The mathematical and numerical analysis associated with optimal guidance concepts
Mathematical and numerical analysis by spacecraft computers for optimal guidance
Ingram, H.↗
SEARCH · Engineering Papers
Results for “mathematical analysis”
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.
Analysis of time-temperature effects in 2219 aluminum welding.
Mathematical analysis of relationships between weld strength, maximum temperature and time at temperature of type 2219 aluminum
ALUMINUM ALLOY↗
Analysis and optimization of cyclic methods in orbit computation
The mathematical analysis and computation of the K=3, order 4; K=4, order 6; and K=5, order 7 cyclic methods and the K=5, order 6 Cowell method and some results of optimizing the 3 backpoint cyclic multistep methods for solving ordinary differential equations are presented. Cyclic methods have the advantage over traditional methods of having higher order for a given number of backpoints while at the same time having more free parameters. After considering several error sources the primary source for the cyclic methods has been isolated. The free parameters for three backpoint methods were used to minimize the effects of some of these error sources. They now yield more accuracy with the same computing time as Cowell's method on selected problems. This work is being extended to the five backpoint methods. The analysis and optimization are more difficult here since the matrices are larger and the dimension of the optimizing space is larger. Indications are that the primary error source can be reduced. This will still leave several parameters free to minimize other sources.
Pierce, S.↗
Heat Transfer Analysis of a Closed Brayton Cycle Space Radiator
This paper presents a mathematical analysis of the heat transfer processes taking place in a radiator for a closed cycle gas turbine (CCGT), also referred to as a Closed Brayton Cycle (CBC) space power system. The resulting equations and relationships have been incorporated into a radiator sub-routine of a numerical triple objective CCGT optimization program to determine operating conditions yielding maximum cycle efficiency, minimum radiator area and minimum overall systems mass. Study results should be of interest to numerical modeling of closed cycle Brayton space power systems and to the design of fluid cooled radiators in general.
Juhasz, Albert J.↗
General Mission Analysis Tool (GMAT) Mathematical Specifications
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.
Hughes, Steve↗
Analysis of requirements for GEOS-C laser cube-corner reflector panels
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%.
Minott, P. O.↗
Advanced analysis technique for the evaluation of linear alternators and linear motors
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.
Holliday, Jeffrey C.↗
Simulated trajectories error analysis program, version 2. Volume 2: Programmer's manual
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.
Vogt, E. D.↗
The stability of swirling flow of a viscous conducting fluid in the presence of a circular magnetic field
Condition for swirling flow stability in circular magnetic field - mathematical analysis
FLOW STABILITY↗
Analysis of possible effects caused by magnetic particles in space
Neutrino scalar magnetic charge and astrophysical effects in mathematical analysis
Dorman, L. I.↗
A theoretical analysis of steady-state charge collection in simple diodes under high-injection conditions
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
Edmonds, Larry D.↗
The potential-sweep method - A theoretical analysis.
Potential sweep method for organic and adsorption analyses, showing relation between galvanostatic and fast potential sweep transients, noting mathematical analysis of current-potential transients
ELECTROCHEMISTRY↗
Analysis and two years of testing of the vee-trough concentrator/evacuated tube solar collector
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.
Selcuk, M. K.↗
Recent Development in the CESE Method for the Solution of the Navier-Stokes Equations Using Unstructured Triangular or Tetrahedral Meshes With High Aspect Ratio
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.
Chang, Sin-Chung↗
Analysis of the dynamic response of a supersonic inlet to flow-field perturbations upstream of the normal shock
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.
Cole, G. L.↗
Observability analysis of inertial navigation systems during in-flight alignment
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.
Bar-Itzhack, I. Y.↗
Linear Spectral Analysis of Plume Emissions Using an Optical Matrix Processor
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.
Gary, C. K.↗
Crystal Growth and Fluid Mechanics Problems in Directional Solidification
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.
Tanveer, Saleh A.↗