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.
The General Mission Analysis Tool (GMAT) is a space trajectory optimization and mission analysis system developed by NASA and private industry in the spirit of the NASA Mission. GMAT contains new technology and is a testbed for future technology development.
A mathematical analysis of the tradeoffs and requirements was performed to develop an improved array design which will give stronger returns at lower elevation angles and reduce pulse spread in the return. It was determined that a zenith angle of 75deg can be obtained with an array with an area of 0.28 sq m, if the array is shaped on the surface of a 45 deg cone whose axis is coincident to the satellite axis. The total weight of the truncated pyramid array with 270 cube corners is calculated to be not more than 50% greater than the GEOS 2 array, while the efficiency is increased 275%.
A method for the mathematical analysis of linear alternator and linear motor devices and designs is described, and an example of its use is included. The technique seeks to surpass other methods of analysis by including more rigorous treatment of phenomena normally omitted or coarsely approximated such as eddy braking, non-linear material properties, and power losses generated within structures surrounding the device. The technique is broadly applicable to linear alternators and linear motors involving iron yoke structures and moving permanent magnets. The technique involves the application of Amperian current equivalents to the modeling of the moving permanent magnet components within a finite element formulation. The resulting steady state and transient mode field solutions can simultaneously account for the moving and static field sources within and around the device.
A series of three computer programs for the mathematical analysis of navigation and guidance of lunar and interplanetary trajectories was developed. All three programs require the integration of n-body trajectories for both interplanetary and lunar missions. The virutal mass technique is used in all three programs. The user's manual contains the information necessary to operate the programs. The input and output quantities of the programs are described. Sample cases are given and discussed.
Condition for swirling flow stability in circular magnetic field - mathematical analysis
Neutrino scalar magnetic charge and astrophysical effects in mathematical analysis
A previous rigorous mathematical analysis of drift-diffusion equations was used to investigate collected charge in a simple reverse-biased p-n junction diode exposed to an ionization source that liberates carriers (electron-hole pairs) in a quasi-neutral region within the diode. Each of two simple models was found to agree with the more rigorous analysis when carrier liberation is sufficiently intense. One is the sensitive volume (SV) model, and the other was called “ambipolar diffusion with a cutoff” (ADC). The earlier rigorous analysis was worked out in detail only for a localized source, i.e., a point source of carrier liberation, so it was able to validate the applicability of each simple model only for that case. The present paper treats an arbitrary spatial distribution of carrier generation and concludes that the ADC model remains valid for this more general case, but the SV model does
Potential sweep method for organic and adsorption analyses, showing relation between galvanostatic and fast potential sweep transients, noting mathematical analysis of current-potential transients
The paper summarizes the mathematical analysis and presents the experimental results for a vee-trough/evacuated tube collector (VTETC). Test results reported represent the performance of the VTETC based on an aperture area. The effectiveness of vee-trough reflectors is demonstrated by comparing the useful heat collected by a receiver tube with and without concentrators.
In the multidimensional CESE development, triangles and tetrahedra turn out to be the most natural building blocks for 2D and 3D spatial meshes. As such the CESE method is compatible with the simplest unstructured meshes and thus can be easily applied to solve problems with complex geometries. However, because the method uses space-time staggered stencils, solution decoupling may become a real nuisance in applications involving unstructured meshes. In this paper we will describe a simple and general remedy which, according to numerical experiments, has removed any possibility of solution decoupling. Moreover, in a real-world viscous flow simulation near a solid wall, one often encounters a case where a boundary with high curvature or sharp corner is surrounded by triangular/tetrahedral meshes of extremely high aspect ratio (up to 106). For such an extreme case, the spatial projection of a space-time compounded conservation element constructed using the original CESE design may become highly concave and thus its centroid (referred to as a spatial solution point) may lie far outside of the spatial projection. It could even be embedded beyond a solid wall boundary and causes serious numerical difficulties. In this paper we will also present a new procedure for constructing conservation elements and solution elements which effectively overcomes the difficulties associated with the original design. Another difficulty issue which was addressed more recently is the wellknown fact that accuracy of gradient computations involving triangular/tetrahedral grids deteriorates rapidly as the aspect ratio of grid cells increases. The root cause of this difficulty was clearly identified and several remedies to overcome it were found through a rigorous mathematical analysis. However, because of the length of the current paper and the complexity of mathematics involved, this new work will be presented in another paper.
A linearized mathematical analysis is presented for determining the response of normal shock position and subsonic duct pressures to flow-field perturbations upstream of the normal shock in mixed-compression supersonic inlets. The inlet duct cross-sectional area variation is approximated by constant-area sections; this approximation results in one-dimensional wave equations. A movable normal shock separates the supersonic and subsonic flow regions, and a choked exit is assumed for the inlet exit condition. The analysis leads to a closed-form matrix solution for the shock position and pressure transfer functions. Analytical frequency response results are compared with experimental data and a method of characteristics solution.
In this work the observability of an Inertial Navigation System (INS) during In-Flight Alignment (IFA) is investigated. A systematic approach to the observability analysis of a piece-wise constant system is presented and its use is justified mathematically. As a tool for the investigation a Stepped Observability Matrix (SOM) is constructed and a corresponding Stepped Space is defined. The INS error model is transformed into the Stepped Space during a specially chosen IFA trajectory and a full observability is carried out. The results of the mathematical analysis are checked against the results of covariance simulation and a full agreement is found between the two. Finally, the practical implications of this analysis are outlined.
Plume spectrometry provides a means to monitor the health of a burning rocket engine, and optical matrix processors provide a means to analyze the plume spectra in real time. By observing the spectrum of the exhaust plume of a rocket engine, researchers have detected anomalous behavior of the engine and have even determined the failure of some equipment before it would normally have been noticed. The spectrum of the plume is analyzed by isolating information in the spectrum about the various materials present to estimate what materials are being burned in the engine. Scientists at the Marshall Space Flight Center (MSFC) have implemented a high resolution spectrometer to discriminate the spectral peaks of the many species present in the plume. Researchers at the Stennis Space Center Demonstration Testbed Facility (DTF) have implemented a high resolution spectrometer observing a 1200-lb. thrust engine. At this facility, known concentrations of contaminants can be introduced into the burn, allowing for the confirmation of diagnostic algorithms. While the high resolution of the measured spectra has allowed greatly increased insight into the functioning of the engine, the large data flows generated limit the ability to perform real-time processing. The use of an optical matrix processor and the linear analysis technique described below may allow for the detailed real-time analysis of the engine's health. A small optical matrix processor can perform the required mathematical analysis both quicker and with less energy than a large electronic computer dedicated to the same spectral analysis routine.
Our work in directional solidification has been in the following areas: (1) Dynamics of dendrites including rigorous mathematical analysis of the resulting equations; (2) Examination of the near-structurally unstable features of the mathematically related Hele-Shaw dynamics; (3) Numerical studies of steady temperature distribution in a vertical Bridgman device; (4) Numerical study of transient effects in a vertical Bridgman device; (5) Asymptotic treatment of quasi-steady operation of a vertical Bridgman furnace for large Rayleigh numbers and small Biot number in 3D; and (6) Understanding of Mullins-Sererka transition in a Bridgman device with fluid dynamics is accounted for.
The task of modern aircraft design has always been complicated due to the number of intertwined technical factors from the various engineering disciplines. Furthermore, this complexity has been rapidly increasing by the development of such technologies as aeroelasticity tailored materials and structures, active control systems, integrated propulsion/airframe controls, thrust vectoring, and so on. Successful designs that achieve maximum advantage from these new technologies require a thorough understanding of the physical phenomena and the interactions among these phenomena. A study commissioned by the Aeronautical Sciences and Evaluation Board of the National Research Council has gone so far as to identify technology integration as a new discipline from which many future aeronautical advancements will arise. Regardless of whether one considers integration as a new discipline or not, it is clear to all engineers involved in aircraft design and analysis that better methods are required. In the past, designers conducted parametric studies in which a relatively small number of principal characteristics were varied to determine the effect on design requirements which were themselves often diverse and contradictory. Once a design was chosen, it then passed through the various engineers' disciplines whose principal task was to make the chosen design workable. Working in a limited design space, the discipline expert sometimes improved the concept, but more often than not, the result was in the form of a penalty to make the original concept workable. If an insurmountable problem was encountered, the process began over. Most design systems that attempt to account for disciplinary interactions have large empirical elements and reliance on past experience is a poor guide in obtaining maximum utilizations of new technologies. Further compounding the difficulty of design is that as the aeronautical sciences have matured, the discipline specialist's area of research has generally narrowed as more sophisticated methods are developed in the specialist's area of expertise. The results have been a decrease in the awareness of the impact of his decisions on other disciplines. This paper will outline the progress and problems encountered in the analysis, design, optimization sensitivity analysis, mathematical modeling, and configurations control and the means by which they are being solved. The breadth versus depth dilemma in analysis and design and the means for coping with that dilemma will be discussed. Finally, the all-important human aspects and the need for a new 'culture ' for doing business in an integrated, multidisciplinary design environment are discussed.
A study is presented of ground effect as applied to the lifting airscrew of the type used in modern gyroplane and helicopters. The mathematical analysis of the problem has been verified by tests made of three rotor models in the presence of a large circular "ground plane." A method of approximating the decelerating effect during vertical approach to the ground has been devised. The results of the study are presented in the form of convenient charts.
Many modeling, simulation and performance analysis studies of sampled imaging systems are inherently incomplete because they are conditioned on a discrete-input, discrete-output model that only accounts for blurring during image acquisition and additive noise. For those sampled imaging systems where the effects of digital image acquisition, digital filtering and reconstruction are significant, the modeling, simulation and performance analysis should be based on a more comprehensive continuous-input, discrete-processing, continuous-output end-to-end model. This more comprehensive model should properly account for the low-pass filtering effects of image acquisition prior to sampling, the potentially important noiselike effects of the aliasing caused by sampling, additive noise due to device electronics and quantization, the generally high-boost filtering effects of digital processing, and the low-pass filtering effects of image reconstruction. This model should not, however, be so complex as to preclude significant mathematical analysis, particularly the mean-square (fidelity) type of analysis so common in linear system theory. We demonstrate that, although the mathematics of such a model is more complex, the increase in complexity is not so great as to prevent a complete fidelity-metric analysis at both the component level and at the end-to-end system level: that is, computable mean-square-based fidelity metrics are developed by which both component-level and system-level performance can be quantified. In addition, we demonstrate that system performance can be assessed qualitatively by visualizing the output image as the sum of three component images, each of which relates to a corresponding fidelity metric. The cascaded, or filtered, component accounts for the end-to-end system filtering of image acquisition, digital processing, and image reconstruction; the random noise component accounts for additive random noise, modulated by digital processing and image reconstruction filtering; and the aliased noise component accounts for the frequency folding effect of sampling, modulated by digital processing and image reconstruction filtering.
Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.