SEARCH · Search NASA

Results for “Differentiability”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 937 records · Page 52

All sources NASA NTRS DOE OSTI

NASA NTRS1978

On the accuracy and convergence of implicit numerical integration of finite element generated ordinary differential equations

A study of accuracy and convergence of linear functional finite element solution to linear parabolic and hyperbolic partial differential equations is presented. A variable-implicit integration procedure is employed for the resultant system of ordinary differential equations. Accuracy and convergence is compared for the consistent and two lumped assembly procedures for the identified initial-value matrix structure. Truncation error estimation is accomplished using Richardson extrapolation.

Baker, A. J.↗

NASA NTRS1979

Photoelectron charge density and transport near differentially charged spacecraft

The effects of photoelectron space charge and current density on differentially charged spacecraft are studied. The steady-state potentials of a sunlit cylinder are calculated using a two-dimensional computer code with a fully self-consistent treatment of space charge and an effective surface conductivity treatment of photoelectron currents. It is found that under conditions of strong differential charging the results do not differ greatly from NASCAP results, which neglect photosheath space charge and currents.

Mandell, M. J.↗

NASA NTRS1980

Absolute elastic differential electron scattering cross sections for He - A proposed calibration standard from 5 to 200 eV

Absolute differential, integral, and momentum-transfer cross sections for electrons elastically scattered from helium are reported for the impact energy range of 5 to 200 eV. Angular distributions for elastically scattered electrons are measured in a crossed-beam geometry using a collimated, differentially pumped atomic-beam source which requires no effective-path-length correction. Below the first inelastic threshold the angular distributions were placed on an absolute scale by use of a phase-shift analysis. Above this threshold, the angular distributions from 10 to 140 deg were fitted using the phase-shift technique, and the resulting integral cross sections were normalized to a semiempirically derived integral elastic cross section. Depending on the impact energy, the data are estimated to be accurate to within 5 to 9%.

NASA NTRS1980

Results of a demonstration of the use of Differential Very Long Baseline Interferometry data for precise navigation of interplanetary spacecraft

A set of experiments in the use of Differential Very Long Baseline Interferometry for spacecraft navigation have been completed. Data using both Voyager spacecraft and a single quasar were acquired during the Jupiter encounter time period. The data were processed and analyzed in order to assess the navigation accuracy of Differential Very Long Baseline Interferometry. The paper focuses on the data reduction and techniques for assessing data quality and consistency.

Christensen, C. S.↗

NASA NTRS1981

Symbolic Solution of Linear Differential Equations

An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

Feinberg, R. B.↗

NASA NTRS1981

Four band differential radiometer for monitoring LNG vapors

The development by JPL of a four band differential radiometer (FBDR) which is capable of providing a fast rate of response, accurate measurements of methane, ethane, and propane concentrations on the periphery of a dispersing LNG cloud. The FBDR is a small, low power, lightweight, portable instrument system that uses differential absorption of near infrared radiation by the LNG cloud as a technique for the determination of concentration of the three gases as the LNG cloud passes the instrument position. Instrument design and data analysis approaches are described. The data obtained from the FBDR prototype instrument system deployed in an instrument array during two 40 cubic meter spill tests are discussed.

Simmonds, J. J.↗

NASA NTRS1981

A program to evaluate a control system based on feedback of aerodynamic pressure differentials, part 1

The use of pressure differentials in a flight control system was evaluated. The pressure profile around the test surface was determined using two techniques: (1) windtunnel data (actual); and (2) NASA/Langley Single Element Airfoil Computer Program (theoretical). The system designed to evaluate the concept of using pressure differentials is composed of a sensor drive and power amplifiers, actuator, position potentiometer, and a control surface. The characteristics (both desired and actual) of the system and each individual component were analyzed. The desired characteristics of the system as a whole are given. The flight control system developed, the testing procedures and data reduction methods used, and theoretical frequency response analysis are described.

Hrabak, R. R.↗

NASA NTRS1980

Differentiation of crusts and cores of the terrestrial planets - Lessons for the early earth

The extent and mechanisms of global differentiation and the early thermal and tectonic histories of the terrestrial planets are surveyed in order to provide constraints on the first billion years of earth history. Indirect and direct seismic evidence for crusts on the moon, Mars and Venus is presented, and it is pointed out that substantial portions of these crusts have been in place since the cessation of heavy bombardment of the inner solar system four billion years ago. Evidence for sizable cores on Mars and Mercury and a small core on the moon is also discussed, and the heat involved in core formation is pointed out. Examination of the volcanic and tectonic histories of planets lacking plate tectonics indicates that core formation was not closely linked to crust formation on the moon or Mars, with chemical differentiation restricted to shallow regions, and was much more extensive on Mercury. Extension of these considerations to the earth results in a model of a hot and vigorously convecting mantle with an easily deformable crust immediately following core formation, and the gradual development of a lithosphere and plates.

Solomon, S. C.↗

NASA NTRS1981

The influence of differential rotation on the equatorial component of the sun's magnetic dipole field

This paper examines the effect that solar differential rotation would have on a hypothetical large-scale equatorial dipole field. The evolving large-scale field pattern is expressed as a series of non-axisymmetric moments. As time increases, power is transferred to progressively higher order moments. In the 27d rotating coordinate system, each moment undergoes a small retrograde drift which remains nearly uniform until that mode begins to fade. The synodic rotation periods of the first few moments are comparable to the observed 28.5d period of the sun's large-scale field near sunspot maximum. Differential rotation may be the source of this 28.5d period, but the eruption of new flux is necessary to keep the pattern going.

Sheeley, N. R., Jr.↗

NASA NTRS1980

Thrust-vectored differential turns

Barrier surface construction in the joint space of the differential turning game for thrust-vectored vs. conventional aircraft is discussed. Differential-turn studies are based on modifications of existing computer programs including an energy-turn program, and one which generates hodograph data. Optimal turning flight in energy approximation is discussed for the conventional aircraft configurations. It is concluded that any advantages realized from thrust-vectoring are minor, unless hover is possible, where advantages would be major at low energies, and affect tactics at high energies as well.

Kelley, H. J.↗

NASA NTRS1981

The differential emission measure of dynamic coronal loops

The effects of time dependent phenomena, such as flare energization and decay, on the temperature and density structure of the transition region and, in particular, on the form of the differential emission measure are studied. It is found that unlike the case of the static models, the form of the differential emission measure can be used to determine the important physical mechanisms in the dynamic models.

Antiochos, S. K.↗

NASA NTRS1982

Differential spacecraft charging on the geostationary operational environmental satellites

Subsystems aboard the Geostationary Operational Environmental Satellites 4 and 5 showed instances of anomalous changes in state corresponding to false commands. Evidence linking the anomalous changes to geomagnetic activity, and presumably static discharges generated by spacecraft differential charging induced by substorm particle injection events is presented. The anomalies are shown to be correlated with individual substorms as monitored by stations of the North American Magnetometer Chain. The relative frequency of the anomalies is shown to be a function of geomagnetic activity. Finally a least squares fit to the time delay between substorm initiation and spacecraft anomaly as a function of spacecraft local time is shown to be consistent with injected electron populations with energy in the range 10 keV to 15 keV, in agreement with present understanding of the spacecraft charging mechanism. The spacecraft elements responsible for the differential charging were not satisfactorily identified. That question is currently under investigation.

Farthing, W. H.↗

NASA NTRS1982

Nonlinear zero-sum differential game analysis by singular perturbation methods

A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane.

Sinar, J.↗

NASA NTRS1982

Global differential geometry: An introduction for control engineers

The basic concepts and terminology of modern global differential geometry are discussed as an introduction to the Lie theory of differential equations and to the role of Grassmannians in control systems analysis. To reach these topics, the fundamental notions of manifolds, tangent spaces, vector fields, and Lie algebras are discussed and exemplified. An appendix reviews such concepts needed for vector calculus as open and closed sets, compactness, continuity, and derivative. Although the content is mathematical, this is not a mathematical treatise but rather a text for engineers to understand geometric and nonlinear control.

Doolin, B. F.↗

NASA NTRS1981

The application of NAVSTAR differential GPS in the civilian community

The NAVSTAR Global Positioning System (GPS), currently being developed by the DOD, is a space based navigation system that will provide the user with precise position, velocity, and time information on a 24 hour basis, in all weather conditions and at any point on the globe. The baseline GPS system will provide guaranteed high accuracy to only a limited number of users, mostly the military. The civilian community has to devise a variation of this system to allow for an assured, uninterrupted level of accuracy. Differential GPS provides such a capability. In connection with the conceived possibility of the use of GPS by an enemy, it is found to be necessary to implement a selective availability technical capability. Differential GPS provides an approach for the civilian community to have a guaranteed level of accuracy better than the 250 meters presently planned for GPS.

Beser, J.↗

NASA NTRS1982

Analysis and design of steady transonic flow over airfoils by the method of parametric differentiation

The results reported here are based on applying the method of parametric differentiation (MPD) to transform the nonlinear differential equation governing small-disturbance transonic flow to a linear equation. Implicit approximate factorization and monotone methods were used to accelerate convergence of the linear problem by an order of magnitude over successive line over-relaxation. The relative merits of using MPD are discussed in comparison to conventional small-disturbance applications. Several MPD analyses are performed on an array of airfoils. A design procedure utilizing MPD is discussed and demonstrated for two nonlifting cases.

Halt, D. W.↗

NASA NTRS1982

Cure kinetics of epoxy matrix resin by differential scanning calorimetry

A study was made on the cure kinetics of an epoxy neat-resin (Narmco 5208) using Differential Scanning Calorimetry (DSC). Two interrelated analytical methods were applied to dynamic DSC data for evaluating the kinetic parameters, such as activation energy, E, the order of reaction, n, and the total heat of polymerization (or crosslinking), delta H sub t. The first method was proposed by Ellerstein (1968), and uses a thorough differential-integral analysis of a single DSC curve to evaluate the kinetic parameters. The second method was proposed by Kissinger (1957), and uses multiple DSC curves obtained at various heating rates to evaluate E regardless of n. Kinetic analysis of Narmco 5208 epoxy resin showed that the reaction order, n, is substantially affected by the rate of heating; i.e., n is approximately 2 at slow scan rates but is reduced to 1.5 at higher scan rates. The activation energy, E, is not affected by the scan rate, and the average value of E is 25.6 + or - 1.8 kcal/mole.

Cizmecioglu, M.↗

NASA NTRS1982

Propagation of local errors in the solutions of the differential equations for orbital elements

The propagation of errors in the solutions of the differential equations for the orbital elements of perturbed two-body motion is investigated. It is shown that the error in the time-element grows linearly for differential equations for orbital elements when only perturbations are present on the right-hand side, cubically for formulations which have a two-body term on the right-hand side, and linearly for formulations based upon extended phase space Hamiltonians.

Bond, V. R.↗