Traditionally, two-body dynamics have been used to design orbital trajectories for interplanetary missions using a series of Lambert’s transfers and gravity assists. Although these are reliable methods, they have extremely high fuel requirements, especially for missions to outer planets. From an orbital mechanics perspective, three ways of reducing fuel requirements for these types of missions are utilizing low energy transfer trajectories, applying low thrust engine parameters, and implementing orbit optimization techniques. The goal of this thesis is to combine low energy transfers created from the dynamics of the Circular Restricted Three-Body Problem (CRTBP) with low-thrust orbit optimization techniques to develop interplanetary missions that require less fuel to reach their destinations when compared to transfers that implement traditional two-body dynamics. A Patched Conics with Manifolds method was used to maneuver a spacecraft from low Earth orbit to a halo orbit and then use exterior manifolds to link a spacecraft along a low-thrust interplanetary trajectory between the halo orbits of Earth and the destination planet. Indirect and direct optimization are applied to both an initial orbit raising maneuver and the low-thrust interplanetary transfer to attempt to reduce the fuel requirements needed for each mission phase. These transfers are tested for missions from Earth to Jupiter and Earth to Saturn and the fuel requirements and time of flight are analyzed. Results from this research showed that applying low thrust optimization to portions of the interplanetary transfer using manifolds reduced the fuel required for each phase of the transfer for both missions to Jupiter and Saturn. For the low thrust orbit raising phase, the fuel requirements were reduced by 13-17%, while for the interplanetary phase fuel requirements were reduced by 23-27% for the mission to Jupiter and 15- 17% for the mission to Saturn when compared to previous methods. In addition, additional fuel savings are found by the elimination of the need for a second stage to arrive at the destination planet due to the low-thrust maneuver accounting for the reduction in speed due to the constant burn throughout the interplanetary phase. Analysis of the flight times for each test case showed that the Patched Conics with Manifolds method combined with low-thrust maneuvers increased the amount of travel time by 6.5 years for a mission to Jupiter and 8.5 years for a mission to Saturn. Overall, the fuel and time of flight results show that there is a trade-off between significantly reducing the fuel needed for this type of transfer and significantly increasing the transfer time that must be considered for each particular mission application.

This thesis describes the models of four common orbital propagators and outlines the process of integrating them into the Horizon Simulation Framework (HSF). The results of the Two-Body, J2, and J4 propagators from the HSF are then compared against the outcomes of these propagators in MATLAB and Satellite Toolkit (STK). The MATLAB algorithms verify the functionality of the propagators and determine the accuracy of the HSF implementation. The compassion against STK validates the formulation of the HSF propagators. In order to equip the HSF with a more precise means of orbit determination, adding the Simplified General Perturbations 4 (SGP4) propagator to the HSF has been the principal goal of this project. A brief description of the algorithm explains the process of configuring the original code into a format compatible with the HSF. Further, the orbital data from the SGP4 propagator across different implementations are examined. The outcomes demonstrate that the HSF algorithm generates reasonably accurate orbital data.

This thesis is directed toward the feasibility of observing satellites on the nano scale and determining an accurate propagated orbit using a Meade LX600-ACF 14” diameter aperture telescope currently located on the California Polytechnic State University campus. The optical telescope is fitted with an f/6.3 focal reducer, SBIG ST-10XME CCD camera and Optec TCF-S Focuser. This instrumentation allowed for a 22’ X 15’ arcminute FOV in order to accurately image passing LEO satellites. Through the use of the Double-r and Gauss Initial Orbit Determination methods as well as Least Squared Differential Correction and Extended Kalman Filter Orbit Determination methods, an accurate predicted orbit can be determined. These calculated values from observational data of satellites within the Globalstar system are compared against the most updated TLEs for each satellite at the time of observation. The determined differential errors from the well-defined TLEs acquired via online database were used to verify the feasibility of the accuracy which can be obtained from independent observations. Through minimization of error caused from imaging noise, pointing error, and timing error, the main determination of accurate orbital determination lies in the instrumentation mechanical capabilities itself. With the ability to acquire up to 7 individual satellite observations during a single transit, the use of both IOD and OD methods, and the recently acquired Cal Poly telescope with an increased 14” aperture, the feasibility of imaging and orbital determination of nanosatellites is greatly improved.

This thesis investigates the orbital debris evolution in the geosynchronous disposal orbit regime and within geosynchronous orbits effected by the geopotential wells. A propagator is developed for the accurate simulation of GEO specific orbits and the required perturbations are determined and described. Collisions are then simulated in the selected regimes using a low velocity breakup model derived from the NASA EVOLVE breakup model. The simulations described in this thesis consider a set of perturbations including the geopotential, solar and lunar gravity, and solar radiation pressure forces. This thesis is based on a prior paper and additionally seeks to address an issue in simulating East-West trapped objects. The results show that this propagator successfully simulates the presence of all wells and the East-West entrapment, and the required perturbations are outlined. Five collision test cases were simulated, one for each type of entrapment and an additional for the disposal orbit.

While landing, birds often perform a perching maneuver, which involves pitching their wings upwards while decelerating to a complete stop. By performing this perching maneuver, the birds can continue generating higher lift and drag force while slowing down, resulting in a smooth landing. The present study is motivated by the perching maneuver and aims to investigate two critical aspects of it. First, we want to explore how the proximity of the ground affects the unsteady forces and the flow field during the perching flight; and second, we want to analyze how a wing sweep influences a perching maneuver. To explore the first aspect of this dissertation, we investigated the finite flat plate undergoing a perching maneuver in the ground effect. Our results showed that the instantaneous and time-averaged lift force increased as the plate came close to the ground, while the instantaneous peak drag coefficient stayed relatively constant with changes in the ground height. However, the negative drag force, or the parasitic thrust, at the latter stages of the perching maneuver increased with the increase of the ground proximity. We found that performing rapid pitching at the end phase of the decelerating motion, which is done by introducing the time offset between the decelerating and pitch-up motion, significantly reduced the parasitic thrust even when the perching plate was in close proximity to the ground. Our results revealed that the dipole jet induced by the counter-rotating vortices was lower for the pitching case executed at the latter stage of the decelerating motion, which affected the advection of the shed vortices, acceleration of the fluid between the wing and the ground, and varied the unsteady forces during the perching maneuver. For the highest shape change number considered in this study, at a time offset of 0.5, the wing generated a positive averaged drag force and near zero averaged lift force, which is appropriate to land smoothly on the initial perching location without gaining altitude. The second aspect of this dissertation is motivated by the observation that some birds fold their wings to create a wing sweep during such perching. This study aims to find out whether such a wing sweep helps during a perching maneuver. We use two flat plates: one with a sweep and another without any sweep, and consider a deceleration maneuver where both decelerate to a complete stop from a Reynolds number, Re = 13000. We consider two cases: one, where the wings undergo only heaving, and another, where the wings perform both heaving and pitching. The latter maneuver was designed to mimic perching. By performing experiments and simulations, we compare the temporal evolution of the instantaneous forces and the vortex dynamics of both these plates. We show that during a major part of the deceleration, the instantaneous lift forces are higher in the case of the plate with sweep compared to the plate with no sweep during both kinematics. Our results indicate that the higher lift in the swept plate case was contributed by a stable leading edge vortex (LEV) which remains attached to the plate. This increase in stability was contributed by the spanwise vorticity convection caused by a distinct spanwise flow on the swept plate, as revealed by the numerical simulation. We also show that combined pitching and heaving resulted in higher force peaks, and the forces also decayed faster in this case compared to the heave-only case. Finally, by using an analytical model for unsteady flows, we prove that the higher lift characteristics of the swept plate were entirely due to higher circulatory forces. We also developed an analytical model that accounts for the variation of unsteady forces on a flat plate undergoing a perching maneuver. We model the flat plate using unsteady lifting line theory while the effect of ground height is incorporated using image vortices. We used Wagner's theory and the unsteady Kutta condition to model pitching and gradual deceleration. To include the ground effect, we updated the added mass force by accounting for the increase in flow acceleration between the wing and the ground. The model's accuracy was tested against the experimental results on a finite wing undergoing identical kinematics. Our result demonstrates that the present analytical model captures the unsteady variation of forces during a perching maneuver.

No description available.

Modern flight control laws are designed utilizing modeled plant aerodynamics, and as such the closed-loop system is sensitive to the actual aerodynamics and flight environment. Control laws such as dynamic inversion rely on an onboard aerodynamic model of the flight controller that is not always accurate because of simplifications in the modeling process or unmodeled dynamics. Typically, the most accurate estimation of the aerodynamics is determined with an expensive wind tunnel test (WTT) supplemented with aerodynamic finite element modeling. The WTT takes a considerable amount of the research and development budget, yet it may not provide an aerodynamic model suitable for flight control. This issue can be overcome by implementing a linear robust control law augmented with an online adaptive control law. The linear robust control law can be designed by any established methods, but in this work we present a new parameter space method that guarantees a desired gain and phase margin. The new method is developed to obtain a desired performance and stability in the presence of the aerodynamic uncertainty. Unlike the conventional s-domain parameter space method that utilizes the pole-placement technique analytically, the new method designs the controller in the frequency domain numerically using the stability margin specification. The linear robust control is enhanced by an adaptive control system that is designed by the online Feed-Forward Neural Network (FFNN). The FFNN adaptive control compensates for the aerodynamic uncertainty and imperfect modeling of aircraft dynamics, and it gradually replaces the linear controller as the network gains converge to a value that minimizes the linear control law. Although the FFNN adaptively adjusts the controller gains, an additional stability augmentation system is designed by Sigma-Pi Neural Network (SPNN) for compensating for the nonlinearity of the aircraft dynamics. The SPNN predicts the control input at a specific flight condition by memorizing the previous flight empirically. The SPNN adapts both the engine speed and elevator commands in the aircraft speed/altitude control. Training the SPNN is performed using a recursive least square estimator, and the control design is demonstrated on a six-degree-of-freedom (6DOF) digital simulation.

In interplanetary trajectory applications, it is common to design arrival trajectories based on B-plane target values. This targeting scheme, B-plane targeting, allows for specific target orbits to be obtained during mission design. A primary objective of this work was to implement B-plane targeting into the Spacecraft Trajectory Optimization Suite (STOpS). This work was based on the previous versions of STOpS done by Fitzgerald and Sheehan, however STOpS was redeveloped from MATLAB to python. This updated version of STOpS implements 3-dimensional computation, departure and arrival orbital phase modeling with patched conics, B-plane targeting, and a trajectory correction maneuver. The optimization process is done with three evolutionary algorithms implemented in an island model paradigm. The algorithms and the island model were successfully verified with known optimization functions before being used in the orbital optimization cases. While the algorithms and island model are not new to this work, they were altered in this redevelopment of STOpS to closer relate to literature. This enhanced literature relation allows for easier comprehension of the both the formulation of the schemes and the code itself. With a validated optimization scheme, STOpS is able to compute near-optimal trajectories for numerous historical missions. New mission types were also easily implemented and modeled with STOpS. A trajectory correction maneuver was shown to further optimize the trajectories end conditions, when convergence was reached. The result is a versatile optimization scheme that is highly customization to the invested user, while remaining simple for novice users.

Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 214-224). Available also in a digital version from Dissertation Abstracts.

This thesis is a brief look at a new solution to a problem that has been approached in many different ways in the past - the N body problem. By focusing on planetary systems, satellite dynamics can be modeled in a fashion similar to the Circular Restricted Three Body Problem (CR3BP) with the Circular Restricted N Body Problem (CRNBP). It was found that this new formulation of the dynamics can then utilize the tools created from all the research into the CR3BP to reassess the possibility of different complex trajectories in systems where there are more than just two large gravitational bodies affecting the dynamics, namely periodic and semi-periodic orbits, halo orbits, and low energy transfers It was also found that not only system dynamics, but models of the Jacobi constant could also be formulated similarly to the CR3BP. Validating the authenticity of these new sets of equations, the CRNBP dynamics are applied to a satellite in the Earth-Moon system and compared to a simulation of the CR3BP under identical circumstances. This test verified the dynamics of the CRNBP, showing that the two systems created almost identical results with relatively small deviations over time and with essentially identical path trends. In the Jovian system, it was found the mass ratio required to validated the assumptions required to integrate the equations of motion was around .1$\%$. Once the mass ratio grew past that limit, trajectories propagated with the CRNBP showed significant deviation from trajectories propagated with a higher fidelity model of Newtonian motion. The results from the derivation of the Jacobi constant are consistent with the 3 body system, but they are fairly standalone.