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At least 1,603 records · Page 89
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Power series solutions of ordinary differential equations in MACSYMA

A program is described which extends the differential equation solving capability of MACSYMA to power series solutions and is available via the SHARE library. The program is directed toward those classes of equations with variable coefficients (in particular, those with singularities) and uses the method of Frobenius. Probably the most important distinction between this package and others currently available or being developed is that, wherever possible, this program will attempt to provide a complete solution to the equation rather than an approximation, i.e., a finite number of terms. This solution will take the form of a sum of infinite series.

Lafferty, E. L.↗
NASA NTRS1977

Computer transformation of partial differential equations into any coordinate system

The use of tensors to provide a compact way of writing partial differential equations in a form valid in all coordinate systems is discussed. In order to find solutions to the equations with their boundary conditions they must be expressed in terms of the coordinate system under consideration. The process of arriving at these expressions from the tensor formulation was automated by a software system, TENSR. An allied system that analyzes the resulting expressions term by term and drops those that are negligible is also described.

Sullivan, R. D.↗
NASA NTRS1977

Optical zero-differential pressure switch and its evaluation in a multiple pressure measuring system

The design of a clamped-diaphragm pressure switch is described in which diaphragm motion is detected by a simple fiber-optic displacement sensor. The switch was evaluated in a pressure measurement system where it detected the zero crossing of the differential pressure between a static test pressure and a tank pressure that was periodically ramped from near zero to fullscale gage pressure. With a ramping frequency of 1 hertz and a full-scale tank pressure of 69 N/sq cm gage (100 psig), the switch delay was as long as 2 milliseconds. Pressure measurement accuracies were 0.25 to 0.75 percent of full scale. Factors affecting switch performance are also discussed.

Powell, J. A.↗
NASA NTRS1977

The application of differential VLBI to planetary approach orbit determination

The application of differential very long baseline interferometry (VLBI) to planetary approach orbit determination is described. VLBI has resulted from the development of multistation tracking techniques and measures spacecraft and nearby extragalactic radio sources. VLBI was found to be at least an order of magnitude improvement over data types currently implemented.

Miller, J. K.↗
NASA NTRS1977

Error behavior of multistep methods applied to unstable differential systems

The problem of modeling a dynamic system described by a system of ordinary differential equations which has unstable components for limited periods of time is discussed. It is shown that the global error in a multistep numerical method is the solution to a difference equation initial value problem, and the approximate solution is given for several popular multistep integration formulas. Inspection of the solution leads to the formulation of four criteria for integrators appropriate to unstable problems. A sample problem is solved numerically using three popular formulas and two different stepsizes to illustrate the appropriateness of the criteria.

Brown, R. L.↗
NASA NTRS1977

Validity of approximate methods in molecular scattering. III - Effective potential and coupled states approximations for differential and gas kinetic cross sections

Two dimensionality-reducing approximations, the j sub z-conserving coupled states (sometimes called the centrifugal decoupling) method and the effective potential method, were applied to collision calculations of He with CO and with HCl. The coupled states method was found to be sensitive to the interpretation of the centrifugal angular momentum quantum number in the body-fixed frame, but the choice leading to the original McGuire-Kouri expression for the scattering amplitude - and to the simplest formulas - proved to be quite successful in reproducing differential and gas kinetic cross sections. The computationally cheaper effective potential method was much less accurate.

Monchick, L.↗
NASA NTRS1976

Differentiation of an Apollo 12 picrite magma

The Apollo 12 olivine basalt suite shows a strong positive correlation of grain size with normative olivine content. This correlation is interpreted to mean that the suite of samples represents the basal portion of a cooling unit which differentiated by simple olivine settling. The grain size of plagioclase observed in the coarsest samples indicates the cooling unit may have been as much as 30 m thick. The amount of olivine concentration observed in the suite is quantitatively internally consistent with simple olivine settling in a magma body of this size which has the composition of the chill margin.

Walker, D.↗
NASA NTRS1977

Study of lunar librations using differential very-long-baseline observations of ALSEPs

Observations of signals from the ALSEP transmitters via differential very-long-baseline interferometry (VLBI) are being made to determine the relative selenocentric coordinates of the ALSEPs and the motion of the moon about its center of mass. By VLBI the relative positions of the ALSEPs can be determined with uncertainties less than 5 meters, and the orientation of the moon within 0.5 second of selenocentric arc.

King, R. W.↗
NASA NTRS1978

Body/bone-marrow differential-temperature sensor

Differential-temperature sensor developed to compare bone-marrow and body temperature in leukemia patients uses single stable amplifier to monitor temperature difference recorded by thermocouples. Errors are reduced by referencing temperatures to each other, not to separate calibration points.

Anselmo, V. J.↗
NASA NTRS1977

Qualitative differential games with two targets

So-called differential games of kind (qualitative games) were considered involving two or more players each of whom possesses a target toward which he wished to steer the response of a dynamical system that was under the control of all players. Sufficient conditions were derived, which assure termination on a particular player's target. In general, these conditions were constructive in that they permited construction of a winning (terminating) strategy for a player. The theory is illustrated by a pursuit-evasion problem.

Getz, W. M.↗
NASA NTRS1977

The method of averages applied to the KS differential equations

A new approach for the solution of artificial satellite trajectory problems is proposed. The basic idea is to apply an analytical solution method (the method of averages) to an appropriate formulation of the orbital mechanics equations of motion (the KS-element differential equations). The result is a set of transformed equations of motion that are more amenable to numerical solution.

Graf, O. F., Jr.↗
NASA NTRS1978

Differential scanning calorimetry of coal

Differential scanning calorimetry studies performed during the first year of this project demonstrated the occurrence of exothermic reactions associated with the production of volatile matter in or near the plastic region. The temperature and magnitude of the exothermic peak were observed to be strongly affected by the heating rate, sample mass and, to a lesser extent, by sample particle size. Thermal properties also were found to be influenced by oxidation of the coal sample due to weathering effects.

Gold, P. I.↗
NASA NTRS1978

Solution of transonic flows by an integro-differential equation method

Solutions of steady transonic flow past a two-dimensional airfoil are obtained from a singular integro-differential equation which involves a tangential derivative of the perturbation velocity potential. Subcritical flows are solved by taking central differences everywhere. For supercritical flows with shocks, central differences are taken in subsonic flow regions and backward differences in supersonic flow regions. The method is applied to a nonlifting parabolic-arc airfoil and to a lifting NACA 0012 airfoil. Results compare favorably with those of finite-difference schemes.

Ogana, W.↗
NASA NTRS1977

Experimental differential and integral electron impact cross sections for the B /1-Sigma-u +/ state of H2 in the intermediate-energy region

Utilizing a crossed electron-beam-molecular-beam scattering technique, differential electron impact cross sections (DCS) for the excitation of the nu prime = 2 vibrational band of the B (1-Sigma-u +) state of H2 have been measured and are presented for the first time. These measurements were made at electron impact energies of 15, 20, 30, 40, 50 and 60 eV. At each energy, DCS between scattering angles of 10 and 135 deg were determined. They were then extrapolated to 0 and 180 deg scattering angles to obtain the integral cross sections. These integral cross sections and the Frank-Condon factor for the nu prime = 2 band were used to calculate the total cross sections for the excitation of the B (1-Sigma-u +).

Srivastava, S. K.↗
NASA NTRS1978

Extrapolation methods for dynamic partial differential equations

Several extrapolation procedures are presented for increasing the order of accuracy in time for evolutionary partial differential equations. These formulas are based on finite difference schemes in both the spatial and temporal directions. On practical grounds the methods are restricted to schemes that are fourth order in time and either second, fourth or sixth order in space. For hyperbolic problems the second order in space methods are not useful while the fourth order methods offer no advantage over the Kreiss-Oliger method unless very fine meshes are used. Advantages are first achieved using sixth order methods in space coupled with fourth order accuracy in time. Computational results are presented confirming the analytic discussions.

Turkel, E.↗
NASA NTRS1978

Characterization of oriented cracks with differential strain analysis

Linear strain of a rock sample as a function of hydrostatic pressure can be measured with a precision of 2 millionths. Such high-precision data for three orthogonal directions allow calculation of the distribution function for the porosity due to cracks' closing completely at a given pressure. Such data for at least six independent directions yield the zero-pressure strain tensor due to cracks' closing completely at a given pressure. The principal values and axes of this tensor distribution function provide information about the orientation of cracks as a function of closure pressure. The mathematical basis for the technique is developed, and the technique is illustrated with differential strain data for two samples, the Westerly (Rhode Island) granite and the Twin Sisters (Washington) dunite. Strain-tensor calculations reveal that each of these samples has a different type of anisotropic crack distribution.

Siegfried, R.↗
NASA NTRS1977

Differential altimetry for satellite orbit determination

Differential altimetry is concerned with the employment of differenced satellite altimeter measurements at orbit ground trace intersections. The employment of this procedure makes it possible to eliminate two of the major error sources found in direct altimetry. Previous applications have not included the appropriate dynamic constraints required to account for correlations due to satellite orbit motion. A description is given of an investigation in which these correlations are included. The methodology produced is consistent with the dynamic environment. The regional or local limitations of previous approaches are overcome by extending the technique to the global scale. Attention is given to the description of the data type, the geometric topography height, altimeter errors, discretization errors, an approximate orbit determination problem, and a comparison of differenced altimeter measurements for retrograde and prograde orbits.

Hagar, H., Jr.↗