Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Aeronautics and Astronautics

Committee Chair

Kathleen C. Howell

Committee Member 1

Christopher N. D’Souza

Committee Member 2

Belinda Marchand

Committee Member 3

James M. Longuski

Committee Member 4

David A. Spencer


In this investigation, the automation of trajectory discretization, in the form of patch point placement, is explored, along with the effects of such automated strategies on differential corrections processes. To begin, current differential corrections algorithms are presented and evaluated. Extensions of these algorithms into a higher-order ephemeris force model are explored and a hybrid differential corrections algorithm suitable for high-fidelity dynamical environments is proposed. With an appropriate differential corrections algorithm in place, a metric for quantifying the sensitivity of a trajectory to small perturbations is detailed. This sensitivity metric, known as a Lyapunov exponent, is subsequently leveraged to provide information regarding the beneficial placement of new patch points along a trajectory path. From the patch point placement information supplied by the Lyapunov exponents, a preliminary, automated trajectory discretization algorithm is developed. The resulting patch point configuration generated from this automated algorithm is then evaluated through the implementation of the previously provided differential corrections algorithm. The remaining sections of this investigation seek to improve the performance of the preliminary, automated patch point placement algorithm through the incorporation of higher-order, nonlinear dynamical information. In the pursuit of this objective, processes for the computation of higher-order state transition matrices, employing both analytical and numerical techniques, are presented, along with the employment of such higher-order state transition matrices in the generation of higher-order Lyapunov exponents. The higher-order information available from this work is then directly implemented within the previously presented automated trajectory discretization algorithm. At the conclusion of this investigation, the performance of both automated algorithms are evaluated and compared to determine the effect that the inclusion of nonlinear information has on the automated placement of patch points along a trajectory path.