Representation and computation of Mathieu functions by means of Lie series
Representation and computation of Mathieu functions by means of Lie series - descriptions and flow diagrams of computer programs used in calculation
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Representation and computation of Mathieu functions by means of Lie series - descriptions and flow diagrams of computer programs used in calculation
Deterministic optimal control, discussing Bellman dynamic programming method, Pontryagin maximum principle, orbital transfer, interplanetary guidance, etc
Optimality condition for singular control problems derived using differential dynamic programming to obtain expression for change in cost produced by control variation
Orbit computation and tracking system for Iris satellite using differential correction program
Review of some of the salient theoretical developments in the specific area of optimal control algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first- and second-variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton-Raphson, or Gauss-Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate-gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these are methods for solving the unconstrained linear quadratic regulator problem, as well as certain constrained minimum-time and minimum-energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional-gradient method, the gradient-projection method, and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called epsilon-methods combine the Ritz method with penalty function techniques.
A program of ALSEP-quasar very-long-baseline interferometry (VLBI) is being carried out. These observations employ primarily a 'four-antenna' technique whereby simultaneous observations with two antennas at each end of an intercontinental baseline are used to derive the differential interferometric phase between a compact extragalactic radio source (usually a quasar) and a number of ALSEP transmitters on the lunar surface. A continuous ALSEP-quasar differential phase history over a period of a few hours will lead to milliarcsecond angular accuracy in measuring the lunar position against the quasar reference frame if suitable calibration measurements are obtained. Development of this application of the four-antenna technique has been underway for more than a year and is producing high-quality data utilizing Deep Space Network stations. These high-accuracy observations are of value to tie the lunar ephemeris to a nearly inertial extragalactic reference frame, to test gravitational theories, and to measure the earth-moon tidal friction interaction.
This is the final report on the Texas Instruments Incorporated (TI) simulations study of Spacecraft Application of Advanced Global Positioning System (GPS) Technology. This work was conducted for the NASA Johnson Space Center (JSC) under contract NAS9-17781. GPS, in addition to its baselined capability as a highly accurate spacecraft navigation system, can provide traffic control, attitude control, structural control, and uniform time base. In Phase 1 of this program, another contractor investigated the potential of GPS in these four areas and compared GPS to other techniques. This contract was for the Phase 2 effort, to study the performance of GPS for these spacecraft applications through computer simulations. TI had previously developed simulation programs for GPS differential navigation and attitude measurement. These programs were adapted for these specific spacecraft applications. In addition, TI has extensive expertise in the design and production of advanced GPS receivers, including space-qualified GPS receivers. We have drawn on this background to augment the simulation results in the system level overview, which is Section 2 of this report.
Educational outreach is an integral part of the International Space Station (ISS) mandate. In a few scant years, the International Space Station has already established a tradition of successful, general outreach activities. However, as the number of outreach events increased and began to reach school classrooms, those events came under greater scrutiny by the education community. Some of the ISS electronic field trips, while informative and helpful, did not meet the generally accepted criteria for education events, especially within the context of the classroom. To make classroom outreach events more acceptable to educators, the ISS outreach program must differentiate between communication events (meant to disseminate information to the general public) and education events (designed to facilitate student learning). In contrast to communication events, education events: are directed toward a relatively homogeneous audience who are gathered together for the purpose of learning, have specific performance objectives which the students are expected to master, include a method of assessing student performance, and include a series of structured activities that will help the students to master the desired skill(s). The core of the ISS education events is an interactive videoconference between students and ISS representatives. This interactive videoconference is to be preceded by and followed by classroom activities which help the students aftain the specified learning objectives. Using the interactive videoconference as the centerpiece of the education event lends a special excitement and allows students to ask questions about what they are learning and about the International Space Station and NASA. Whenever possible, the ISS outreach education events should be congruent with national guidelines for student achievement. ISS outreach staff should recognize that there are a number of different groups that will review the events, and that each group has different criteria for acceptance. For example, school administrators are more likely to be concerned about an event meeting national standards and the cost of the event. In contrast, a teacher's acceptance of an education event may be directly related to the amount of extra work the event imposes upon that teacher. ISS education events must be marketed differently to the different groups of educators, and must never increase the workload of the average teacher.
Symbolic execution is a well-known program analysis technique which represents values of program inputs with symbolic values instead of concrete (initialized) data and executes the program by manipulating program expressions involving the symbolic values. Symbolic execution has been proposed over three decades ago but recently it has found renewed interest in the research community, due in part to the progress in decision procedures, availability of powerful computers and new algorithmic developments. We provide a survey of some of the new research trends in symbolic execution, with particular emphasis on applications to test generation and program analysis. We first describe an approach that handles complex programming constructs such as input data structures, arrays, as well as multi-threading. We follow with a discussion of abstraction techniques that can be used to limit the (possibly infinite) number of symbolic configurations that need to be analyzed for the symbolic execution of looping programs. Furthermore, we describe recent hybrid techniques that combine concrete and symbolic execution to overcome some of the inherent limitations of symbolic execution, such as handling native code or availability of decision procedures for the application domain. Finally, we give a short survey of interesting new applications, such as predictive testing, invariant inference, program repair, analysis of parallel numerical programs and differential symbolic execution.
Solar electric propulsion (SEP) is the dominant design option for employing low-thrust propulsion on a space mission. Spacecraft solar arrays power the SEP system but are subject to blackout periods during solar eclipse conditions. Discontinuity in power available to the spacecraft must be accounted for in trajectory optimization, but gradient-based methods require a differentiable power model. This work presents a power model that smooths the eclipse transition from total eclipse to total sunlight with a logistic function. Example trajectories are computed with differential dynamic programming, a second-order gradient-based method.
Solar electric propulsion (SEP) is the dominant design option for employing low-thrust propulsion on a space mission. Spacecraft solar arrays power the SEP system but are subject to blackout periods during solar eclipse conditions. Discontinuity in power available to the spacecraft must be accounted for in trajectory optimization, but gradient-based methods require a differentiable power model. This work presents a power model that smooths the eclipse transition from total eclipse to total sunlight with a logistic function. Example trajectories are computed with differential dynamic programming, a second-order gradient-based method.
A program of Apollo Lunar Surface Experiments Package (ALSEP)-Quasar Very Long Baseline Interferometry (VLBI) is being reported. These observations primarily employ a 4 antenna technique, whereby simultaneous observations with two antennas at each end of an intercontinental baseline are used to derive the differential interferometric phase between a compact extragalactic radio source (usually a quasar) and a number of ALSEP transmitters on the lunar surface. A continous ALSEP-quasar differential phase history over a few hour period leads to extremely high angular accuracy in measuring the lunar position against the quasar reference frame. This application of the 4 antenna technique has been underway for more than a year and is now producing high quality data utilizing Deep Space Network (DSN) stations in Australia, Spain, and Goldstone, California, as well as the Spaceflight Tracking and Data Network (STDN) Apollo station at Goldstone.
DIANA, a digital-analog simulation program for IBM 1620 2 computer, simulates physical systems by solving the simultaneous differential equations describing the systems. It expands and optimizes the input-output capabilities, permits additional flexibility in midstream program alternation, and minimizes the computational time.
NASA is conducting a research program to evaluate differential Global Positioning System (GPS) concepts for civil helicopter navigation. It is pointed out that the civil helicopter community will probably be an early user of GPS because of the unique mission operations in areas where precise navigation aids are not available. Applications with very demanding accuracy requirements are related to remote area search and rescue, offshore oil platform approach, remote area precision landing, and other precise navigation operations. Differential GPS appears to provide a solution for meeting the accuracy requirements involved in the considered operations. The present investigation is concerned with results obtained in three areas studied in connection with the conducted research program. Attention is given to mission-tailored satellite selection, a satellite selection algorithm concept, satellite selection algorithm simulation results, and differential GPS ground station design.
A program is described which extends the differential equation solving capability of MACSYMA to power series solutions and is available via the SHARE library. The program is directed toward those classes of equations with variable coefficients (in particular, those with singularities) and uses the method of Frobenius. Probably the most important distinction between this package and others currently available or being developed is that, wherever possible, this program will attempt to provide a complete solution to the equation rather than an approximation, i.e., a finite number of terms. This solution will take the form of a sum of infinite series.
Fortran ii computer program for evaluation of donnell type differential equation for orthotropic circular-conical shell
Writing programs in interactive FORMAC language to implement Picard iteration in solving systems of ordinary differential equations
NASA-Langley has conducted a flight test program evaluating a differential GPS/inertial navigation system's (DGPS/INS) utility as an approach/landing aid. The DGPS/INS airborne and ground components are based on off-the-shelf transport aircraft avionics, namely a global positioning/inertial reference unit (GPIRU) and two GPS sensor units (GPSSUs). Systematic GPS errors are measured by the ground GPSSU and transmitted to the aircraft GPIRU, allowing the errors to be eliminated or greatly reduced in the airborne equipment. Over 120 landings were flown; 36 of these were fully automatic DGPS/INS landings.