Orbit transfer using Theory of Functional Connections via change of variables

TL;DR

This paper demonstrates how the Theory of Functional Connections, combined with a strategic change of variables, can efficiently solve constrained orbit transfer problems in astrodynamics by transforming nonlinear constraints into linear ones.

Contribution

It introduces a novel coordinate transformation approach that enables the application of TFC to complex orbit transfer problems with mission constraints.

Findings

Successfully applied to perturbed Hohmann transfer problems

Effectively isolates constraint components for easier solution

Transforms nonlinear constraints into linear form

Abstract

This work shows that a class of astrodynamics problems subject to mission constraints can be efficiently solved using the Theory of Functional Connections (TFC) mathematical framework by a specific change of coordinates. In these problems, the constraints are initially written in non-linear and coupled mathematical forms using classical rectangular coordinates. The symmetries of the constrained problem are used to select a new system of coordinates that transforms the non-linear constraints into linear. This change of coordinates is also used to isolate the components of the constraints. This way the TFC technique can be used to solve the ordinary differential equations governing orbit transfer problems subject to mission constraints. Specifically, this paper shows how to apply the change of coordinates method to the perturbed Hohmann-type and the one-tangent burn transfer problems.