Perturbing accelerations in low thrust trajectory optimization

Feistel, Andrew S.
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This thesis describes an implementation of perturbing accelerations in a low-thrust trajectory optimization program. The program uses an indirect method with the equinoctial elements as the states. Earth Centered Inertial expressions for perturbing accelerations are transformed into the rotating radial frame, and the Jacobian matrix of the rotating radial acceleration with respect to the equinoctial elements is formulated. Using this approach, any perturbing effect can be included into the optimization program simply by knowing the Earth Centered Inertial representation of the perturbing acceleration. This thesis includes a description of the application and testing of the new method to include third-body and zonal harmonic (J₂, J₃, J₄, J₅, and J₆) effects. Additionally, the modifications of the trajectory optimization program to utilize the optimizer SNOPT are discussed. Analytically derived partial derivatives are numerically compared with finite differences, force model results are compared with other software tools, and continuous low-thrust LEO-GEO orbit transfer problems are solved and discussed.