Seminars

Although there has been work on relative motion and formation flying in non-Keplerian dynamics, many of the solutions for the motion are highly tailored to a specific problem, relatively slow, possess a restrictive region of convergence, or have multiple of these drawbacks at once. This dissertation develops and applies a system for modeling non-Keplerian relative motion addressing the issues of general applicability, speed, and accuracy, sufficient for a broad class of scenarios relevant to the challenges of current mission design. To obtain increased accuracy, the trajectory phase flow around a reference trajectory are expanded to second order. Additionally, in order to avoid the use of numerical integration while propagating relative trajectories, the tensor elements are interpolated over a mission period of interest using both Chebyshev interpolants and splines associated with dense Runge-Kutta numerical integration methods. Regularization of the dynamics using Sundman transformation was also investigated, and one of the questions addressed by the research is when to regularize in a nonlinear relative motion context. The relative motion model developed in the dissertation is compatible with ephemeris dynamical models along with modeled by spherical harmonics expansions. The reference trajectory for the model is arbitrary, and can be any interpolated orbit contained in the ubiquitous SPICE kernel format. Finally, the resulting model is used to perform robust relative trajectory optimization in combination with industry mission design software. The resulting model’s source code is made available.