Study of the solutions of low-thrust orbital transfers in the two and three body problem

Helen Clare Henninger 1
1 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The technique of averaging is an effective way to simplify optimal low-thrust satellite transfers in a controlled two-body Kepler problem. This study takes the form of both an analytical and numerical investigation of low-thrust time-optimal transfers, extending the application of averaging from the two-body problem to transfers in the perturbed low-thrust two body problem and a low-thrust transfer from Earth orbit to the L1 Lagrange point in the bicircular four-body setting. In the low-thrust two-body transfer, we compare the time-minimal case with the energy-minimal case, and determine that the elliptic domain under time-minimal orbital transfers (reduced in some sense) is geodesically convex. We then consider the Lunar perturbation of an energy-minimal low-thrust satellite transfer, finding a representation of the optimal Hamiltonian that relates the problem to a Zermelo navigation problem and making a numerical study of the conjugate points. Finally, we construct and implement numerically a transfer from an Earth orbit to the L1 Lagrange point, using averaging on one (near-Earth) arc in order to simplify analytic and numerical computations. In this last result we see that such a `time-optimal' transfer is indeed comparable to a true time-optimal transfer (without averaging) in these coordinates.
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Helen Clare Henninger. Study of the solutions of low-thrust orbital transfers in the two and three body problem. General Mathematics [math.GM]. Université Nice Sophia Antipolis, 2015. English. ⟨NNT : 2015NICE4074⟩. ⟨tel-01219382⟩

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