Peter F Gath

Improvements to a Hybrid Algorithm for Rapid Generation of 3-D Optimal Launch Vehicle Ascent Trajectories Peter F Gath

Diplomarbeit, die am 15.12.1998 erfolgreich an einer Universität in Deutschland im Fachbereich Luft- und Raumfahrttechnik eingereicht wurde. Abstract: This thesis presents improvements to FLOAT, a hybrid analytical/numerical algorithm for rapid generation of three dimensional, optimal launch vehicle ascent trajectories. Improvements have been made to the terminal constraints, which are now available in a more general form to allow for an optimal attachment point to the target orbit. The existing algorithm also has been extended with logic that allows for vehicles with low thrust to weight ratios in the upper stage and successful convergence of problems with path constraints for normal force and angle of attack Another major extension made to the code is the introduction of coasting arcs. Coasting arcs are implemented using a completely analytical solution for the prediction of states and costates as well as for the required sensitivity matrix. This allows for a very fast and accurate calculation even with long coasting arcs. Finally, an approach for the optimization of start and end time of coast arcs is presented. This approach was implemented and the results of a test case compare very well with results generated with OTIS for the same case. At the end, suggestions for future development are made. Table of Contents: |Summary|i |Acknowledgements|ii |Contents|iii |Nomenclature|v |Figures|viii |Introduction|1 1.|Problem description|3 1.1|Describing the final orbit|3 1.2|Coordinate frame|5 1.3|Dynamic system|6 1.4|Initial conditions|7 1.5|Path constraints|7 1.6|Performance index|7 1.7|Terminal constraints|8 1.8|Solution method|8 1.9|Non-dimensionalization of the variables|9 2.|Solving the two-point boundary value problem|10 2.1|Vacuumsolution|10 2.1.1|Simplified model equations|10 2.1.2|Optimal control for vacuum solution|11 2.1.3|Thrust integrals and closed form solution for ascent in vacuum|12 2.2|Atmospheric solu