THE THEORY OF CONNECTIONS APPLIED TO PERTURBED LAMBERT'S PROBLEM

2018 Univelt Inc. All rights reserved. Lamberts problem remains important in celestial mechanics for application such as rendezvous, targeting, guidance, and orbit determination and has many robust algorithms for solving this type of problem using Keplers equation of motion. Solutions to the unperturbed case have been studied extensively and are leverage and built upon by developing an algorithm that allows for the solution of the perturbed Lambert problem by the addition of all perturbations at once. By doing this, both analytical and numerical perturbation models to be handled in a unified manner. Since at its core, Lamberts problem is simply a two point boundary value problem for the differential equation of motion, extension of the Theory of Connections (ToC) for this case is immediate. In this paper, a new solution to the perturbed Lambert Problem is developed using the Theory of Connection (ToC) where first Lamberts problem is solved for the unperturbed case, then this solution is adjusted for all incorporated perturbations simultaneously utilizing a constrained expression. From this, a solution is produced with sub-meter accuracy.

THE THEORY OF CONNECTIONS APPLIED TO PERTURBED LAMBERT'S PROBLEM Conference Paper