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At least 289 records · Page 16

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NASA NTRS1991

Spatial-Operator Algebra For Robotic Manipulators

Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.

Rodriguez, Guillermo↗

NASA NTRS1991

Rotor-to-stator Partial Rubbing and Its Effects on Rotor Dynamic Response

Results from experimental and analytical studies on rotor to stationary element partial rubbings at several locations and their effects on rotor dynamic responses are presented. The mathematical model of a rubbing rotor is given. The computer program provides numerical results which agree with experimentally obtained rotor responses.

Muszynska, Agnes↗

NASA NTRS1999

Mathematical model to estimate risk of calcium-containing renal stones

BACKGROUND/AIMS: Astronauts exposed to microgravity during the course of spaceflight undergo physiologic changes that alter the urinary environment so as to increase the risk of renal stone formation. This study was undertaken to identify a simple method with which to evaluate the potential risk of renal stone development during spaceflight. METHOD: We used a large database of urinary risk factors obtained from 323 astronauts before and after spaceflight to generate a mathematical model with which to predict the urinary supersaturation of calcium stone forming salts. RESULT: This model, which involves the fewest possible analytical variables (urinary calcium, citrate, oxalate, phosphorus, and total volume), reliably and accurately predicted the urinary supersaturation of the calcium stone forming salts when compared to results obtained from a group of 6 astronauts who collected urine during flight. CONCLUSIONS: The use of this model will simplify both routine medical monitoring during spaceflight as well as the evaluation of countermeasures designed to minimize renal stone development. This model also can be used for Earth-based applications in which access to analytical resources is limited.

NASA Center JSC↗

NASA NTRS2006

Three-Dimensional Field Solutions for Multi-Pole Cylindrical Halbach Arrays in an Axial Orientation

This article presents three-dimensional B field solutions for the cylindrical Halbach array in an axial orientation. This arrangement has applications in the design of axial motors and passive axial magnetic bearings and couplers. The analytical model described here assumes ideal magnets with fixed and uniform magnetization. The field component functions are expressed as sums of 2-D definite integrals that are easily computed by a number of mathematical analysis software packages. The analysis is verified with sample calculations and the results are compared to equivalent results from traditional finite-element analysis (FEA). The field solutions are then approximated for use in flux linkage and induced EMF calculations in nearby stator windings by expressing the field variance with angular displacement as pure sinusoidal function whose amplitude depends on radial and axial position. The primary advantage of numerical implementation of the analytical approach presented in the article is that it lends itself more readily to parametric analysis and design tradeoffs than traditional FEA models.

Thompson, William K.↗

NASA NTRS1985

Estimation of dynamic rotor loads for the rotor systems research aircraft: Methodology development and validation

The Rotor Systems Research Aircraft uses load cells to isolate the rotor/transmission systm from the fuselage. A mathematical model relating applied rotor loads and inertial loads of the rotor/transmission system to the load cell response is required to allow the load cells to be used to estimate rotor loads from flight data. Such a model is derived analytically by applying a force and moment balance to the isolated rotor/transmission system. The model is tested by comparing its estimated values of applied rotor loads with measured values obtained from a ground based shake test. Discrepancies in the comparison are used to isolate sources of unmodeled external loads. Once the structure of the mathematical model has been validated by comparison with experimental data, the parameters must be identified. Since the parameters may vary with flight condition it is desirable to identify the parameters directly from the flight data. A Maximum Likelihood identification algorithm is derived for this purpose and tested using a computer simulation of load cell data. The identification is found to converge within 10 samples. The rapid convergence facilitates tracking of time varying parameters of the load cell model in flight.

Duval, R. W.↗

NASA NTRS1972

A study analysis of cable-body systems totally immersed in a fluid stream

A general stability analysis of a cable-body system immersed in a fluid stream is presented. The analytical portion of this analysis treats the system as being essentially a cable problem, with the body dynamics giving the end conditions. The mathematical form of the analysis consists of partial differential wave equations, with the end and auxiliary conditions being determined from the body equations of motion. The equations uncouple to give a lateral problem and a longitudinal problem as in first order airplane dynamics. A series of tests on a tethered wind tunnel model provide a comparison of the theory with experiment.

Delaurier, J. D.↗

NASA NTRS1978

Industrial ion source technology

An analytical model was developed to describe the development of a coned surface texture with ion bombardment and simultaneous deposition of an impurity. A mathematical model of sputter deposition rate from a beveled target was developed in conjuction with the texturing models to provide an important input to that model. The establishment of a general procedure that will allow the treatment of manay different sputtering configurations is outlined. Calculation of cross sections for energetic binary collisions was extened to Ar, Kr.. and Xe with total cross sections for viscosity and diffusion calculated for the interaction energy range from leV to 1000eV. Physical sputtering and reactive ion etching experiments provided experimental data on the operating limits of a broad beam ion source using CF4 as a working gas to produce reactive species in a sputtering beam. Magnetic clustering effects are observed when Al is seeded with Fe and sputtered with Ar(?) ions. Silicon was textured at a micron scale by using a substrate temperature of 600 C.

Kaufman, H. R.↗

NASA NTRS1980

Orbiter Landing Loads Math Model Description and Correlation with ALT Flight Data

Results of the space shuttle approach and landing test are examined in order to assess landing gear characteristics and performance and verify landing dynamic analyses. The landing gears were instrumented with load-calibrated strain gages, a wheel-speed sensor, and strut stroke measurement devices. The mathematical procedure used in predicting the shuttle touchdown loads and dynamics is presented together with the comparisons between measured flight data and the analytical predictions. Conclusions from these data are also presented.

Hamilton, D. A.↗

NASA NTRS1980

Temperature control simulation for a microwave transmitter cooling system

The thermal performance of a temperature control system for the antenna microwave transmitter (klystron tube) of the Deep Space Network antenna tracking system is discussed. In particular the mathematical model is presented along with the details of a computer program which is written for the system simulation and the performance parameterization. Analytical expressions are presented.

Yung, C. S.↗

NASA NTRS1981

Global function approach in structural analysis: Basic approach, numerical results

The structural response to a given environment is described by the differential equations of motion of deformable bodies. Analytic solutions of such problems for a reasonably large class of structural configurations are not within the realm of the possible. Consequently, the mathematical problem is recast into a numerical problem for solution on the computer. New technology in the space and energy fields led to a growing demand for accurate analysis which at times cannot be met due to the limits set by available budgets for computer time. In response to this need for more efficient numerical analysis, the possibilities of reducing the number of freedoms in the system through a revival of the global function approach were explored.

Almroth, B. O.↗

NASA NTRS1987

A comparison of analytical and numerical models for steadily driven magnetic reconnection

The effect of boundary conditions in both analytical and numerical solutions of steadily driven reconnection on the reconnection of antiparallel magnetic fields is considered, with special attention given to the mathematical problem of properly specifying boundary conditions for the MHD equation. A unified formulation developed by Priest and Forbes (1986) for steady state reconnection, which includes the Petschek solution and the Sonnerup (1970) solution as special cases, is used to reinterpret the previous numerical experiments of steadily driven reconnection. It is shown that many contradictory features of these experiments were caused by the use of boundary conditions which are different from those required by Petschek's (1964) theory.

Forbes, T. G.↗

NASA NTRS1990

A simple analytic model for the evolution of captured galactic disks

The general analytic solution developed by Steinman-Cameron and Durisen and published in 1988 for the evolution of dissipative nonplanar disks is applied to captured galactic disks in model galaxies with nonspherical, scale-free, logarithmic gravitational potentials. Such potentials produce flat rotation curves, similar to those seen in real galaxies. In this case, the analytic solution yields a self-similar structure for the warps and twists that develop while the disks is settling. Being scale-free in a simple, analytic form, this solution is completely defined by only a few dimensionless fitting parameters. As a result, it can be utilized as a mathematical tool to fit settling disks in real galaxies. The minimum time it takes for a disk to settle into a steady state orientation is also a scale-free quantity when expressed in units of the precession period or the orbit period. For realistic parameters, settling times are on the order of one-half to two periods. The use of the time-dependent structure of settling disks as a probe of the three-dimensional mass distribution of the host galaxies, including dark halos, is discussed.

Steiman-Cameron, Thomas Y.↗

NASA NTRS1990

On the numerical computation of nonlinear force-free magnetic fields

An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from the photosphere, given the proper boundary conditions. This paper presents the results of this work, describing the mathematical formalism that was developed, the numerical techniques employed, and comments on the stability criteria and accuracy developed for these numerical schemes. An analytical solution is used for a benchmark test; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent (less than 5 percent). This newly developed scheme was applied to analyze a solar vector magnetogram, and the results were compared with the results deduced from the classical potential field method. The comparison shows that additional physical features of the vector magnetogram were revealed in the nonlinear force-free case.

Wu, S. T.↗

NASA NTRS2012

Model-Based Method for Sensor Validation

Fault detection, diagnosis, and prognosis are essential tasks in the operation of autonomous spacecraft, instruments, and in situ platforms. One of NASA s key mission requirements is robust state estimation. Sensing, using a wide range of sensors and sensor fusion approaches, plays a central role in robust state estimation, and there is a need to diagnose sensor failure as well as component failure. Sensor validation can be considered to be part of the larger effort of improving reliability and safety. The standard methods for solving the sensor validation problem are based on probabilistic analysis of the system, from which the method based on Bayesian networks is most popular. Therefore, these methods can only predict the most probable faulty sensors, which are subject to the initial probabilities defined for the failures. The method developed in this work is based on a model-based approach and provides the faulty sensors (if any), which can be logically inferred from the model of the system and the sensor readings (observations). The method is also more suitable for the systems when it is hard, or even impossible, to find the probability functions of the system. The method starts by a new mathematical description of the problem and develops a very efficient and systematic algorithm for its solution. The method builds on the concepts of analytical redundant relations (ARRs).

Vatan, Farrokh↗

NASA NTRS2019

On the Calculation of Exact Cumulative Distribution Statistics for Burgers Equation

A mathematical procedure is presented for the calculation of exact cumulative distribution statistics for a viscosity-free variant of Burgers nonlinear partial differential equation (PDE) in one space dimension and time subject to sinusoidal initial data with uncertain (random variable) amplitude or phase shift. Analytical solutions of nonlinear PDEs with uncertain initial and/or boundary data are invaluable benchmarks in assessing approximate uncertainty quantification techniques. The Burgers equation solution with uncertain initial data results in nonsmooth solution behavior in both physical and random variable dimensions which provides a severe test for approximate uncertainty quantification techniques. Mathematical proofs are provided to verify that exact cumulative distribution statistics can be systematically and robustly obtained for all forward time.

Burgers↗

NASA NTRS1972

Generalized simulation technique for turbojet engine system analysis

A nonlinear analog simulation of a turbojet engine was developed. The purpose of the study was to establish simulation techniques applicable to propulsion system dynamics and controls research. A schematic model was derived from a physical description of a J85-13 turbojet engine. Basic conservation equations were applied to each component along with their individual performance characteristics to derive a mathematical representation. The simulation was mechanized on an analog computer. The simulation was verified in both steady-state and dynamic modes by comparing analytical results with experimental data obtained from tests performed at the Lewis Research Center with a J85-13 engine. In addition, comparison was also made with performance data obtained from the engine manufacturer. The comparisons established the validity of the simulation technique.

Seldner, K.↗

NASA NTRS1972

Comparison of satellite theories

The accuracy of five mathematical models in computing a nominal orbit for the Vanguard 2 satellite by using a position velocity vector is considered. Either numerical integration or analytical theories are used in all models as well as the same force model that corresponds to a potential with the zonal harmonics to order four. The amounts of spread in the values of the total energy and the z-component of the angular momentum for a set of times are considered as measures of accuracy.

Hertz, H. G.↗

NASA NTRS1972

Photogrammetric calibration of the NASA-Wallops Island image intensifier system

An image intensifier was designed for use as one of the primary tracking systems for the barium cloud experiment at Wallops Island. Two computer programs, a definitive stellar camara calibration program and a geodetic stellar camara orientation program, were originally developed at Wallops on a GE 625 computer. A mathematical procedure for determining the image intensifier distortions is outlined, and the implementation of the model in the Wallops computer programs is described. The analytical calibration of metric cameras is also discussed.

Harp, B. F.↗