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Results for “MATHEMATICS - CALCULUS, OPERATIONAL”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Toward a mathematical formalism of performance, task difficulty, and activation

The rudiments of a mathematical formalism for handling operational, physiological, and psychological concepts are developed for use by the man-machine system design engineer. The formalism provides a framework for developing a structured, systematic approach to the interface design problem, using existing mathematical tools, and simplifying the problem of telling a machine how to measure and use performance.

Samaras, George M.↗
NASA NTRS1996

Exponential Formulae and Effective Operations

One of standard methods to predict the phenomena of squeezing consists in splitting the unitary evolution operator into the product of simpler operations. The technique, while mathematically general, is not so simple in applications and leaves some pragmatic problems open. We report an extended class of exponential formulae, which yield a quicker insight into the laboratory details for a class of squeezing operations, and moreover, can be alternatively used to programme different type of operations, as: (1) the free evolution inversion; and (2) the soft simulations of the sharp kicks (so that all abstract results involving the kicks of the oscillator potential, become realistic laboratory prescriptions).

Mielnik, Bogdan↗
NASA NTRSDate not supplied

Define Minimum Safe Operational Volume for Aerial Vehicles in Upper Class E Airspace

The variety of vehicle performance in upper Class E airspace requires a method that can efficiently compute the minimum safe operational boundary between aircraft. This work presents a mathematical method to define the minimum safe operational boundary needed for aerial vehicles operating in upper Class E airspace. This method focuses on the extra separation required by vehicle maneuverability, communication delay, and control/operator response time. A sensitivity study is then performed to provide a general understanding of the impact of these factors on the extra separation needed. Experiments with pairwise encounters are conducted to verify the results generated by the proposed methods.

Separation standard↗
NASA NTRSDate not supplied

Define Minimum Safe Operational Volume for Aerial Vehicles in Upper Class E Airspace

The variety of vehicle performance in upper Class E airspace requires a method that can efficiently compute the minimum safe operational boundary between aircraft. This work presents a mathematical method to define the minimum safe operational boundary needed for aerial vehicles operating in upper Class E airspace. This method focuses on the extra separation required by vehicle maneuverability, communication delay, and control/operator response time. A sensitivity study is then performed to provide a general understanding of the impact of these factors on the extra separation needed. Experiments with pairwise encounters are conducted to verify the results generated by the proposed methods.

Separation↗
NASA NTRS1979

Dynamics and control of Stirling engines in a 15 kWe solar electric generation concept

This paper discusses the application of kinematic and free piston Stirling engines in a 15 kWe dish-electric approach for solar thermal electric generation. Initially, the principle of operation of Stirling engines in solar thermal electric generation is discussed. Then, under certain simplifying assumptions, mathematical models describing the dynamic operation of the kinematic and free piston Stirling engines are developed. It is found that the engine dynamics may be approximated by second order models. Control mechanisms for both types of Stirling engines are discussed. An approach based on the modulation of the working fluid mean pressure is presented. It is concluded that this approach offers a fast and effective means of control. The free piston Stirling engine, being a thermally driven mechanical oscillator, presents unique control requirements. These are discussed in this paper.

Das, R. L.↗
NASA NTRS1998

Smart Sensor System for NDE or Corrosion in Aging Aircraft

The extension of the operation life of military and civilian aircraft rather than replacing them with new ones is increasing the probability of aircraft component failure as a result of aging. Aircraft that already have endured a long srvice life of more than 40 years are now being considered for another 40 years of service.

monitoring system mathematical transformation oper↗
NASA NTRS1978

An investigation for the development of an integrated optical data preprocessor

The successful fabrication and demonstration of an integrated optical circuit designed to perform a parallel processing operation by utilizing holographic subtraction to simultaneously compare N analog signal voltages with N predetermined reference voltages is summarized. The device alleviates transmission, storage and processing loads of satellite data systems by performing, at the sensor site, some preprocessing of data taken by remote sensors. Major accomplishments in the fabrication of integrated optics components include: (1) fabrication of the first LiNbO3 waveguide geodesic lens; (2) development of techniques for polishing TIR mirrors on LiNbO3 waveguides; (3) fabrication of high efficiency metal-over-photoresist gratings for waveguide beam splitters; (4) demonstration of high S/N holographic subtraction using waveguide holograms; and (5) development of alignment techniques for fabrication of integrated optics circuits. Important developments made in integrated optics are the discovery and suggested use of holographic self-subtraction in LiNbO3, development of a mathematical description of the operating modes of the preprocessor, and the development of theories for diffraction efficiency and beam quality of two dimensional beam defined gratings.

Verber, C. M.↗
NASA NTRS1997

Error Analysis System for Spacecraft Navigation Using the Global Positioning System (GPS)

The Flight Dynamics Division (FDD) at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) is currently developing improved space-navigation filtering algorithms to use the Global Positioning System (GPS) for autonomous real-time onboard orbit determination. In connection with a GPS technology demonstration on the Small Satellite Technology Initiative (SSTI)/Lewis spacecraft, FDD analysts and programmers have teamed with the GSFC Guidance, Navigation, and Control Branch to develop the GPS Enhanced Orbit Determination Experiment (GEODE) system. The GEODE system consists of a Kalman filter operating as a navigation tool for estimating the position, velocity, and additional states required to accurately navigate the orbiting Lewis spacecraft by using astrodynamic modeling and GPS measurements from the receiver. A parallel effort at the FDD is the development of a GPS Error Analysis System (GEAS) that will be used to analyze and improve navigation filtering algorithms during development phases and during in-flight calibration. For GEAS, the Kalman filter theory is extended to estimate the errors in position, velocity, and other error states of interest. The estimation of errors in physical variables at regular intervals will allow the time, cause, and effect of navigation system weaknesses to be identified. In addition, by modeling a sufficient set of navigation system errors, a system failure that causes an observed error anomaly can be traced and accounted for. The GEAS software is formulated using Object Oriented Design (OOD) techniques implemented in the C++ programming language on a Sun SPARC workstation. The Phase 1 of this effort is the development of a basic system to be used to evaluate navigation algorithms implemented in the GEODE system. This paper presents the GEAS mathematical methodology, systems and operations concepts, and software design and implementation. Results from the use of the basic system to evaluate navigation algorithms implemented on GEODE are also discussed. In addition, recommendations for generalization of GEAS functions and for new techniques to optimize the accuracy and control of the GPS autonomous onboard navigation are presented.

Truong, S. H.↗
NASA NTRS1998

A Self-Tuning Kalman Filter for Autonomous Spacecraft Navigation

Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman Filter and Global Positioning System (GPS) data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. Current techniques of Kalman filtering, however, still rely on manual tuning from analysts, and cannot help in optimizing autonomy without compromising accuracy and performance. This paper presents an approach to produce a high accuracy autonomous navigation system fully integrated with the flight system. The resulting system performs real-time state estimation by using an Extended Kalman Filter (EKF) implemented with high-fidelity state dynamics model, as does the GPS Enhanced Orbit Determination Experiment (GEODE) system developed by the NASA Goddard Space Flight Center. Augmented to the EKF is a sophisticated neural-fuzzy system, which combines the explicit knowledge representation of fuzzy logic with the learning power of neural networks. The fuzzy-neural system performs most of the self-tuning capability and helps the navigation system recover from estimation errors. The core requirement is a method of state estimation that handles uncertainties robustly, capable of identifying estimation problems, flexible enough to make decisions and adjustments to recover from these problems, and compact enough to run on flight hardware. The resulting system can be extended to support geosynchronous spacecraft and high-eccentricity orbits. Mathematical methodology, systems and operations concepts, and implementation of a system prototype are presented in this paper. Results from the use of the prototype to evaluate optimal control algorithms implemented are discussed. Test data and major control issues (e.g., how to define specific roles for fuzzy logic to support the self-learning capability) are also discussed. In addition, architecture of a complete end-to-end candidate flight system that provides navigation with highly autonomous control using data from GPS is presented.

Truong, Son H.↗
DOE OSTI2025

Scattering theory in noncanonical phase space: A Drift-Kinetic collision operator for weakly collisional plasmas

After developing a scattering theory for grazing collisions in general noncanonical phase spaces, we introduce a guiding center collision operator in five-dimensional phase space designed for plasma regimes characterized by long wavelengths (relative to the Larmor radius), low frequencies (relative to the cyclotron frequency), and weak collisionality (where repeated Coulomb collisions induce cumulatively small changes in particle magnetic moment). The collision operator is fully determined by the noncanonical Hamiltonian structure of guiding center dynamics and exhibits a metriplectic structure, ensuring the conservation of particle number, momentum, energy, and interior Casimir invariants. It also satisfies an H-theorem, allowing for deviations from an equilibrium Maxwellian distribution due to the nontrivial kernel of the noncanonical guiding center Poisson tensor, spanned by the magnetic moment. We propose that this collision operator and its underlying mathematical structure may offer valuable insight into the study of turbulence, transport, and self-organizing phenomena in both laboratory and astrophysical plasmas.

Hamiltonian mechanics↗
NASA NTRS1968

Rocket engine analog simulation

Mathematical equations simulate the operation of a rocket engine, simulate destructive and nondestructive tests to verify engine design feasibility, and investigate nonlinear variations in engine performance.

Philyaw, B. K.↗
NASA NTRS1972

Redundancy approaches in bubble domain memories

Fabrication of integrated circuit chips to compensate for faulty memory elements is discussed. Procedure for testing chips to determine extent of redundancy and faults is described. Mathematical model to define operation is presented. Schematic circuit diagram of test equipment is provided.

Almasi, G. S.↗
NASA NTRS1986

Optical processing for future computer networks

In the development of future data management systems, such as the NASA Space Station, a major problem represents the design and implementation of a high performance communication network which is self-correcting and repairing, flexible, and evolvable. To obtain the goal of designing such a network, it will be essential to incorporate distributed adaptive network control techniques. The present paper provides an outline of the functional and communication network requirements for the Space Station data management system. Attention is given to the mathematical representation of the operations being carried out to provide the required functionality at each layer of communication protocol on the model. The possible implementation of specific communication functions in optics is also considered.

Husain, A.↗
NASA NTRS1990

Research reports: 1990 NASA/ASEE Summer Faculty Fellowship Program

Reports on the research projects performed under the NASA/ASEE Summer Faculty Fellowship Program are presented. The program was conducted by The University of Alabama and MSFC during the period from June 4, 1990 through August 10, 1990. Some of the topics covered include: (1) Space Shuttles; (2) Space Station Freedom; (3) information systems; (4) materials and processes; (4) Space Shuttle main engine; (5) aerospace sciences; (6) mathematical models; (7) mission operations; (8) systems analysis and integration; (9) systems control; (10) structures and dynamics; (11) aerospace safety; and (12) remote sensing

Freeman, L. Michael↗