original Lambert problems one by one. Furthermore, the investigation of the parameter space of Lambert’s problem yields useful insights to the selection of higher-order expansion points.
Higher-Order Lambert Problem Solution Based on Differential Algebra
Journal of Guidance, Control, and Dynamics ; 45 , 10 ; 1913-1926
2022-06-28
14 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
AIAA | 2015
|Energy-Optimal Solution to the Lambert Problem
Online Contents | 2010
|Solution Based on Dynamical Approach for Multiple-Revolution Lambert Problem
Online Contents | 2011
|