Efficient methods for phase space analysis in spaceflight machanics: Application to the optimization of stable transfers

This research presents algorithms for the numerical phase space analysis of large sets of trajectories. These involve propagating sections of phase space and studying the evolution of orbital characteristics which can be viewed as mapping dynamical properties of the system. Generating these maps is tedious and computationally expensive. This research proposes using an efficient numerical integration method based on a modified Picard integration for generating these maps. This numerical integration method is selected based on its potential use for developing parallel integration algorithms for massively parallel hardware such as Graphic Processing Units (GPUs). A requirement for the modified Picard integration is a method to transform vector fields to polynomial form in astrodynamics problems. This thesis demonstrates the transformation to polynomial form for simple and complex vector fields encountered in astrodynamics. This research also discusses the improvements of using this method for both parallel and sequential integrations. The integration method additionally provides the possibility to study nonlinear uncertainty propagations for a system by offering an efficient method to calculate high order state transition tensors. In the case of uncertainty propagation for large sets of trajectories, unscented transformation can be used to enhance the grid generation for maps. Besides the difficulties involved in generating maps, they are not immediately usable in practice. This research proposes the use of image processing and clustering analysis algorithms to autonomously detect and extract dynamical features from these maps. To do so, image segmentation algorithms such as k-mean clustering, contrast segmentation, and texture segmentation have been used. Additionally, this thesis discuses representing these sections of phase space using sets of B-spline and Gaussian mixtures. Based on data clustering, an enhanced map generation method is also introduced, which significantly reduces the computational efforts associated with integrating many trajectories. The application of these detected features from a chaoticity map has been demonstrated in an optimization of stable transfers in a planar circular restricted three-body problem.