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A transformation between minimum dimension adjoint variables and redundant adjoint variables is derived in this dissertation. The transformation is then applied between the adjoint variables associated with Cartesian position and velocity vectors and a set of redundant adjoint variables associated with certain regularized variables (Schumacher variables). This transformation proves to be very beneficial when it is applied to minimum-fuel space rendezvous and intercept problems. It facilitates using attributes from the two systems simultaneously; a new necessary condition in Schumacher adjoints is derived in this dissertation, and this together with classical necessary conditions for fuel-optimal transfer (existing in the position and velocity space) leads to a numerical algorithm which seems to be quite robust in finding candidate optimal control solutions for space transfer problems. / Ph. D.

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Thesis (Ph. D.)--University of Hawaii at Manoa, 1991. / Includes bibliographical references (leaves 152-154) / Microfiche. / xvi,154 leaves, bound ill. 29 cm

Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Grain regression analysis forms an essential part of solid rocket motor simulation. In this thesis a numerical grain regression analysis module is developed as an alternative to cumbersome and time consuming analytical methods. The surface regression is performed by the level-set method, a numerical interface advancement scheme. A novel approach to the integration of the surface area and volume of a numerical interface, as defined implicitly in a level-set framework, by means of Monte-Carlo integration is proposed. The grain regression module is directly coupled to a quasi -1D internal ballistics solver in an on-line fashion, in order to take into account the effects of spatially varying burn rate distributions. A multi-timescale approach is proposed for the direct coupling of the two solvers. / AFRIKAANSE OPSOMMING: Gryn regressie analise vorm ’n integrale deel van soliede vuurpylmotor simulasie. In hierdie tesis word ’n numeriese gryn regressie analise model, as ’n alternatief tot dikwels omslagtige en tydrowende analitiese metodes, ontwikkel. Die oppervlak regressie word deur die vlak-set metode, ’n numeriese koppelvlak beweging skema uitgevoer. ’n Nuwe benadering tot die integrasie van die buite-oppervlakte en volume van ’n implisiete numeriese koppelvlak in ’n vlakset raamwerk, deur middel van Monte Carlo-integrasie word voorgestel. Die gryn regressie model word direk en aanlyn aan ’n kwasi-1D interne ballistiek model gekoppel, ten einde die uitwerking van ruimtelik-wisselende brand-koers in ag te neem. ’n Multi-tydskaal benadering word voorgestel vir die direkte koppeling van die twee modelle.

Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Includes bibliographical references. / M.S.

A study has been performed to determine the advantages and disadvantages of variable thrust and variable specific impulse (Isp) trajectories for solar system exploration. There have been several numerical research efforts for variable thrust, variable Isp, power-limited trajectory optimization problems. All of these results conclude that variable thrust, variable Isp (variable specific impulse, or VSI) engines are superior to constant thrust, constant Isp (constant specific impulse, or CSI) engines. However, most of these research efforts assume a mission from Earth to Mars, and some of them further assume that these planets are circular and coplanar. Hence they still lack the generality. This research has been conducted to answer the following questions: - Is a VSI engine always better than a CSI engine or a high thrust engine for any mission to any planet with any time of flight considering lower propellant mass as the sole criterion? - If a planetary swing-by is used for a VSI trajectory, is the fuel savings of a VSI swing-by trajectory better than that of a CSI swing-by or high thrust swing-by trajectory? To support this research, an unique, new computer-based interplanetary trajectory calculation program has been created. This program utilizes a calculus of variations algorithm to perform overall optimization of thrust, Isp, and thrust vector direction along a trajectory that minimizes fuel consumption for interplanetary travel. It is assumed that the propulsion system is power-limited, and thus the compromise between thrust and Isp is a variable to be optimized along the flight path. This program is capable of optimizing not only variable thrust trajectories but also constant thrust trajectories in 3-D space using a planetary ephemeris database. It is also capable of conducting planetary swing-bys. Using this program, various Earth-originating trajectories have been investigated and the optimized results have been compared to traditional CSI and high thrust trajectory solutions. Results show that VSI rocket engines reduce fuel requirements for any mission compared to CSI rocket engines. Fuel can be saved by applying swing-by maneuvers for VSI engines, but the effects of swing-bys due to VSI engines are smaller than that of CSI or high thrust engines.

Hall Effect Thrusters (HETs) are a form of electric propulsion device which uses external electrical energy to produce thrust. When compared to various other electric propulsion devices, HETs are excellent candidates for future orbit transfer and interplanetary missions due to their relatively simple configuration, moderate thrust capability, higher thrust to power ratio, and lower thruster mass to power ratio. Due to the short history of HETs, the current design process of a new HET is a largely empirical and experimental science, and this has resulted in previous designs being developed in a narrow design space based on experimental data without systematic investigations of parameter correlations. In addition, current preliminary low-thrust trajectory optimizations, due to inherent difficulties in solution procedure, often assume constant or linear performances with available power in their applications of electric thrusters. The main obstacles come from the complex physics involved in HET technology and relatively small amounts of experimental data. Although physical theories and numerical simulations can provide a valuable tool for design space exploration at the inception of a new HET design and preliminary low-thrust trajectory optimization, the complex physics makes theoretical and numerical solutions difficult to obtain. Numerical implementations have been quite extensively conducted in the last two decades. An investigation of current methodologies reveals that to date, none provide a proper methodology for a new HET design at the conceptual design stage and the coupled low-thrust trajectory optimization. Thus, in the first half of this work, an efficient, robust, and self-consistent numerical method for the analysis of HETs is developed with a new approach. The key idea is to divide the analysis region into two regions in terms of electron dynamics based on physical intuition. Intensive validations are conducted for existing HETs from 1 kW to 50 kW classes. The second half of this work aims to construct a simultaneous design optimization environment though collaboration with experts in low-thrust trajectory optimization where a new HET and associated optimal low-thrust trajectory can be designed simultaneously. A demonstration for an orbit raising mission shows that the constructed simultaneous design optimization environment can be used effectively and synergistically for space missions involving HETs. It is expected that the present work will aid and ease the current expensive experimental HET design process and reduce preliminary space mission design cycles involving HETs.