Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Differential”

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.

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

At least 1,639 records · Page 91
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

On approximating hereditary dynamics by systems of ordinary differential equations

The paper deals with methods of obtaining approximate solutions to linear retarded functional differential equations (hereditary systems). The basic notion is to project the infinite dimensional space of initial functions for the hereditary system onto a finite dimensional subspace. Within this framework, two particular schemes are discussed. The first uses well-known piecewise constant approximations, while the second is a new method based on piecewise linear approximating functions. Numerical results are given.

Cliff, E. M.↗
NASA NTRS1979

A note on a corrector formula for the numerical solution of ordinary differential equations

A new corrector formula for predictor-corrector methods for numerical solutions of ordinary differential equations is presented. Two considerations for choosing corrector formulas are given: (1) the coefficient in the error term and (2) its stability properties. The graph of the roots of an equation plotted against its stability region, of different values, is presented along with the tables that correspond to various corrector equations, including Hamming's and Milne and Reynolds'.

Chien, Y.-C.↗
NASA NTRS1979

Origin of differentiated meteorites

The larger asteroids with low inclination in the inner portion of the asteroid belt are evaluated as sources of differentiated meteorites (irons, stony irons and achondrites). It is found that the calculated earth impact rate is in agreement with the observed flux of these bodies. The frequent occurrence of elapsed times before impact of 0-1000 m.y. is in agreement with the observed typical exposure ages of iron meteorites, and the observed occurrence of some very young (less than 100 m.y.) exposure ages. The absence of many greater than 1000 m.y. iron meteorite exposure ages and greater than 50 m.y. achondrite exposure ages must be attributed to collisional destruction as the calculations predict a significant number of these older ages. Chemical and isotopic data on these bodies suggest a relationship to the earth and moon, and it may be that they represent residual material from earth's accretional zone.

Wetherill, G. W.↗
NASA NTRS1979

Differential capacitance sensor as position detector for a magnetic suspension densimeter

In the present work, which consists of adapting a magnetic suspension densimeter for use at pressures up to 350 bars, a differential capacitance sensor is developed for use in the servosystem of a magnetic suspension densimeter for detecting the position of a magnetic buoy. This type of sensor has not been used previously in magnetic suspension densimeters. Its design, performance, and advantages are outlined. A cutaway drawing and a schematic diagram of the capacitance sensor and magnetic buoy are presented and described. The concentric-disk design of the sensor capacitor plates and the high degree of symmetry which results from the printed circuit fabrication approach minimize the sensor sensitivity to lateral displacement of the buoy and to the dielectric constant of the surrounding medium. A high-power microscope is necessary to monitor the position of the buoy relative to the support coil.

Frederick, N. V.↗
NASA NTRS1979

System theory as applied differential geometry

The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.

Hermann, R.↗
NASA NTRS1979

Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Jezewski, D. J.↗
NASA NTRS1980

Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary, differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scalar or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Vezewski, D. J.↗
NASA NTRS1979

Numerical methods for large-scale, time-dependent partial differential equations

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.

Turkel, E.↗
NASA NTRS1980

Application of functional analysis to perturbation theory of differential equations

The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

Bogdan, V. M.↗
NASA NTRS1980

Differential correction capability of the GTDS using TDRSS data

A differential correction (DC) capability was implemented in the Goddard Trajectory Determination System (GTDS) to process satellite tracking data acquired via the Tracking and Data Relay Satellite System (TRDRSS). Configuration of the TDRSS is reviewed, observation modeling is presented, and major features of the capability are discussed. The following types of TDRSS data can be processed by GTDS: two way relay range and Doppler measurements, hybrid relay range and Doppler measurements, one way relay Doppler measurements, and differenced one way relay Doppler measurements. These data may be combined with conventional ground based direct tracking data. By using Bayesian weighted least squares techniques, the software allows the simultaneous determination of the trajectories of up to four different satellites - one user satellite and three relay satellites. In addition to satellite trajectories, the following parameters can be optionally solved: for drag coefficient, reflectivity of a satellite for solar radiation pressure, transponder delay, station position, and biases.

Liu, S. Y.↗
NASA NTRS1980

Differential radio astronomy of galactic objects

A differential astrometry technique is discussed. An improved proper motion and a parallax limit for pulsar 1929 + 10 is presented as well as a limit on the space velocity of the enigmatic object in SgrA.

Backer, D. C.↗
NASA NTRS1979

Sm-Nd constraints on early lunar differentiation and the evolution of KREEP

The internal Sm-Nd systematics of lunar KREEP basalt 15386 and its implications for the evolutionary history of KREEP on the moon are reported. The age of the 15386 rocklet indicated by the measured Sm-Nd mineral isochron is consistent with the reported Rb-Sr and (Ar-39)-(Ar-40) ages of other KREEP-rich samples, which is interpreted as the time 15386 crystallized from a liquid on or near the lunar surface. This suggests that the eruption of these incompatible element-rich liquids was related to deep impact events during the final bombardment phase of the surface of the moon. It is concluded that the extremely narrow spread of Sm-Nd model ages for these samples around 4.36 AE, and the compatibility of this age with that indicated by the U-Pb and Rb-Sr systems, indicate that the source of later KREEP volcanism was produced in the closing stages of an early global scale lunar differentiation episode.

Carlson, R. W.↗
NASA NTRS1979

Water vapor differential absorption lidar development and evaluation

A ground-based differential absorption lidar (DIAL) system is described which has been developed for vertical range-resolved measurements of water vapor. The laser transmitter consists of a ruby-pumped dye laser, which is operated on a water vapor absorption line at 724.372 nm. Part of the ruby laser output is transmitted simultaneously with the dye laser output to determine atmospheric scattering and attenuation characteristics. The dye and ruby laser backscattered light is collected by a 0.5-m diam telescope, optically separated in the receiver package, and independently detected using photomultiplier tubes. Measurements of vertical water vapor concentration profiles using the DIAL system at night are discussed, and comparisons are made between the water vapor DIAL measurements and data obtained from locally launched rawinsondes. Agreement between these measurements was found to be within the uncertainty of the rawinsonde data to an altitude of 3 km. Theoretical simulations of this measurement were found to give reasonably accurate predictions of the random error of the DIAL measurements. Confidence in these calculations will permit the design of aircraft and Shuttle DIAL systems and experiments using simulation results as the basis for defining lidar system performance requirements

Browell, E. V.↗
NASA NTRS1979

Automatic mesh-point clustering near a boundary in grid generation with elliptic partial differential equations

Elliptic partial differential equations are used to generate a smooth grid that permits a one-to-one mapping in such a way that mesh lines of the same family do not cross. Problems that arise due to lack of clustering at crucial points or intersections of mesh lines at highly acute angles, are examined and various forcing or source terms are used (to correct the problems) that are either compatible with the maximum principle or are so locally controlled that mesh lines do not intersect. Attention is given to various schematics of unclustered grids and grid detail about (highly cambered) airfoils.

Steger, J. L.↗
NASA NTRS1980

A neutral functional differential equation of Lurie type

The problem of Lurie is posed for systems described by a functional differential equation of neutral type. Sufficient conditions are obtained for absolute stability for the controlled system if it is assumed that the uncontrolled plant equation is uniformly asymptotically stable. Both the direct and indirect control cases are treated.

Chukwu, E. N.↗
NASA NTRS1979

The asteroids - Accretion, differentiation, fragmentation, and irradiation

Various types of meteorites have experienced processes of condensation, accretion, metamorphism, differentiation, brecciation, irradiation and fragmentation. A typical view of meteorite formation has been that the processes following accretion take place in a few asteroidal-sized (approximately 100 km) objects. Discovery of decay products of now extinct Al-26 and Pd-107 in meteorites, discovery of isotopic heterogeneity among meteorite types, re-analysis of meteorite cooling rates, and continuing study of meteoritic compositions have led some meteoriticists to conclude that meteorites obtained their chemical, isotopic, and some textural characteristics in objects initially less than 10 km in diameter. Such a scenario, which is described in this paper, raises the possibility that some of these small planetesimals may have been 'condensation nuclei' for the formation of comets as well as the precursors of asteroids.

Wilkening, L. L.↗
NASA NTRS1980

Trace elements as quantitative probes of differentiation processes in planetary interiors

The characteristic trace element signature that each mineral in the source region imparts on the magma constitutes the conceptual basis for trace element modeling. It is shown that abundances of trace elements in extrusive igneous rocks may be used as petrological and geochemical probes of the source regions of the rocks if differentiation processes, partition coefficients, phase equilibria, and initial concentrations in the source region are known. Although compatible and incompatible trace elements are useful in modeling, the present review focuses primarily on examples involving the rare-earth elements.

Drake, M. J.↗
NASA NTRS1980

Gigahertz analog modulation and differential delay of GaAlAs lasers - Temperature and current behavior

Gigahertz analog modulation characteristics of broad-area commercially available GaAlAs lasers have been investigated as a function of temperature and current in the vicinity of the upper frequency limit, where the resonance phenomena occur. The optimum temperature for small-signal amplitude modulation was found to be around -15 C for our particular broad-stripe geometry double-heterostructure laser. The Q was found to increase by a factor of 2 and the bandwidth by about 2%; the external quantum efficiency was maximized in this range. The optimum dc current bias was about 2% above the threshold current. Differential delays have also been measured down to a few picosecond accuracy by a unique phase-angle measurement method using a vector voltmeter. Some of the temperature effects observed may be related to mode changes and multimode and superradiance behavior.

Eng, S. T.↗