https://doi.org/10.1140/epjs/s11734-023-01013-1
Regular Article
Orbit transfer using Theory of Functional Connections via change of variables
1 CICGE, Faculdade de Ciências da Universidade do Porto, 4169-007, Porto, Portugal
2 INPE-National Institute for Space Research, São José dos Campos, SP, Brazil
3 Aerospace Engineering, Texas A &M University, 77843, College Station, TX, USA
Received:
23
April
2023
Accepted:
9
November
2023
Published online: 22 December 2023
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 nonlinear 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 nonlinear 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.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
