Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “high order”

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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1967

Computer program provides linear sampled- data analysis for high order systems

Computer program performs transformations in the order S-to W-to Z to allow arithmetic to be completed in the W-plane. The method is based on a direct transformation from the S-plane to the W-plane. The W-plane poles and zeros are transformed into Z-plane poles and zeros using the bilinear transformation algorithm.

Bunn, D. B.↗
NASA NTRS1972

Generation and application of the equations of condition for high order Runge-Kutta methods

This thesis develops the equations of condition necessary for determining the coefficients for Runge-Kutta methods used in the solution of ordinary differential equations. The equations of condition are developed for Runge-Kutta methods of order four through order nine. Once developed, these equations are used in a comparison of the local truncation errors for several sets of Runge-Kutta coefficients for methods of order three up through methods of order eight.

Haley, D. C.↗
NASA NTRS1972

Reflecting Solutions of High Order Elliptic Differential Equations in Two Independent Variables Across Analytic Arcs

Consideration is given specifically to sixth order elliptic partial differential equations in two independent real variables x, y such that the coefficients of the highest order terms are real constants. It is assumed that the differential operator has distinct characteristics and that it can be factored as a product of second order operators. By analytically continuing into the complex domain and using the complex characteristic coordinates of the differential equation, it is shown that its solutions, u, may be reflected across analytic arcs on which u satisfies certain analytic boundary conditions. Moreover, a method is given whereby one can determine a region into which the solution is extensible. It is seen that this region of reflection is dependent on the original domain of difinition of the solution, the arc and the coefficients of the highest order terms of the equation and not on any sufficiently small quantities; i.e., the reflection is global in nature. The method employed may be applied to similar differential equations of order 2n.

Carleton, O.↗
NASA NTRS1973

Periodicity of high-order neural functions

The results of recent studies on higher order, integrative processes in the central nervous system are reported. Attempts were made to determine whether these processes exhibit any ongoing rhythmicity which might manifest itself in alterations of attention and alertness. Experiments were also designed to determine if a periodicity approximating that of the REM could be detected in various parameters of brain electrical activity.

Kellaway, P.↗
NASA NTRS1974

Equations of condition for high order Runge-Kutta-Nystrom formulae

Derivation of the equations of condition of order eight for a general system of second-order differential equations approximated by the basic Runge-Kutta-Nystrom algorithm. For this general case, the number of equations of condition is considerably larger than for the special case where the first derivative is not present. Specifically, it is shown that, for orders two through eight, the number of equations for each order is 1, 1, 1, 2, 3, 5, and 9 for the special case and is 1, 1, 2, 5, 13, 34, and 95 for the general case.

Bettis, D. G.↗
NASA NTRS1975

Effect of damping on excitability of high-order normal modes

The effect of localized structural damping on the excitability of higher-order large space telescope spacecraft modes is investigated. A preprocessor computer program is developed to incorporate Voigt structural joint damping models in a finite-element dynamic model. A postprocessor computer program is developed to select critical modes for low-frequency attitude control problems and for higher-frequency fine-stabilization problems. The selection is accomplished by ranking the flexible modes based on coefficients for rate gyro, position gyro, and optical sensor, and on image-plane motions due to sinusoidal or random PSD force and torque inputs.

Merchant, D. H.↗
NASA NTRS1975

High-order numerical solutions using cubic splines

The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.

Rubin, S. G.↗
NASA NTRS1975

High order software - A methodology for defining software

Higher order software (HOS) is a formal methodology for reliable systems specification and development. HOS is concerned only with computable functions and their relationships for any given system. Questions of methodology are considered, taking into account aspects of formulation meta-language principles, and HOS analyzers. Details of system design are discussed, giving attention to aspects of immediate self-control and indirect self-control. A description is given of the approaches used for software management.

Hamilton, M.↗
NASA NTRS1975

High-order magnetic multipoles as a source of gross asymmetry in the distant Jovian magnetosphere

The longitudinal asymmetry of the surface magnetic-field strength at Jupiter causes a longitudinal asymmetry in the equatorial plasma mass density within the Jovian magnetosphere. The rotation of these density variations with the planet causes a diurnal variation of the radial distance on the night side at which the centrifugal stress of the magnetospheric plasma exceeds the local magnetic-field tension. This is approximately the distance at which the magnetic field opens to interplanetary space; we estimate that the opening distance can vary by as much as 14% as a result of the observed surface field asymmetry. Such a diurnal variation of the boundary of the particle trapping region can account for the observed ten-hour modulation of relativistic electrons emitted from Jupiter into interplanetary space.

Dessler, A. J.↗