Local-error control and its effects on the optimization of orbital integration
Local error control for optimization of numerical integration orbit calculation techniques
Velez, C. E.↗
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Computation of radiation patterns involving numerical double integration.
Numerical double integral evaluation technique for antenna radiation patterns, discussing error data
Ludwig, A. C.↗
Deconvolution of Physical Data
Numerical, digital, and analog techniques for deconvolution of physical data
Rarick, J. P.↗
Near field antenna patterns of obstructed Cassegrainian telescopes
The near field antenna pattern of an obstructed optical transmitter, such as a Cassegrainian telescope, has been computed using the Fresnel approximation to the scalar diffraction integral. A number of cases have been considered. These include uniformly illuminated, obstructed circular apertures, and apertures coherently illuminated with a divergent gaussian beam wave. Other beam profiles that may be derived by energy redistribution of the laser beam have also been considered. The techniques used for the numerical evaluation of the Fresnel integral are discussed and results for the optical systems to be used on the High Altitude Aircraft Optical Communications Experiment are presented.
Webb, W. E.↗
Phase change materials handbook
This handbook is intended to provide theory and data needed by the thermal design engineer to bridge the gap between research achievements and actual flight systems, within the limits of the current state of the art of phase change materials (PCM) technology. The relationship between PCM and more conventional thermal control techniques is described and numerous space and terrestrial applications of PCM are discussed. Material properties of the most promising PCMs are provided; the purposes and use of metallic filler materials in PCM composites are presented; and material compatibility considerations relevant to PCM design are included. The engineering considerations of PCM design are described, especially those pertaining to the thermodynamic and heat transfer phenomena peculiar to PCM design. Methods of obtaining data not currently available are presented. The special problems encountered in the space environment are described. Computational tools useful to the designer are discussed. In summary, each aspect of the PCM problem important to the design engineer is covered to the extent allowed by the scope of this effort and the state of the art.
Hale, D. V.↗
Scientific and engineering analyses of Jupiter's energetic electrons and protons
Details of magnetic field conclusions, UHF radio data sets, and the theoretical synchrotron radiation descriptions are summarized for several published and unpublished analyses. The relatively compact set of electron models inspires some confidence in their validity, particularly as they have been derived from numerous data and analysis techniques. Although the models have serious consequences for spacecraft design, the problems they imply are probably soluble with technologies anticipated for spacecraft to be designed for Jupiter encounter. By contrast, the proton models are very diverse, fluxes and energies spanning several orders of magnitude even for those models based on physical considerations; this results from the absence of applicable data. However, even in the midrange of these models, the proton energies and fluxes would be severely hazardous to several spacecraft subsystems. It is therefore desirable to apply further technical consideration to the modeling of Jupiter's energetic proton population.
Divine, N.↗
The elastic layer with a cylindrical hole subjected to a nonuniform axisymmetric radial displacement.
A problem in the linear theory of elasticity is considered wherein a layer with a circular cylindrical hole is subjected to a nonuniform axisymmetric radial displacement. The solution utilizes Navier's equations of elasticity which are solved by means of extended Hankel transforms. A special case in which the radial displacement is a linear function of the axial coordinate is presented. Numerical results are given in graphical form for the case when hole radius and layer thickness are equal. The inversion integrals were evaluated numerically using Longman's technique for computing infinite integrals of oscillatory functions.
Grissom, D. S.↗
Special perturbations employing osculating reference states
The concept of employing osculating reference position and velocity vectors in the numerical integration of the equations of motion of a satellite is examined. The choice of the reference point is shown to have a significant effect upon numerical efficiency and the class of trajectories described by the differential equations of motion. For example, when the position and velocity vectors on the osculating orbit at a fixed reference time are chosen, a universal formulation is yielded. For elliptical orbits, however, this formulation is unattractive for numerical integration purposes due to Poisson terms (mixed secular) appearing in the equations of motion. Other choices for the reference point eliminate this problem but usually at the expense of universality. A number of these formulations, including a universal one, are considered here. Comparisons of the numerical characteristics of these techniques with those of the Encke method are presented.
Born, G. H.↗
Investigation of the three-dimensional turbulent flow downstream of swept slot injection in hypersonic flow
Results of an experimental and numerical investigation of tangential swept slot injection (sweep angles of 22.5 and 45 deg) into a thick turbulent boundary layer at Mach 6 are presented. Film cooling effectiveness, skin friction, and flow structure downstream of the swept slot injection are investigated. The data are compared to that for unswept slots, and it is found that cooling effectiveness and skin-friction reductions are not significantly affected by sweeping the slot. Predictions of cooling effectiveness and skin friction obtained by a numerical finite-difference technique agree reasonably well with experimental surface variables. As in previous supersonic two-dimensional slot research, reduced mixing was found downstream of the slot lip in the present three-dimensional case.
Hefner, J. N.↗
Multi-community command and control systems in law enforcement: An introductory planning guide
A set of planning guidelines for multi-community command and control systems in law enforcement is presented. Essential characteristics and applications of these systems are outlined. Requirements analysis, system concept design, implementation planning, and performance and cost modeling are described and demonstrated with numerous examples. Program management techniques and joint powers agreements for multicommunity programs are discussed in detail. A description of a typical multi-community computer-aided dispatch system is appended.
Sohn, R. L.↗
Mathematical theory of the Goddard trajectory determination system
Basic mathematical formulations depict coordinate and time systems, perturbation models, orbital estimation techniques, observation models, and numerical integration methods.
Cappellari, J. O.↗
Numerical modeling of pollutant transport using a Lagrangian marker particle technique
A derivation and code were developed for the three-dimensional mass transport equation, using a particle-in-cell solution technique, to solve coastal zone waste discharge problems where particles are a major component of the waste. Improvements in the particle movement techniques are suggested and typical examples illustrated. Preliminary model comparisons with analytic solutions for an instantaneous point release in a uniform flow show good results in resolving the waste motion. The findings to date indicate that this computational model will provide a useful technique to study the motion of sediment, dredged spoils, and other particulate waste commonly deposited in coastal waters.
Spaulding, M.↗
Development of an inflatable radiator system
Conceptual designs of an inflatable radiator system developed for supplying short duration supplementary cooling of space vehicles are described along with parametric trade studies, materials evaluation/selection studies, thermal and structural analyses, and numerous element tests. Fabrication techniques developed in constructing the engineering models and performance data from the model thermal vacuum tests are included. Application of these data to refining the designs of the flight articles and to constructing a full scale prototype radiator is discussed.
Leach, J. W.↗
Laminar free convection from a vertical cone with uniform surface heat flux
The laminar free convection flow from a right circular cone with prescribed uniform wall flux condition is studied. The governing boundary-layer equations are analyzed by the technique of similarity transformation. Numerical solutions to the transformed equations are given for Prandtl numbers 0.72, 1, 2, 4, 6, 8, 10, and 100. Expressions for both wall temperature distribution and wall skin friction distribution at Prandtl number tending to infinity are also presented.
Lin, F. N.↗
Macroscopic aspects of interfacial reactions
The extent of interdiffusion and formation of new phases is determined by the constitution diagram of the alloy system, the interdiffusion coefficients of the phases present, and the thermal conditions (temperature and time) associated with the bonding process and/or subsequent use of the bonded structure. In many instance, the kinetics of interdiffusion and phase formation can be predicted from known parameters using numerical methods and computer techniques. Predictions are compared with experimentally determined parameters for a variety of metallurgical alloy systems.
Heckel, R. W.↗
Forebody and afterbody solutions of the Navier-Stokes equations for supersonic flow over blunt bodies in a generalized orthogonal coordinate system
A coordinate transformation, which can approximate many different two-dimensional and axisymmetric body shapes with an analytic function, is used as a basis for solving the Navier-Stokes equations for the purpose of predicting 0 deg angle of attack supersonic flow fields. The transformation defines a curvilinear, orthogonal coordinate system in which coordinate lines are perpendicular to the body and the body is defined by one coordinate line. This system is mapped in to a rectangular computational domain in which the governing flow field equations are solved numerically. Advantages of this technique are that the specification of boundary conditions are simplified and, most importantly, the entire flow field can be obtained, including flow in the wake. Good agreement has been obtained with experimental data for pressure distributions, density distributions, and heat transfer over spheres and cylinders in supersonic flow. Approximations to the Viking aeroshell and to a candidate Jupiter probe are presented and flow fields over these shapes are calculated.
Gnoffo, P. A.↗
GEOS-3 coherent C-band tracking data reduction and analysis
The availability of a coherent C-Band transponder on an orbiting vehicle has permitted the development of calibration techniques for C-Band radars. Prior coherent tracking was limited to test vehicles in powered flight or skin tracking of orbiting spacecraft. The pulse Doppler range rate data available concurrently and independently with normal range and angle data provides an extremely useful data set for assessing the internal consistency of the radars measurements, particularly when coupled with a trajectory well constrained by orbit dynamics. In order to further assess the precision of the range rate data, a technique was developed to numerically integrate the rate measurements into a pseudo-range data set showing extremely low noise and high sensitivity to systematic radar errors. Evaluation of integrated range data led to improvements in calibration of both the rate and conventional range data. In particular, proper evaluation of the very sensitive integrated ranges required the development of a processing correction for beacon delay variation with signal strength, a significant error in the conventional ranging data.
Krabill, W. B.↗
The dynamics and control of large flexible space structures, 2. Part A: Shape and orientation control using point actuators
The equations of planar motion for a flexible beam in orbit which includes the effects of gravity gradient torques and control torques from point actuators located along the beam was developed. Two classes of theorems are applied to the linearized form of these equations to establish necessary conditions for controlability for preselected actuator configurations. The feedback gains are selected: (1) based on the decoupling of the original coordinates and to obtain proper damping, and (2) by applying the linear regulator problem to the individual model coordinates separately. The linear control laws obtained using both techniques were evaluated by numerical integration of the nonlinear system equations. Numerical examples considering pitch and various number of modes with different combination of actuator numbers and locations are presented. The independent model control concept used earlier with a discretized model of the thin beam in orbit was reviewed for the case where the number of actuators is less than the number of modes. Results indicate that although the system is controllable it is not stable about the nominal (local vertical) orientation when the control is based on modal decoupling. An alternate control law not based on modal decoupling ensures stability of all the modes.
Bainum, P. M.↗