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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

On the stability of numerical integration routines for ordinary differential equations.

Numerical integration methods for the solution of initial value problems for ordinary vector differential equations may be modelled as discrete time feedback systems. The stability criteria discovered in modern control theory are applied to these systems and criteria involving the routine, the step size and the differential equation are derived. Linear multistep, Runge-Kutta, and predictor-corrector methods are all investigated.

Glover, K.↗
NASA NTRS1972

Differential games.

General discussion of the theory of differential games with two players and zero sum. Games starting at a fixed initial state and ending at a fixed final time are analyzed. Strategies for the games are defined. The existence of saddle values and saddle points is considered. A stochastic version of a differential game is used to examine the synthesis problem.

Varaiya, P. P.↗
NASA NTRS1973

Low-energy elastic differential scattering of He/++/ by He.

Experimental results are developed for the relative elastic differential scattering of He(++) by He for collision energies in the range 4 equal to or less than E equal to or less than 75 eV. In the analysis of the data, semiclassical considerations are utilized, assuming that the dynamics of the scattering is governed solely by the B and E states of He2(++). It is shown that existing ab initio calculations for the intermolecular potentials predict differential cross sections which are not in particularly good agreement with the experimental data.

Lam, S. K.↗
NASA NTRS1973

PLZT block data composers operated in differential phase mode

The use of a PLTZ block data composer as a matrix type phase modulator to record and process digital data by the differential phase mode in a holographic recording/processing system was investigated. The system has readout contrast ratios of between 10 and 15 to 1. The differential phase mode has the advantage that strain bias is not required and thickness and strain variations in the PLZT are cancelled out.

Drake, M. D.↗
NASA NTRS1974

Differential phase shift keyed signal resolver

A differential phase shift keyed signal resolver resolves the differential phase shift in the incoming signal to determine the data content thereof overcoming phase uncertainty without requiring a transmitted reference signal.

Hopkins, P. M.↗
NASA NTRS1971

Numerical solution of stiff systems of ordinary differential equations with applications to electronic circuits

Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.

Rosenbaum, J. S.↗
NASA NTRS1974

Spherical means of solutions of partial differential equations in a conical region

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear ti surfaces. The spherical mean is the average of u over a constant ti surface. The conditions on the linear differential operator, L, and on the orthogonal coordinates (ti, eta, zeta) are established so that the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be determined directly as a problem with only space variable. Conditions are then established so that the spherical mean of the solution in one concial region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

Ting, L.↗
NASA NTRS1974

Post-flight differential correction analysis using Vinti's spheroidal method for the small astronomy satellite orbit

The results of an intensive analysis of a differential orbit improvement method utilizing observational data for a 550-kilometer altitude, near-circular, near-equatorial satellite orbit are presented. Observations of the Small Astronomy Satellite (SAS-1) are in the form of direction cosines as measured at two ground interferometer tracking stations near the Equator during the first 22 orbital revolutions (approximately 37 hours) after launch of the spacecraft. Numerical results, in both tabular and graphical form, are displayed for numerous iterated fittings of various observational arcs by differential correction of the orbital elements. Parameters varied in these comparative cases include the time duration of the observational data block, the number of pairs of direction cosine data and the number of tracking station passes included in the solution, the distribution of such passes between the two available tracking stations, and the acceptance criterion for the observational residuals in the least squares fitting procedure. It was found that three observational pairs of direction cosine data, the minimum number possible for a uniquely determined solution in theory, are sufficient to promote covergence to an accurate solution, if properly selected.

Walden, H.↗
NASA NTRS1973

Differential equation of exospheric lateral transport and its application to terrestrial hydrogen

The differential equation description of exospheric lateral transport of Hodges and Johnson is reformulated to extend its utility to light gases. Accuracy of the revised equation is established by applying it to terrestrial hydrogen. The resulting global distributions for several static exobase models are shown to be essentially the same as those that have been computed by Quessette using an integral equation approach. The present theory is subsequently used to elucidate the effects of nonzero lateral flow, exobase rotation, and diurnal tidal winds on the hydrogen distribution. Finally it is shown that the differential equation of exospheric transport is analogous to a diffusion equation. Hence it is practical to consider exospheric transport as a continuation of thermospheric diffusion, a concept that alleviates the need for an artificial exobase dividing thermosphere and exosphere.

Hodges, R. R., Jr.↗
NASA NTRS1973

The lunar crust - A product of heterogeneous accretion or differentiation of a homogeneous moon

The outer portion of the moon (including the aluminum-rich crust and the source regions of mare basalts) was either accreted heterogeneously or was the product of widespread differentiation of an originally homogeneous source. Existing evidence for and against each of these two models is reviewed. It is concluded that the accretionary model presents more problems than it solves, and the model involving differentiation of an originally homogeneous moon is considered to be more plausible. A hypothesis for the formation of mare basalts is advanced.

Brett, R.↗
NASA NTRS1974

Rigid and differential rotation of the solar corona

The rotation of the solar corona has been studied using recurrence properties of the green coronal line (5303 A) for the interval from 1947 to 1970. Short-lived coronal activity is found to show the same differential rotation as short-lived photospheric magnetic field features. Long-lived recurrences show rigid rotation in the latitude interval of plus or minus 57.5 deg. It is proposed that at least part of the variability of rotational properties of the solar atmosphere may be understood as a consequence of coexistence of differential and rigid solar rotation.

Antonucci, E.↗
NASA NTRS1973

Analysis of laser differential absorption remote sensing using diffuse reflection from the earth

A computer model analysis of an infrared laser differential absorption remote sensing technique (DARS) is presented. An infrared laser source operating at two or more wavelengths and a heterodyne detection system are considered to be mounted on either an aircraft or satellite platform to monitor the differential absorption between the laser source and the earth surface. The capability of this technique for measuring gas concentrations in the lower 5 kilometers of the atmosphere is emphasized. Numerical results are presented simulating measurements of vertical burdens of CO, NO, CH4, CO2, and O3. These results indicate that measurements of expected concentrations of these gases can be made with greater than 80% accuracy using realistic laser powers and system parameters.

Seals, R. K., Jr.↗
NASA NTRS1974

Changing stepsize in the integration of differential equations using modified divided differences

Multistep methods for solving differential equations based on numerical integration formulas or numerical differentiation formulas (for stiff equations) require special provision for changing the stepsize. New algorithms are given which make the use of modified divided differences an attractive way to carry out the change in stepsize for such methods. Error estimation and some of the important factors in stepsize selection and the selection of integration order are also considered.

Krogh, F. T.↗
NASA NTRS1974

Multi-off-grid methods in multi-step integration of ordinary differential equations

Description of methods of solving first- and second-order systems of differential equations in which all derivatives are evaluated at off-grid locations in order to circumvent the Dahlquist stability limitation on the order of on-grid methods. The proposed multi-off-grid methods require off-grid state predictors for the evaluation of the n derivatives at each step. Progressing forward in time, the off-grid states are predicted using a linear combination of back on-grid state values and off-grid derivative evaluations. A comparison is made between the proposed multi-off-grid methods and the corresponding Adams and Cowell on-grid integration techniques in integrating systems of ordinary differential equations, showing a significant reduction in the error at larger step sizes in the case of the multi-off-grid integrator.

Beaudet, P. R.↗
NASA NTRS1974

Differential rotation of solar filaments

The latitudinal component of solar differential rotation and the possibility of a radial component are discussed and compared to the observed rotational velocities of solar filaments. The author's values of rotational rate versus heliographic latitude for 100 points in the solar atmosphere derived from 17 quiescent filaments are shown to be comparable to the rates found by d'Azambuja and d'Azambuja (1948). The filament rate is significantly greater than the spot rate (Newton and Nunn, 1951); the difference cannot be accounted for by the poleward migration of filaments and seems to reflect a true radial gradient of rotational velocity in the sun. It is shown that filaments in closer proximity to active regions usually exhibit no differential rotation, while those far from active regions generally show it clearly. Comparison with Mt. Wilson photospheric Doppler measurements shows that filaments rotate faster than the general photosphere and that the spot rate exceeds that for the general photosphere.

Glackin, D. L.↗
NASA NTRS1975

NASTRAN solutions of problems described by simultaneous parabolic differential equations

NASTRAN solution techniques are shown for a numerical analysis of a class of coupled vector flow processes described by simultaneous parabolic differential equations. To define one physical problem type where equations of this form arise, the differential equations describing the coupled transfers of heat and mass in mechanical equilibrium with negligible mass average velocity are presented and discussed. Also shown are the equations describing seepage when both electrokinetic and hydrodynamic forces occur. Based on a variational statement of the general problem type, the concepts of scalar transfer elements and parallel element systems are introduced. It is shown that adoptation of these concepts allows the direct use of NASTRAN's existing Laplace type elements for uncoupled flow (the heat transfer elements) for treating multicomponent coupled transfer. Sample problems are included which demonstrate the application of these techniques for both steady-state and transient problems.

Mason, J. B.↗
NASA NTRS1975

Precision Selenodesy via Differential Very-Long-Baseline Interferometry

The technique of differential very-long baseline interferometry was used to measure the relative positions of the ALSEP transmitters at the Apollo 12, 14, 15, 16, and 17 lunar landing sites with uncertainties less than 0.005 of geocentric arc. These measurements yielded improved determinations of the selenodetic coordinates of the Apollo landing sites, and of the physical libration of the moon. By means of a new device, the differential Doppler receiver (DDR), instrumental errors were reduced to less than the equivalent of 0.001. DDRs were installed in six stations of the NASA spaceflight tracking and data network and used in an extensive program of observations beginning in March 1973.

King, R. W., Jr.↗