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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Hollow cathodes as electron emitting plasma contactors Theory and computer modeling

Several researchers have suggested using hollow cathodes as plasma contactors for electrodynamic tethers, particularly to prevent the Shuttle Orbiter from charging to large negative potentials. Previous studies have shown that fluid models with anomalous scattering can describe the electron transport in hollow cathode generated plasmas. An improved theory of the hollow cathode plasmas is developed and computational results using the theory are compared with laboratory experiments. Numerical predictions for a hollow cathode plasma source of the type considered for use on the Shuttle are presented, as are three-dimensional NASCAP/LEO calculations of the emitted ion trajectories and the resulting potentials in the vicinity of the Orbiter. The computer calculations show that the hollow cathode plasma source makes vastly superior contact with the ionospheric plasma compared with either an electron gun or passive ion collection by the Orbiter.

Davis, V. A.↗
NASA NTRS1974

Neighboring optimal guidance theory and computer program

Developments of the linear quadratic optimal control problem are discussed. The theory is applicable to the development of neighboring optimal feedback guidance gains, and is useful as a tool for synthesizing feedback control laws. A computer program which requires only the pertinent matrices of the linear quadratic problem is described.

Powers, W. F.↗
NASA NTRS1991

The expansion of polarization charge layers into magnetized vacuum - Theory and computer simulations

The formation and evolution of polarization charge layers on cylindrical plasma streams moving in vacuum are investigated using analytic theory and 2D electrostatic particle-in-cell computer simulations. It is shown that the behavior of the electron charge layer goes through three stages. An early time expansion is driven by electrostatic repulsion of electrons in the charge layer. At the intermediate stage, the simulations show that the electron-charge-layer expansion is halted by the positively charged plasma stream. Electrons close to the stream are pulled back to the stream and a second electron expansion follows in time. At the late stage, the expansion of the ion charge layer along the magnetic field lines accompanies the electron expansion to form an ambipolar expansion. It is found that the velocities of these electron-ion expansions greatly exceed the velocities of ambipolar expansions which are driven by plasma temperatures.

Galvez, Miguel↗
NASA NTRS1980

Theory for computing the size and shape of a region of influence associated with a maneuvering vehicle

A general procedure for computing the region of influence of a maneuvering vehicle is described. Basic differential geometric relations, including the use of a general trajectory parameter and the introduction of auxiliary variables in the envelope theory are presented. To illustrate the application of the method, the destruct region for a maneuvering fighter firing missiles is computed.

Barger, R. L.↗
NASA NTRS1993

Decision theory for computing variable and value ordering decisions for scheduling problems

Heuristics that guide search are critical when solving large planning and scheduling problems, but most variable and value ordering heuristics are sensitive to only one feature of the search state. One wants to combine evidence from all features of the search state into a subjective probability that a value choice is best, but there has been no solid semantics for merging evidence when it is conceived in these terms. Instead, variable and value ordering decisions should be viewed as problems in decision theory. This led to two key insights: (1) The fundamental concept that allows heuristic evidence to be merged is the net incremental utility that will be achieved by assigning a value to a variable. Probability distributions about net incremental utility can merge evidence from the utility function, binary constraints, resource constraints, and other problem features. The subjective probability that a value is the best choice is then derived from probability distributions about net incremental utility. (2) The methods used for rumor control in Bayesian Networks are the primary way to prevent cycling in the computation of probable net incremental utility. These insights lead to semantically justifiable ways to compute heuristic variable and value ordering decisions that merge evidence from all available features of the search state.

Linden, Theodore A.↗
NASA NTRS1996

Theory and Computation of Optimal Low- and Medium- Thrust Orbit Transfers

This report presents new theoretical results which lead to new algorithms for the computation of fuel-optimal multiple-burn orbit transfers of low and medium thrust. Theoretical results introduced herein show how to add burns to an optimal trajectory and show that the traditional set of necessary conditions may be replaced with a much simpler set of equations. Numerical results are presented to demonstrate the utility of the theoretical results and the new algorithms. Two indirect methods from the literature are shown to be effective for the optimal orbit transfer problem with relatively small numbers of burns. These methods are the Minimizing Boundary Condition Method (MBCM) and BOUNDSCO. Both of these methods make use of the first-order necessary conditions exactly as derived by optimal control theory. Perturbations due to Earth's oblateness and atmospheric drag are considered. These perturbations are of greatest interest for transfers that take place between low Earth orbit altitudes and geosynchronous orbit altitudes. Example extremal solutions including these effects and computed by the aforementioned methods are presented. An investigation is also made into a suboptimal multiple-burn guidance scheme. The FORTRAN code developed for this study has been collected together in a package named ORBPACK. ORBPACK's user manual is provided as an appendix to this report.

Goodson, Troy D.↗
NASA NTRS2001

Geomagnetic Cutoff Rigidity Computer Program: Theory, Software Description and Example

The access of charged particles to the earth from space through the geomagnetic field has been of interest since the discovery of the cosmic radiation. The early cosmic ray measurements found that cosmic ray intensity was ordered by the magnetic latitude and the concept of cutoff rigidity was developed. The pioneering work of Stoermer resulted in the theory of particle motion in the geomagnetic field, but the fundamental mathematical equations developed have 'no solution in closed form'. This difficulty has forced researchers to use the 'brute force' technique of numerical integration of individual trajectories to ascertain the behavior of trajectory families or groups. This requires that many of the trajectories must be traced in order to determine what energy (or rigidity) a charged particle must have to penetrate the magnetic field and arrive at a specified position. It turned out the cutoff rigidity was not a simple quantity but had many unanticipated complexities that required many hundreds if not thousands of individual trajectory calculations to solve. The accurate calculation of particle trajectories in the earth's magnetic field is a fundamental problem that limited the efficient utilization of cosmic ray measurements during the early years of cosmic ray research. As the power of computers has improved over the decades, the numerical integration procedure has grown more tractable, and magnetic field models of increasing accuracy and complexity have been utilized. This report is documentation of a general FORTRAN computer program to trace the trajectory of a charged particle of a specified rigidity from a specified position and direction through a model of the geomagnetic field.

Smart, D. F.↗
NASA NTRS1973

Research in mathematical theory of computation

Research progress in the following areas is reviewed: (1) new version of computer program LCF (logic for computable functions) including a facility to search for proofs automatically; (2) the description of the language PASCAL in terms of both LCF and in first order logic; (3) discussion of LISP semantics in LCF and attempt to prove the correctness of the London compilers in a formal way; (4) design of both special purpose and domain independent proving procedures specifically program correctness in mind; (5) design of languages for describing such proof procedures; and (6) the embedding of ideas in the first order checker.

Mccarthy, J.↗
NASA NTRS1979

Postseismic viscoelastic deformation and stress. Part 2: Stress theory and computation; dependence of displacement, strain, and stress on fault parameters

A viscoelastic model for deformation and stress associated with earthquakes is reported. The model consists of a rectangular dislocation (strike slip fault) in a viscoelastic layer (lithosphere) lying over a viscoelastic half space (asthenosphere). The time dependent surface stresses are analyzed. The model predicts that near the fault a significant fraction of the stress that was reduced during the earthquake is recovered by viscoelastic softening of the lithosphere. By contrast, the strain shows very little change near the fault. The model also predicts that the stress changes associated with asthenospheric flow extend over a broader region than those associated with lithospheric relaxation even though the peak value is less. The dependence of the displacements, stresses on fault parameters studied. Peak values of strain and stress drop increase with increasing fault height and decrease with fault depth. Under many circumstances postseismic strains and stresses show an increase with decreasing depth to the lithosphere-asthenosphere boundary. Values of the strain and stress at distant points from the fault increase with fault area but are relatively insensitive to fault depth.

Cohen, S. C.↗
NASA NTRS1981

On the utility of finite element theory for computational fluid dynamics

An implicit finite element numerical solution algorithm is derived for the compressible Navier-Stokes equations expressed in generalized coordinates. The theoretical basis utilizes a Galerkin-Weighted Residuals formulation, and extremization of approximation error within the context of a multipole expansion. A von Neumann analysis for a simplified form indicates the algorithm fourth- to sixth-order phase accurate, with third-order dissipation for the elementary linear element construction. Performance is improved for the algorithm constructed using quadratic interpolation. Numerical experiments for shocked duct flows are employed to optimize the several algorithm parameters. Additional numerical solutions validate algorithm accuracy and utility for aerodynamics applications.

Baker, A. J.↗
NASA NTRS1993

Theory and computation of optimal low- and medium-thrust transfers

This report presents the formulation of the optimal low- and medium-thrust orbit transfer control problem and methods for numerical solution of the problem. The problem formulation is for final mass maximization and allows for second-harmonic oblateness, atmospheric drag, and three-dimensional, non-coplanar, non-aligned elliptic terminal orbits. We setup some examples to demonstrate the ability of two indirect methods to solve the resulting TPBVP's. The methods demonstrated are the multiple-point shooting method as formulated in H. J. Oberle's subroutine BOUNDSCO, and the minimizing boundary-condition method (MBCM). We find that although both methods can converge solutions, there are trade-offs to using either method. BOUNDSCO has very poor convergence for guesses that do not exhibit the correct switching structure. MBCM, however, converges for a wider range of guesses. However, BOUNDSCO's multi-point structure allows more freedom in quesses by increasing the node points as opposed to only quessing the initial state in MBCM. Finally, we note an additional drawback for BOUNDSCO: the routine does not supply information to the users routines for switching function polarity but only the location of a preset number of switching points.

Chuang, C.-H.↗
NASA NTRS1994

Theory and computation of optimal low- and medium-thrust transfers

This report presents two numerical methods considered for the computation of fuel-optimal, low-thrust orbit transfers in large numbers of burns. The origins of these methods are observations made with the extremal solutions of transfers in small numbers of burns; there seems to exist a trend such that the longer the time allowed to perform an optimal transfer the less fuel that is used. These longer transfers are obviously of interest since they require a motor of low thrust; however, we also find a trend that the longer the time allowed to perform the optimal transfer the more burns are required to satisfy optimality. Unfortunately, this usually increases the difficulty of computation. Both of the methods described use small-numbered burn solutions to determine solutions in large numbers of burns. One method is a homotopy method that corrects for problems that arise when a solution requires a new burn or coast arc for optimality. The other method is to simply patch together long transfers from smaller ones. An orbit correction problem is solved to develop this method. This method may also lead to a good guidance law for transfer orbits with long transfer times.

Chuang, C.-H.↗
NASA NTRS1994

Theory and computation of optimal low- and medium-thrust transfers

This report describes the current state of development of methods for calculating optimal orbital transfers with large numbers of burns. Reported on first is the homotopy-motivated and so-called direction correction method. So far this method has been partially tested with one solver; the final step has yet to be implemented. Second is the patched transfer method. This method is rooted in some simplifying approximations made on the original optimal control problem. The transfer is broken up into single-burn segments, each single-burn solved as a predictor step and the whole problem then solved with a corrector step.

Chuang, C.-H.↗
NASA NTRS1997

How Difficult is it to Add 1? A Pedagogical Example of How Theory of Computing May be Useful

We show that while adding two generic b-bit integers requires = b bit operations, adding 1 to an integer requires, on average, only 2 bit operations. This fact explains why the operation of adding 1 is often separately hardware supported, and why this operation is often separately described in high-level programming languages like C++. This result shows that theoretical analysis can help in deciding which operations must be hardware supported, and thus, hopefully, will help in designing faster computers.

Hampton, Michael↗
NASA NTRS1997

How the Theory of Computing Can Help in Space Exploration

The opening of the NASA Pan American Center for Environmental and Earth Sciences (PACES) at the University of Texas at El Paso made it possible to organize the student Center for Theoretical Research and its Applications in Computer Science (TRACS). In this abstract, we briefly describe the main NASA-related research directions of the TRACS center, and give an overview of the preliminary results of student research.

Kreinovich, Vladik↗
NASA NTRS1979

Vortex development on slender missiles at supersonic speeds

A theoretical and experimental effort has been made to develop a vortex-prediction capability on circular and noncircular missiles at supersonic speeds. Predicted vortex patterns are computed by two linear-theory computer codes. One calculates the strengths and initial locations of the vortices, and the other calculates their trajectories. A short color motion picture has been produced from the calculations to illustrate the predicted vortex patterns on a typical missile. Experimental vapor-screen photographs are presented to show the longitudinal development of the vortices on a fin-control missile. Comparisons are made between these data and the predicted vortices to assess the accuracy of the theory. The theory appears to be fairly accurate in predicting the number, locations, and relative strengths of individual vortices which develop over the missile, but cannot predict vortex sheets or diffuse vorticity whenever they occur.

Allen, J. M.↗