SEARCH · Search NASA
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.
Some recent developments in coherent optical processing are described in this paper. Specifically, the use of one or more elementary gratings to perform useful processing operations and computer-generated spatial filters to obtain generalized transforms are discussed. Applications incorporating nonlinear optical elements and optical feedback into the processing system are also presented.
Mathematical model for human operator
Mathematical models and orbital mechanics for space shuttle guidance, control, and navigation during deorbit and atmospheric operations
Mathematical models and an associated computer program for heat pipe startup from the frozen state have been developed. Finite element formulations of the governing equations are written for each heat pipe region for each operating condition during startup from the frozen state. The various models were checked against analytical and experimental data available in the literature for three specific types of operation. Computations using the methods developed were made for a space shuttle reentry mission where a heat pipe cooled leading edge was used on the wing.
Mathematical models and associated solution procedures which can be used to design heat pipe cooled structures for use on hypersonic vehicles are being developed. The models should also have the capability to predict off-design performance for a variety of operating conditions. It is expected that the resulting models can be used to predict startup behavior of liquid metal heat pipes to be used in reentry vehicles, hypersonic aircraft, and space nuclear reactors. Work to date related to numerical solutions of governing differential equations for the outer shell and the combination capillary structure and working fluid is summarized. Finite element numerical equations using both implicit, explicit, and combination methods were examined.
Mathematical formulation of guidance equations and solutions for orbital space missions
The Generate, Prune & Prove (GPP) methodology for discovering definitions of mathematical operators is introduced. GPP is a task within the IL exploration discovery system. We developed GPP for use in the discovery of mathematical operators with a wider class of representations than was possible with the previous methods by Lenat and by Shen. GPP utilizes the purpose for which an operator is created to prune the possible definitions. The relevant search spaces are immense and there exists insufficient information for a complete evaluation of the purpose constraint, so it is necessary to perform a partial evaluation of the purpose (i.e., pruning) constraint. The constraint is first transformed so that it is operational with respect to the partial information, and then it is applied to examples in order to test the generated candidates for an operator's definition. In the GPP process, once a candidate definition survives this empirical prune, it is passed on to a theorem prover for formal verification. We describe the application of this methodology to the (re)discovery of the definition of multiplication for Conway numbers, a discovery which is difficult for human mathematicians. We successfully model this discovery process utilizing information which was reasonably available at the time of Conway's original discovery. As part of this discovery process, we reduce the size of the search space from a computationally intractable size to 3468 elements.
Several computer programs which are available through the NASA Technology Utilization Program are outlined. Presented are: (1) Computer operational programs which can be applied to resolve procedural problems swiftly and accurately. (2) Mathematical applications for the resolution of problems encountered in numerous industries. Although the functions which these programs perform are not new and similar programs are available in many large computer center libraries, this collection may be of use to centers with limited systems libraries and for instructional purposes for new computer operators.
The Expressions Module is a software module that has been incorporated into the Satellite Orbit Analysis Program (SOAP). The module includes an expressions- parser submodule built on top of an analytical system, enabling the user to define logical and numerical variables and constants. The variables can capture output from SOAP orbital-prediction and geometric-engine computations. The module can combine variables and constants with built-in logical operators (such as Boolean AND, OR, and NOT), relational operators (such as >, <, or =), and mathematical operators (such as addition, subtraction, multiplication, division, modulus, exponentiation, differentiation, and integration). Parentheses can be used to specify precedence of operations. The module contains a library of mathematical functions and operations, including logarithms, trigonometric functions, Bessel functions, minimum/ maximum operations, and floating- point-to-integer conversions. The module supports combinations of time, distance, and angular units and has a dimensional- analysis component that checks for correct usage of units. A parser based on the Flex language and the Bison program looks for and indicates errors in syntax. SOAP expressions can be built using other expressions as arguments, thus enabling the user to build analytical trees. A graphical user interface facilitates use.
Specification of the mathematical equations required to define the dynamic response of a linear continuous plant, subject to sampled data control, is complicated by the fact that the digital components of the control system cannot be modeled via linear ordinary differential equations. This complication can be overcome by introducing two new mathematical operations; namely, the operation of zero order hold and digial delay. It is shown that by direct utilization of these operations, a set of linear mixed operation equations can be written and used to define the dynamic response characteristics of the controlled system. It also is shown how these linear mixed operation equations lead, in an automatable manner, directly to a set of finite difference equations which are in a format compatible with follow on time and frequency domain analysis methods.
A stream of raw data is compressed prior to transmissio in a communication channel by a system which includes modules for choosing a current segment of the raw data stream for processing and defining a set of operators for representing data segments by a mathematical operation and parameters thereof. The system performs a competitive evaluation of different tools comprising different combinations of one or more of the operators and the parameters threrof with respect to the current data segment in order to determine relative abilities among the different tools to reduce the number of bits required to represent the current data segment. The system then selects a tool and a set of parameters thereof found in the competitive evaluation to have a superior ability relative to others of the different tools to reduce a number of bits required to represent the current data segment.
Gravitational physics research at ISPAE is connected with NASA's Relativity Mission (Gravity Probe B (GP-B)) which will perform a test of Einstein's General Relativity Theory. GP-B will measure the geodetic and motional effect predicted by General Relativity Theory with extremely stable and sensitive gyroscopes in an earth orbiting satellite. Both effects cause a very small precession of the gyroscope spin axis. The goal of the GP-B experiment is the measurement of the gyroscope precession with very high precision. GP-B is being developed by a team at Stanford University and is scheduled for launch in the year 2001. The related UAH research is a collaboration with Stanford University and MSFC. This research is focussed primarily on the error analysis and data reduction methods of the experiment but includes other topics concerned with experiment systems and their performance affecting the science measurements. The hydrogen maser is the most accurate and stable clock available. It will be used in future gravitational physics missions to measure relativistic effects such as the second order Doppler effect. The HMC experiment, currently under development at the Smithsonian Astrophysical Observatory (SAO), will test the performance and capability of the hydrogen maser clock for gravitational physics measurements. UAH in collaboration with the SAO science team will study methods to evaluate the behavior and performance of the HMC. The GP-B data analysis developed by the Stanford group involves complicated mathematical operations. This situation led to the idea to investigate alternate and possibly simpler mathematical procedures to extract the GP-B measurements form the data stream. Comparison of different methods would increase the confidence in the selected scheme.
Tachometer circuit operates in conjunction with brushless shaft-angle resolver. By performing sequence of straightforward mathematical operations on resolver signals and utilizing simple trigonometric identity, generates voltage proportional to rate of rotation of shaft. One advantage is use of brushless shaft-angle resolver as main source of rate signal: no brushes to wear out, no brush noise, and brushless resolvers have proven robustness. No switching of signals to generate noise. Another advantage, shaft-angle resolver used as shaft-angle sensor, tachometer input obtained without adding another sensor. Present circuit reduces overall size, weight, and cost of tachometer.
Preparation for the Mariner Mars 1971 mission is reported, including an extensive training program for operations personnel during which the primary source of spacecraft data was a computer program simulating the spacecraft. The objectives of a simulation model for training purposes differed from objectives appropriate to a design or analysis model. Model subsystems were designed to provide realistic telemetry data reflecting changes due both to commands and environmental parameters affecting the spacecraft at various times during the mission. The spacecraft is modeled along two separate functional lines. Boolean operations are concentrated in the spacecraft logic model, which determines the spacecraft state or mode, while mathematical operations or algorithms are executed in computational subsystem models. Although logic parameters are interrogated as a part of each computational pass, actual logic model processing occurs only when a change-of-state input is generated by the operations organization. The program design, some of the special characteristics of each of the modeled subsystems, and how the model was used in support of mission operations training are presented.
A relaxation labeling algorithm is developed. The major advantage of this algorithm over the existing ones is that the mathematic operation is simplified. The simplification eases the analysis of the convergence properties. Both the theoretical and application aspects of the proposed algorithm are investigated. The local convergence properties of a labeling process with n labels and m labels are established. The investigation of the interaction among the nodes in a multinode labeling process reveals some insight into the mathematical issues involved in the relaxation operations.
This paper presents an approach to modeling the dynamics of flexible multibody systems such as flexible spacecraft and limber space robotic systems. A large number of degrees of freedom and complex dynamic interactions are typical in these systems. This paper uses spatial operators to develop efficient recursive algorithms for the dynamics of these systems. This approach very efficiently manages complexity by means of a hierarchy of mathematical operations.
A digital communications signal is a sinusoidal waveform that is modified by a binary (digital) information signal. The sinusoidal waveform is called the carrier. The carrier may be modified in amplitude, frequency, phase, or a combination of these. In this project a binary phase shift keyed (BPSK) signal is the communication signal. In a BPSK signal the phase of the carrier is set to one of two states, 180 degrees apart, by a binary (i.e., 1 or 0) information signal. A digital signal is a sampled version of a "real world" time continuous signal. The digital signal is generated by sampling the continuous signal at discrete points in time. The rate at which the signal is sampled is called the sampling rate (f(s)). The device that performs this operation is called an analog-to-digital (A/D) converter or a digitizer. The digital signal is composed of the sequence of individual values of the sampled BPSK signal. Digital signal processing (DSP) is the modification of the digital signal by mathematical operations. A device that performs this processing is called a digital signal processor. After processing, the digital signal may then be converted back to an analog signal using a digital-to-analog (D/A) converter. The goal of this project is to develop a system that will recover the digital information from a BPSK signal using DSP techniques. The project is broken down into the following steps: (1) Development of the algorithms required to demodulate the BPSK signal; (2) Simulation of the system; and (3) Implementation a BPSK receiver using digital signal processing hardware.
FORTRAN 4 digital computer program calculates equilibrium composition of complex, multiphase chemical systems. This is a free energy minimization method with solution of the problem reduced to mathematical operations, without concern for the chemistry involved. Also certain thermodynamic properties are determined as byproducts of the main calculations.