Thesis (M.S.)--University of Wisconsin--Madison, 1964. / eContent provider-neutral record in process. Description based on print version record. Bibliography: l. 49-55.

Thesis (Ph. D.)--University of Wisconsin, 1965. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (M.S.)--University of Missouri--Rolla, 2007. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed October 24, 2007) Includes bibliographical references (p. 95-98).

Thesis (MScEng)--University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.

The C and Ku bands that have been the backbone of satellite telephony and data networks in the past are limited in the amount of bandwidth they provide. Consequently, some broadband Internet services have started to move into the Ka band in order to utilise the bandwidth at these higher frequencies. The use of higher frequencies led to fade mitigation design considerations that had not previously been necessary, as fixed power margins had been sufficient to guarantee high availability. This thesis reviews the majority of fade mitigation techniques that are available and simulates a scenario with several combined in a hybrid scheme. The simulations were made possible by several innovative components, including a near-optimum short-term fade predictor, a procedure capable of simulating the effect of site diversity with a single time series of attenuation and a dual-channel protocol structure that is able to increase availability of control information at V band. The near-optimum short-term fade predictor is compared with several other short-term fade predictors and is shown to perform better in terms of the root-mean-square error and by the cumulative distribution of over-predictions. Also noteworthy is the fact that predictors based on fade slope perform very poorly when compared with signal processing and statistical methods of prediction. The procedure capable of producing the effects of site diversity on a single time series of attenuation is described. The results of this procedure are compared with the ITU-R model for site diversity improvement and an acceptable fit is shown. A dual-channel protocol structure capable of increasing control information availability at V band is presented and the availability of this scheme is compared to the availability of current fixed-margin C and Ku band satellite links. While the availability at V band improves via this technique, it does not improve enough to compare favourably with that found in the lower frequency bands. A software turbo decoder capable of decoding the DVB-RCS turbo code is also described in this work since this was not available through other means. The fade dynamics at V band are reviewed and compared with the ITU-R models. The fade slope model gives a good visual fit but the fade duration model is very inaccurate. Finally, the simulation results show that high availability satellite communication is possible at V band, critically, if both site diversity and frequency diversity are available to mitigate the hub and VSAT fading respectively. Signal processing and power control are also found to be complementary techniques.

A computer-controlled tracking system has been designed and constructed for the two metre antenna of the 22 GHz radio telescope at Rhodes University. The control system has been tested and its step response has been analysed with a view to response time optimization. Computer programs for tracking the sun and the moon have been written. Initial results of tracking the sun have revealed linearity and temperature stability problems. These problems have been investigated and suggestions have been made as to how they might be removed

The influence of inertia, eccentricity and atmospheric forces on the attitude dynamics of gravity oriented, non-spinning, axi-symmetric satellites, executing general librational motion is investigated using analytical, numerical and analog techniques. The problem is studied in the increasing order of complexity. For the case of a circular orbit, the autonomous, conservative system represented by constant Hamiltonian yields zero-velocity curves and motion envelopes which identify regions of instability from conditional and guaranteed stable motion. The non-linear, coupled equations of motion are solved using approximate analytical techniques: Butenin’s variation of parameter method and invariant integral approach. A comparison with the numerical response, establishes their suitability in studies involving motion in the small. The invariant integral method maintains reasonable accuracy even for larger, predominantly planar, disturbances. However, for a general motion in the large, the analytical solutions provide only qualitative information and one is forced to resort to numerical, analogic or hybrid procedures. The analysis suggests strong dependence of system response on the in-plane disturbances and satellite inertia. The librational and orbital frequencies are of the same order of magnitude. It also shows that the stable solution, when represented in a three dimensional phase space may lead to 'regular', 'ergodic' or 'island' type regions. The limiting integral manifolds, given here for a few representative values of Hamiltonian, provide all possible combinations of initial conditions, which a satellite can withstand without tumbling. The results, for a range of satellite inertia, are condensed in the form of design plots, indicating allowable disturbances for stable motion. In general, the slender satellites exhibit better stability characteristics. The presence of aerodynamic torque destroys the symmetry properties of the integral manifolds. The stability of the equilibrium configuration, which now deviates from the local vertical, is established through Routh's as well as Liapunov's criteria. As the system is still autonomous and conservative, the Hamiltonian remains constant leading to the bounds of libration. Numerical analysis of the system response indicates increased sensitivity to planar disturbances. The distortion and contraction of the regular, ergodic and island type stability regions show the adverse effects of aerodynamic torque. The design plots suggest that the shorter satellites, normally not preferred from gravity-gradient considerations, could exhibit better stability characteristics in the presence of large aerodynamic torque. An alternate, economical approach to the dynamical analysis of the satellites is attempted using an analog computer. A comparison with the digital data establishes the suitability of the method for design purposes and real time simulation. As the regular surface represents the only usable stability region from design considerations, a detailed study to establish the bound between regular and ergodic type stability was undertaken. The periodic solutions, obtained numerically using variable secant iteration show their spinal character with the body of stability region built around them. Of particular significance is the fundamental periodic solution (two planar oscillations in one out-of- plane cycle) associated with the regular region, suitable for practical operation of a satellite. The remaining periodic solutions represent degeneration of the island-like areas surrounding the mainland. The results lead to a set of fundamental periodic solutions over a wide range of system parameters. Floquet's variational analysis is used to establish the critical disturbance [formula omitted], beyond which no stable motion can be expected. The periodic solutions together with the regular stability region are presented here as functions of Hamiltonian, satellite inertia and aerodynamic torque. The case study of GEOS-A satellite is also included. In elliptic orbit, the Butenin's analysis of coupled forced systems is found to give an approximate solution of good accuracy. However for this non-autonomous situation, where Hamiltonian is no longer a constant of the motion, the concept of integral manifold breaks down. Fortunately, the design plots can still be generated by direct utilization of the response characteristics. In general the stability region diminishes with increasing eccentricity and disappears completely for e > 0.35. The presence of atmosphere adds to the complex behaviour of this non-autonomous system, where even the equilibrium configuration now becomes periodic in character. The stability regions are further reduced with instabilities normally initiating in the planar degree of freedom. Finally, a possibility of using the atmospheric forces in attitude control is explored. The use of a set of horizontal flaps in conjunction with a semi-passive, velocity-sensitive controller appears to be promising. With a suitable choice of system parameters even a large disturbance can be damped in approximately two orbits. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The influence of the major environmental forces on the attitude response of gravity gradient satellites is investigated using analytical and numerical techniques. The study establishes not only the effect of these forces on system performance but also their relative importance. The problem is investigated in the order of increasing difficulty which corresponds to a systematic reduction in altitude. In general, the non-linear, non-autonomous nature of the system renders the determination of a closed form solution virtually impossible. Hence, numerical techniques are employed, in conjunction with invariant surfaces or integral manifolds, to analyse the system. For a given set of parameters, the largest such surface defines the bound of stable motion; on the other hand, the smallest surface that can be found (i.e., a line or set of lines) represents the dominant periodic solution with which these manifolds are associated. The analysis establishes the importance of periodic solutions as they provide the 'frame' about which stability charts are built. Furthermore, a variational stability analysis of these solutions, using Floquet theory, accurately determines the termination of the spikes and establishes the critical eccentricity for stable motion. Phase I investigates the attitude dynamics of satellites at high altitudes where gravity gradient and direct solar radiation constitute the predominant torques. The approximate closed form solution, obtained using the WKBJ and Harmonic Balance methods, was found to predict the librational response of a satellite with considerable accuracy. As the satellites requiring station keeping permit only small amplitude motion, the analytical results are of sufficient accuracy to be useful during preliminary design stages. The response and stability bounds of the system, obtained numerically, are shown through the use of 'system plots' and 'stability charts'. The results indicate a considerable effect due to solar radiation on the attitude dynamics of a satellite. The use of solar radiation in controlling the satellite attitude is explored. The optimized results show this system to be quite effective, being capable of providing a pointing accuracy of 0-5° depending on orbit eccentricity. The extension of the analysis to the intermediate altitude ranges, where direct earth radiation, its albedo and shadow become significant, is undertaken in phase II. A comprehensive investigation was made possible by the determination of closed form expressions for earth radiation forces. This was accomplished through the concept of cutting plane distance ratios. The analysis shows only local variations due to earth radiations without substantially affecting the maximum librational amplitude or mainland stability area. Hence, for all practical purposes, direct earth radiation, its albedo and shadow can be neglected in such studies. Phase III investigates the dynamics of close earth satellites in the presence of aerodynamic and radiation forces, thus covering the remaining altitude range. The results show that a precise dynamic analysis requires the consideration of both aerodynamic and direct solar radiation forces. The investigation helps in establishing an altitude range in which a pure gravity gradient analysis is likely to be most applicable. The application of this analysis to the representative gravity gradient satellite, GEOS-A, over the entire altitude range, exemplifies the findings of the parametric study. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The dynamics of slowly spinning axisymmetric satellites under the influence of gravity gradient torque is investigated using analytical and numerical techniques. Particular emphasis is on motion near the equilibrium position in which the spin axis is normal to the orbital plane. The problem is studied in increasing orders of difficulty. Phase I deals with the response and stability of a simplified model free to librate in roll while the more general problem is treated in Phase II. Phase I serves as a proving ground for techniques to be used in subsequent analysis. A closed form solution is obtained in terms of elliptic functions for the autonomous case. In general, for non-circular orbits, motion in the large is studied using the concept of the invariant solution surface. These surfaces, obtained numerically, reveal the nature of motion in the large in terms of the dominant periodic solutions and allow one to determine the limits of oscillatory motion in terms of the state parameters. Floquet theory is employed in conjunction with numerical solutions of the linearized equations of motion to study stability in the small. This technique is extended to assess the variational stability of the dominant periodic motions in the large. Phase II investigates a more general model with three degrees of freedom in attitude motion. The presence of an ignorable coordinate gives a fourth order, non-autonomous system for an elliptic trajectory. Motion in the small is studied extensively, again using Floquet theory, and stability charts suitable for design purposes are presented. The invariant surface concept is successfully extended to the study of the autonomous case in the large. Methods are developed for determining the maximum response to a given disturbance resulting in a set of charts which are useful in assessing the effects of non-linearities and the validity of the analysis in the small. Procedures are explained for determining periodic solutions of the problem, as well as their stability, for arbitrary eccentricity. The analysis suggests the possibility of attitude instability during spin-up operations. It is shown that stable motion can be established by providing either a positive or negative spin to the satellite with the former preferrable. Given sufficient spin any configuration, even those with an adverse gravity gradient effect, can be stabilized. Eccentricity affects the attitude motion of a satellite adversely as regions of unstable motion increase in size and number with it. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

A general formulation is presented for the librational dynamics of satellites having an arbitrary number, type, and orientation of flexible appendages, each capable of deploying independently. In particular, the case of beam-type appendages deploying from a satellite in an arbitrary orbit is considered. The governing nonlinear, nonautonomous, coupled system equations are not amenable to any closed form solution, hence are integrated numerically using a digital computer. Effect of important system parameters is assessed through illustrative configurations representing a large class of gravity gradient and spinning spacecraft. Rather than accumulation of a large amount of data, the emphasis is on evolution of a generalized and organized methodology for coping with such complex dynamical systems. The analysis examines the degree of interaction between flexibility, deployment, and attitude motion through systematic variation of system parameters. A study of appendage vibration characteristics suggest that an orbiting beam cannot be treated simply as a rotating beam because of the presence of the gravitational field. Rate of rotation plays a dominant role in stiffening the beam as evidenced by the noticeable straightening of the eigen-functions for even relatively low spin rates (2 rpm). Results also show that the deployment-related Coriolis force can play a major role in causing large in-plane deformations. This implies that, in some cases, deployment should be carried out in stages so as to limitthe time available to build up large amplitude oscillations. Investigation of librational response shows that the coupled character of the motion can significantly affect system dynamics, hence caution should be exercised in utilizing results based on simplified planar analyses. Depending on orbital parameters and physical properties of booms, there are critical values of appendage length and deployment rate for which the satellite can tumble over. On the other hand, in general, appendage offset and shifting center of mass were found to have insignificant effect on response for the cases considered. This may permit considerable simplification of the complex hybrid equations with associated saving in computational time and effort. Also, the small amplitude oscillations evident both with the gravity gradient and spin-stabilized configurations tends to substantiate the adoption of a linear vibration analysis. The simulation of such diverse classes of satellites with relative ease demonstrates the versatility of the formulation. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate