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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.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

REDUCE 2: A computer program for the symbolic reduction of large block diagrams

REDUCE 2 is reported as a FORMAC program which symbolically calculates the transfer function(s) of any linear-block-diagram output variable to any or all input variables. The program requires as input a set of algebraic expressions representing the block diagram, the desired transfer function(s), and a string of variables indicating the desired order of reduction. The solution is presented in the compact form of a set of nested functions (super G's). The program can handle systems as large as 600 equations and is intended as a tool for the analysis of complex control and dynamic systems. A companion FORTRAN program, EVAL 2, which numerically evaluates the solution set to obtain amplitude ratio and phase angle as functions of frequency is also presented.

Lorenzo, C. F.↗
NASA NTRS1974

Symbolic integration of a class of algebraic functions

An algorithm is presented for the symbolic integration of a class of algebraic functions. This class consists of functions made up of rational expressions of an integration variable x and square roots of polynomials, trigonometric and hyperbolic functions of x. The algorithm is shown to consist of the following components:(1) the reduction of input integrands to conical form; (2) intermediate internal representations of integrals; (3) classification of outputs; and (4) reduction and simplification of outputs to well-known functions.

Ng, E. W.↗
NASA NTRS1975

The transformation of aerodynamic stability derivatives by symbolic mathematical computation

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

Howard, J. C.↗
NASA NTRS1976

Space telescope coordinate systems, symbols, and nomenclature definitions

The major coordinate systems as well as the transformations and transformation angles between them, for the Space Telescope are defined. The coordinate systems were primarily developed for use in pointing and control system analysis and simulation. Additional useful information (on nomenclature, symbols, quaternion operations, etc.) is also contained.

Kennel, H. F.↗
NASA NTRS1977

Symbolic calculations in a finite dynamic element analysis

A second order problem is outlined for which MACSYMA was used only for checking purpose. A fourth order problem is briefly described for which a symbolic system is necessary. At the end, some sample output is displayed to indicate the complexity of the computational problem.

Gupta, K. K.↗
NASA NTRS1977

Symbolic manipulation techniques for vibration analysis of laminated elliptic plates

A computational scheme is presented for the free vibration analysis of laminated composite elliptic plates. The scheme is based on Hamilton's principle, the Rayleigh-Ritz technique and symmetry considerations and is implemented with the aid of the MACSYMA symbolic manipulation system. The MACYSMA system, through differentiation, integration, and simplification of analytic expressions, produces highly-efficient FORTRAN code for the evaluation of the stiffness and mass coefficients. Multiple use is made of this code to obtain not only the frequencies and mode shapes of the plate, but also the derivatives of the frequencies with respect to various material and geometric parameters.

Andersen, C. M.↗
NASA NTRS1977

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

Geddes, K. O.↗
NASA NTRS1981

A Simulation System for Validating the Analytical Prediction of Performance of the Convolutional Encoded and Symbol Interleaved TDRSS S-band Return Link Service in a Pulsed RFI Environment

A hardware integrated convolutional coding/symbol interleaving and integrated symbol deinterleaving/Viterbi decoding simulation system is described. Validation on the system of the performance of the TDRSS S-band return link with BPSK modulation, operating in a pulsed RFI environment is included. The system consists of three components, the Fast Linkabit Error Rate Tester (FLERT), the Transition Probability Generator (TPG), and a modified LV7017B which includes rate 1/3 capability as well as a periodic interleaver/deinterleaver. Operating and maintenance manuals for each of these units are included.

Source record↗
NASA NTRS1984

Flap-lag damping of an elastic rotor blade with torsion and dynamic inflow in hover from symbolically generated equations

A program written in FORTRAN IV and coded into subroutines for subsequent numerical study is used to derive symbolically the governing equations of motion of the elastic rotor blade and the dynamic inflow equations. By rearranging the coefficients of the equations, the blade and dynamic inflow equations are converted into equations in a multiblade coordinated system. The final multiblade equations can accommodate any number of elastic blade modes. It is noted that with a given data set, the entire process, from the derivation of the equations to the numerical calculations, is computerized and requires only limited user interface. To demonstrate the usefulness of the approach, damping data in hover with and without dynamic inflow effects are presented for various rotor blade models, including flap-lag, flap-lag-torsion, quasi-static torsion, and rigid blade lag-flap.

Reddy, T. S. R.↗
NASA NTRS1986

Intercontinental antenna arraying by symbol stream combining at ICE Giacobini-Zinner encounter

Deep space tracking stations on different continents were arrayed during the encounter of the International Cometary Explorer (ICE) spacecraft with the comet Giacobini-Zinner during September 9 through 12, 1985. This is the first time that telemetry signals received on different continents have been combined to enhance signal to noise ratio. The arraying was done in non-real time using the method of symbol stream combining. The improvement in signal to noise ratio was typically 2 dB over the stronger of the two stations in each array.

Hurd, W. J.↗
NASA NTRS1984

The influence of dynamic inflow and torsional flexibility on rotor damping in forward flight from symbolically generated equations

The combined effects of blade torsion and dynamic inflow on the aeroelastic stability of an elastic rotor blade in forward flight are studied. The Helicopter Equations for Stability and Loads (HESL) program is extended to derive the governing equations of motion for the blade, and a Lagrangian formulation is used to obtain the equations in generalized coordinates. The program generates the steady-state and linearized perturbation equations in symbolic form and then codes them into FORTRAN subroutines. The coefficients for each equation and for each mode are identified through a numerical program; the latter can also be used to obtain the harmonic balance equations. The governing multiblade equations are derived explicitly using HESL. These equations can accommodate any number of elastic blade modes. Stability results are presented for several hingeless rotor blade structural models, and the influence of dynamic inflow in forward flight with an elastic hingeless rotor is investigated.

Reddy, T. S. R.↗
NASA NTRS1988

Spatial vision processes: From the optical image to the symbolic structures of contour information

The significance of machine and natural vision is discussed together with the need for a general approach to image acquisition and processing aimed at recognition. An exploratory scheme is proposed which encompasses the definition of spatial primitives, intrinsic image properties and sampling, 2-D edge detection at the smallest scale, the construction of spatial primitives from edges, and the isolation of contour information from textural information. Concepts drawn from or suggested by natural vision at both perceptual and physiological levels are relied upon heavily to guide the development of the overall scheme. The scheme is intended to provide a larger context in which to place the emerging technology of detector array focal-plane processors. The approach differs from many recent efforts in edge detection and image coding by emphasizing smallest scale edge detection as a foundation for multi-scale symbolic processing while diminishing somewhat the importance of image convolutions with multi-scale edge operators. Cursory treatments of information theory illustrate that the direct application of this theory to structural information in images could not be realized.

Jobson, Daniel J.↗
NASA NTRS1988

Optical production systems using neural networks and symbolic substitution

Two optical implementations of production systems are advanced. The production systems operate on a knowledge base where facts and rules are encoded as formulas in propositional calculus. The first implementation is a binary neural network. An analog neural network is used to include reasoning with uncertainties. The second implementation uses a new optical symbolic substitution correlator. This implementation is useful when a set of similar situations has to be handled in parallel on one processor.

Botha, Elizabeth↗
NASA NTRS1988

Symbolic generation of constitutive equations

The use of the symbolic manipulation program MACSYMA for the automatic generation of constitutive equations describing the thermomechanical behavior of complex materials such as metal-matrix composites is demonstrated. Problem-specific algorithms are developed; e.g., for partial differentiation by the chain rule, automatic generation of tree structures, special tensor analysis, and the simplification of expressions. The resulting subprogram package, SDICE, is shown to be fully applicable to both isotropic and anisotropic materials; its potential usefulness as a basis for FEM analyses is indicated.

Tan, H. Q.↗
NASA NTRS1989

Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation.

Arnold, S. M.↗
NASA NTRS1990

Symbolic description of periodic orbits for the quadratic Zeeman effect

The organization of the periodic orbits of a hydrogen atom in a uniform magnetic field is studied. It is shown that the dynamics is qualitatively different from that for weak fields and negative energies. The orbits can be mapped one-to-one onto a ternary symbolic tree, an organization which turns out to be applicable for all values of energy and field strength. The results indicate that the field-free hydrogen atom has a purely chaotic limit for positive energies.

Eckhardt, Bruno↗
NASA NTRS1991

Multiple-Symbol Differential Detection Of MPSK

Multiple-symbol differential detection proposed for reception of radio-frequency signals modulated by mutliple-phase-shift keying (MPSK). Offers advantage of less complexity in not requiring equipment to acquire and track carrier signal. Performance approaches that of ideal coherent detection. Applicable to coded as well as uncoded MPSK, and to other forms of modulation.

Divsalar, Dariush↗