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Random events were simulated by computer and subjected to various statistical methods to extract important parameters. Various forms of curve fitting were explored, such as least squares, least distance from a line, maximum likelihood. Problems considered were dead time, exponential decay, and spectrum extraction from cosmic ray data using binned data and data from individual events. Computer programs, mostly of an iterative nature, were developed to do these simulations and extractions and are partially listed as appendices. The mathematical basis for the compuer programs is given.
The modal test program for the Galileo Spacecraft was completed at the Jet Propulsion Laboratory in the summer of 1983. The multiple sine dwell method was used for the baseline test. The Galileo Spacecraft is a rather complex 2433 kg structure made of a central core on which seven major appendages representing 30 percent of the total mass are attached, resulting in a high modal density structure. The test revealed a strong nonlinearity in several major modes. This nonlinearity discovered in the course of the test necessitated running additional tests at the unusually high response levels of up to about 21 g. The high levels of response were required to obtain a model verification valid at the level of loads for which the spacecraft was designed. Because of the high modal density and the nonlinearity, correlation between the dynamic mathematical model and the test results becomes a difficult task. Significant changes in the pre-test analytical model are necessary to establish confidence in the upgraded analytical model used for the final load verification. This verification, using a test verified model, is required by NASA to fly the Galileo Spacecraft on the Shuttle/Centaur launch vehicle in 1986.
Digital computer program for minimizing weight of fuel cell power systems - prelaunch startup and instrumentation - mathematical model of static moisture removal process - fuel cell model
Science in Action is an education outreach program for pre-collegiate students. It is based on the concept that, in order to interest students in science, they must see science and scientists at work. The program encompasses the full range of scientific disciplines - the core sciences, engineering, and mathematics. A unique aspect of the program is the involvement and support of scientists and engineers representing local professional societies, industries, business, and academic institutions. An outline of the program is given.
The transport and diffusion models and algorithms developed for use by NASA in predicting concentrations and dosages downwind from normal and abnormal launches of rocket vehicles are described along with the associated computer programs for use in performing the calculations. Topics discussed include: the mathematical specifications and procedures used in the Preprocessor Program to calculate rocket exhaust cloud rise, cloud dimensions, and other input parameters to the transport and diffusion models; the revised mathematical specifications for the Multilayer Diffusion Models; users' instructions for implementing the Preprocessor and Multilayer Diffusion Models Programs; and worked example problems illustrating the use of the models and computer programs.
The Intelligent Math Tutor (IMT) is a computer program for training students in pre-college and college-level mathematics courses, including fundamentals, intermediate algebra, college algebra, and trigonometry. The IMT can be executed on a server computer for access by students via the Internet; alternatively, it can be executed on students computers equipped with compact- disk/read-only-memory (CD-ROM) drives. The IMT provides interactive exercises, assessment, tracking, and an on-line graphing calculator with algebraic-manipulation capabilities. The IMT provides an innovative combination of content, delivery mechanism, and artificial intelligence. Careful organization and presentation of the content make it possible to provide intelligent feedback to the student based on performance on exercises and tests. The tracking and feedback mechanisms are implemented within the capabilities of a commercial off-the-shelf development software tool and are written in the Unified Modeling Language to maximize reuse and minimize development cost. The graphical calculator is a standard feature of most college and pre-college algebra and trigonometry courses. Placing this functionality in a Java applet decreases the cost, provides greater capabilities, and provides an opportunity to integrate the calculator with the lessons.
Phase variable transformations are used to construct the mathematical model of an aeroelastic aircraft in a form that is amenable to partial or piecemeal acceptance of parameters estimated from flight data. The problem is one of parameter identification of large scale dynamic systems involving a system matrix characterized by about 200 elements. A mathematical model of the USAF Total In-Flight Simulator was computed using the FLEXSTAB program. As data became available during the progress of the flight test program, it was processed and substituted in the mathematical model for parameters obtained from the FLEXSTAB program. Results tend to show a progressive and orderly transition from an analytically defined mathematical model to one obtained from the flight tests of the actual aircraft.
MatLab(R) (MATrix LABoratory) is a numerical computation and simulation tool that is used by thousands Scientists and Engineers in many cou ntries. MatLab does purely numerical calculations, which can be used as a glorified calculator or interpreter programming language; its re al strength is in matrix manipulations. Computer algebra functionalities are achieved within the MatLab environment using "symbolic" toolbo x. This feature is similar to computer algebra programs, provided by Maple or Mathematica to calculate with mathematical equations using s ymbolic operations. MatLab in its interpreter programming language fo rm (command interface) is similar with well known programming languag es such as C/C++, support data structures and cell arrays to define c lasses in object oriented programming. As such, MatLab is equipped with most ofthe essential constructs of a higher programming language. M atLab is packaged with an editor and debugging functionality useful t o perform analysis of large MatLab programs and find errors. We belie ve there are many ways to approach real-world problems; prescribed methods to ensure foregoing solutions are incorporated in design and ana lysis of data processing and visualization can benefit engineers and scientist in gaining wider insight in actual implementation of their perspective experiments. This presentation will focus on data processing and visualizations aspects of engineering and scientific applicati ons. Specifically, it will discuss methods and techniques to perform intermediate-level data processing covering engineering and scientifi c problems. MatLab programming techniques including reading various data files formats to produce customized publication-quality graphics, importing engineering and/or scientific data, organizing data in tabu lar format, exporting data to be used by other software programs such as Microsoft Excel, data presentation and visualization will be discussed. The presentation will emphasize creating practIcal scripts (pro grams) that extend the basic features of MatLab TOPICS mclude (1) Ma trix and vector analysis and manipulations (2) Mathematical functions (3) Symbolic calculations & functions (4) Import/export data files (5) Program lOgic and flow control (6) Writing function and passing parameters (7) Test application programs
Theoretical basis of orbit determination - mathematical model, computation and correction of observables, and regression coefficients
Various Symbolic Manipulation Programs (SMP) were tested to check the functioning of their commands and suitability under various operating systems. Support systems for SMP were found to be relatively better than the one for MACSYMA. The graphics facilities for MACSYMA do not work as expected under the UNIX operating system. Not all commands for MACSYMA function as described in the manuals. Shape representation is a central issue in computer graphics and computer-aided design. Aside from appearance, there are other application dependent, desirable properties like continuity to certain order, symmetry, axis-independence, and variation-diminishing properties. Several shape representations are studied, which include the Osculatory Method, a Piecewise Cubic Polynomial Method using two different slope estimates, Piecewise Cubic Hermite Form, a method by Harry McLaughlin, and a Piecewise Bezier Method. They are applied to collected physical and chemical data. Relative merits and demerits of these methods are examined. Kinematics of a single link, non-dissipative robot arm is studied using MACSYMA. Lagranian is set-up and Lagrange's equations are derived. From there, Hamiltonian equations of motion are obtained. Equations suggest that bifurcation of solutions can occur, depending upon the value of a single parameter. Using the characteristic function W, the Hamilton-Jacobi equation is derived. It is shown that the H-J equation can be solved in closed form. Analytical solutions to the H-J equation are obtained.
Diverse cost-estimating techniques and data combined into single program. Selected Tether Applications Cost Model (STACOM 1.0) is interactive accounting software tool providing means for combining several independent cost-estimating programs into fully-integrated mathematical model capable of assessing costs, analyzing benefits, providing file-handling utilities, and putting out information in text and graphical forms to screen, printer, or plotter. Program based on Lotus 1-2-3, version 2.0. Developed to provide clear, concise traceability and visibility into methodology and rationale for estimating costs and benefits of operations of Space Station tether deployer system.
The CHAOS and Thermal Sciences Laboratory (CaTs) at James Madison University evolved into a noteworthy effort to increase minority representation in the sciences and mathematics. Serving ten students and faculty directly, and nearly 50 students indirectly, CaTs, through recruitment efforts, workshops, mentoring programs, tutorial services and research and computational laboratories, fulfilled its intent to initiate an academically enriched research program aimed at strengthening the academic and self-actualization skills of undergraduate students with potential to pursue doctoral study in the sciences. The stated goal of the program was to increase by 5% the number of enrolled mathematics and science students into the program. Success far exceeded the program goals by producing 100% graduation rate of all supported recipients during its tenure, with 30% of the students subsequently in pursuit of graduate degrees. Student retention in the program exceeded 90% and faculty participation exceeded the three members involved in mentoring and tutoring, gaining multi-disciplinary support. Aggressive marketing of the program resulted in several paid summer internships and commitments from NASA and an ongoing relationship with CHROME, a nationally recognized organization which focuses on developing minority students in the sciences and mathematics. Success of the program was only limited by the limited fiscal resources at NASA which resulted in phasing out of the program.
For the last several years the Science Directorate at Marshall Space Flight Center has carried out a diverse program of Internet-based science communication. The Directorate's Science Roundtable includes active researchers, NASA public relations, educators, and administrators. The Science@NASA award-winning family of Web sites features science, mathematics, and space news. The program includes extended stories about NASA science, a curriculum resource for teachers tied to national education standards, on-line activities for students, and webcasts of real-time events. The focus of sharing science activities in real-time has been to involve and excite students and the public about science. Events have involved meteor showers, solar eclipses, natural very low frequency radio emissions, and amateur balloon flights. In some cases, broadcasts accommodate active feedback and questions from Internet participants. Through these projects a pattern has emerged in the level of interest or popularity with the public. The pattern differentiates projects that include science from those that do not, All real-time, event-based Internet activities have captured public interest at a level not achieved through science stories or educator resource material exclusively. The worst event-based activity attracted more interest than the best written science story. One truly rewarding lesson learned through these projects is that the public recognizes the importance and excitement of being part of scientific discovery. Flying a camera to 100,000 feet altitude isn't as interesting to the public as searching for viable life-forms at these oxygen-poor altitudes. The details of these real-time, event-based projects and lessons learned will be discussed.
For the last several years the Science Directorate at Marshall Space Flight Center has carried out a diverse program of Internet-based science communication. The Directorate's Science Roundtable includes active researchers, NASA public relations, educators, and administrators. The Science@NASA award-winning family of Web sites features science, mathematics, and space news. The program includes extended stories about NASA science, a curriculum resource for teachers tied to national education standards, on-line activities for students, and webcasts of real-time events. Science stories cover a variety of space-related subjects and are expressed in simple terms everyone can understand. The sites address such questions as: what is space weather, what's in the heart of a hurricane, can humans live on Mars, and what is it like to live aboard the International Space Station? Along with a new look, the new format now offers articles organized by subject matter, such as astronomy, living in space, earth science or biology. The focus of sharing real-time science related events has been to involve and excite students and the public about science. Events have involved meteor showers, solar eclipses, natural very low frequency radio emissions, and amateur balloon flights. In some cases broadcasts accommodate active feedback and questions from Internet participants. Information will be provided about each member of the Science@NASA web sites.
The ROVer Ranch is an interactive computer program designed to help secondary-school students learn about space-program robotics and related basic scientific concepts by involving the students in simplified design and programming tasks that exercise skills in mathematics and science. The tasks involve building simulated robots and then observing how they behave. The program furnishes (1) programming tools that a student can use to assemble and program a simulated robot and (2) a virtual three-dimensional mission simulator for testing the robot. First, the ROVer Ranch presents fundamental information about robotics, mission goals, and facts about the mission environment. On the basis of this information, and using the aforementioned tools, the student assembles a robot by selecting parts from such subsystems as propulsion, navigation, and scientific tools, the student builds a simulated robot to accomplish its mission. Once the robot is built, it is programmed and then placed in a three-dimensional simulated environment. Success or failure in the simulation depends on the planning and design of the robot. Data and results of the mission are available in a summary log once the mission is concluded.
Four-D Global Reference Atmosphere computer program (GRAM) developed from empirical mathematical model of atmosphere generating values for pressure, density, temperature, and winds from surface level to orbital altitudes. Generates altitude profiles of parameters of atmosphere along any simulated trajectory through atmosphere. Developed from design applications in Space Shuttle program. Other potential applications include studies of global circulation and diffusion and generation of profiles for comparison with results of other atmospheric-measurement techniques such as satellite-measured temperature profiles and wind profiles from infrasonic measurements. Written in STANDARD FORTRAN 77.
A mathematical model and a digital computer program were developed for the design and evaluation of inducers for pumping two-phase oxygen. The mathematical model indicated that any design would have to be run at relatively low speeds to pump two-phase oxygen and that the J-2S oxygen inducer was close to optimum and should perform the task. A J-2S pump was built up and tested in two-phase oxygen at speeds indicated by the mathematical model. The pump was able to handle two-phase oxygen over a wide range of inducer incidence angles and up to a vapor content of 37 percent by volume with very little loss in head. The pump was still able to produce some head at vapor fractions approaching 60 percent.