Colloquium: Aalok Parkash (Space Flight)

20 september 2019 08:30 - Locatie: Lecture Room C, Faculty of Aerospace Engineering, Kluyverweg 1, Delft

Application of Lagrangian Coherent Structures to the computation and understanding of ballistic capture trajectories

In this research three new areas within the field relating Lagrangian Coherent Structures (LCS) to ballistic capture are explored. Firstly, it has not yet been shown what LCS can be found in an area around a planet, without making use of a priori stable set information. Furthermore, it is unclear what the effect is of changing the integration time in the procedure of extracting LCS. Finally, there has not yet been an analysis to show how the LCS relate to stable sets with different number of revolutions.In this work two algorithms for extracting LCS have been developed. One is based on the simple but efficient computation of the Finite Time Lyapunov Exponent (FTLE). Another is based on the more involved Variational Theory. Both algorithms are validated on a toy problem used frequently in LCS extraction studies, and are then applied to the Elliptic Restricted Three BodyProblem (ERTBP).It is shown that LCS around a planet yield resemblance with stable set results. The FTLE-based algorithm is able to quickly and efficiently identify the shape of the stable set. The Weak Stability Boundary, however, can not be extracted distinctly. The Variational Theory-based algorithm yields more distinguishable results for the Weak Stability Boundary. It is shown that large and constant integration times are beneficial. It is shown that extracted LCS form an approximation of the average resulting WSB for all stable sets.