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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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NASA NTRS2004

The Interaction of Hot and Cold Gas in the Disk and Halo of Galaxies

Most of the thermal energy in the Galaxy and perhaps most of the baryons in the Universe are found in hot (log T approximately 5.5 - 7) gas. Hot gas is detected in the local interstellar medium, in supernova remnants (SNR), the Galactic halo, galaxy clusters and the intergalactic medium (IGM). In our own Galaxy, hot gas exists in large superbubbles up to several hundred pc in diameter that locally dominate the interstellar medium (ISM) and determine its thermal and dynamic evolution. While X-ray observations using ROSAT, Chandra and XMM have allowed us to make dramatic progress in mapping out the morphology of the hot gas and in understanding some of its spectral characteristics, there remain fundamental questions that are unanswered. Chief among these questions is the way that hot gas interacts with cooler phase gas and the effects these interactions have on hot gas energetics. The theoretical investigations we proposed in this grant aim to explore these interactions and to develop observational diagnostics that will allow us to gain much improved information on the evolution of hot gas in the disk and halo of galaxies. The first of the series of investigations that we proposed was a thorough exploration of turbulent mixing layers and cloud evaporation. We proposed to employ a multi-dimensional hydrodynamical code that includes non-equilibrium ionization (NEI), radiative cooling and thermal conduction. These models are to be applied to high velocity clouds in our galactic halo that are seen to have O VI by FUSE (Sembach et ai. 2000) and other clouds for which sufficient constraining observations exist.

Slavin, Jonathan↗
NASA NTRS2004

The Influence of Solar Proton Events in Solar Cycle 23 on the Neutral Middle Atmosphere

Solar proton events (SPEs) can cause changes in constituents in the Earth's middle atmosphere. The highly energetic protons cause ionizations, excitations, dissociations, and dissociative ionizations of the background constituents, which lead to the production of HO(x) (H, OH, HO2) and NO(y) (N, NO, NO2, NO3, N2O5, HNO3, HO2NO2, ClONO2, BrONO2). The HO(x) increases lead to short-lived ozone decreases in the mesosphere and upper stratosphere due to the short lifetimes of the HO, constituents. The NO(x) increases lead to long-lived stratospheric ozone changes because of the long lifetime of NO(y) constituents in this region. Solar cycle 23 was quite active with SPEs and very large fluxes of high energy protons occurred in July and November 2000, November 200 1, and April 2002. Smaller, but still substantial, proton fluxes impacted the Earth during other months in the 1997-2003 time period. The impact of the very large SPEs on the neutral middle atmosphere during solar cycle 23 will be discussed, including the HO(x), NO(y), ozone variations and induced atmospheric transport changes. Two multi-dimensional models, the Goddard Space Flight Center (GSFC) Two-dimensional (2D) Model and the Thermosphere Ionosphere Mesosphere Electrodynamic General Circulation Model (TIME-GCM), were used in computing the influence of the SPEs. The results of the GSFC 2D Model and the TIME-GCM will be shown along with comparisons to the Upper Atmosphere Research Satellite (UARS) Halogen Occultation Experiment (HALOE) and Solar Backscatter Ultraviolet 2 (SBUV/2) instruments.

Jackman, Charles H.↗
NASA NTRS2004

Error Analysis for Discontinuous Galerkin Method for Parabolic Problems

In the proposal, the following three objectives are stated: (1) A p-version of the discontinuous Galerkin method for a one dimensional parabolic problem will be established. It should be recalled that the h-version in space was used for the discontinuous Galerkin method. An a priori error estimate as well as a posteriori estimate of this p-finite element discontinuous Galerkin method will be given. (2) The parameter alpha that describes the behavior double vertical line u(sub t)(t) double vertical line 2 was computed exactly. This was made feasible because of the explicitly specified initial condition. For practical heat transfer problems, the initial condition may have to be approximated. Also, if the parabolic problem is proposed on a multi-dimensional region, the parameter alpha, for most cases, would be difficult to compute exactly even in the case that the initial condition is known exactly. The second objective of this proposed research is to establish a method to estimate this parameter. This will be done by computing two discontinuous Galerkin approximate solutions at two different time steps starting from the initial time and use them to derive alpha. (3) The third objective is to consider the heat transfer problem over a two dimensional thin plate. The technique developed by Vogelius and Babuska will be used to establish a discontinuous Galerkin method in which the p-element will be used for through thickness approximation. This h-p finite element approach, that results in a dimensional reduction method, was used for elliptic problems, but the application appears new for the parabolic problem. The dimension reduction method will be discussed together with the time discretization method.

Kaneko, Hideaki↗
NASA NTRS2004

Analysis of Fuel Vaporization, Fuel-Air Mixing, and Combustion in Integrated Mixer-Flame Holders

Requirements to limit pollutant emissions from the gas turbine engines for the future High-Speed Civil Transport (HSCT) have led to consideration of various low-emission combustor concepts. One such concept is the Integrated Mixer-Flame Holder (IMFH). This report describes a series of IMFH analyses performed with KIVA-II, a multi-dimensional CFD code for problems involving sprays, turbulence, and combustion. To meet the needs of this study, KIVA-II's boundary condition and chemistry treatments are modified. The study itself examines the relationships between fuel vaporization, fuel-air mixing, and combustion. Parameters being considered include: mixer tube diameter, mixer tube length, mixer tube geometry (converging-diverging versus straight walls), air inlet velocity, air inlet swirl angle, secondary air injection (dilution holes), fuel injection velocity, fuel injection angle, number of fuel injection ports, fuel spray cone angle, and fuel droplet size. Cases are run with and without combustion to examine the variations in fuel-air mixing and potential for flashback due to the above parameters. The degree of fuel-air mixing is judged by comparing average, minimum, and maximum fuel/air ratios at the exit of the mixer tube, while flame stability is monitored by following the location of the flame front as the solution progresses from ignition to steady state. Results indicate that fuel-air mixing can be enhanced by a variety of means, the best being a combination of air inlet swirl and a converging-diverging mixer tube geometry. With the IMFH configuration utilized in the present study, flashback becomes more common as the mixer tube diameter is increased and is instigated by disturbances associated with the dilution hole flow.

Deur, J. M.↗
NASA NTRS2003

Coordinated turn-and-reach movements. II. Planning in an external frame of reference

The preceding study demonstrated that normal subjects compensate for the additional interaction torques generated when a reaching movement is made during voluntary trunk rotation. The present paper assesses the influence of trunk rotation on finger trajectories and on interjoint coordination and determines whether simultaneous turn-and-reach movements are most simply described relative to a trunk-based or an external reference frame. Subjects reached to targets requiring different extents of arm joint and trunk rotation at a natural pace and quickly in normal lighting and in total darkness. We first examined whether the larger interaction torques generated during rapid turn-and-reach movements perturb finger trajectories and interjoint coordination and whether visual feedback plays a role in compensating for these torques. These issues were addressed using generalized Procrustes analysis (GPA), which attempts to overlap a group of configurations (e.g., joint trajectories) through translations and rotations in multi-dimensional space. We first used GPA to identify the mean intrinsic patterns of finger and joint trajectories (i.e., their average shape irrespective of location and orientation variability in the external and joint workspaces) from turn-and-reach movements performed in each experimental condition and then calculated their curvatures. We then quantified the discrepancy between each finger or joint trajectory and the intrinsic pattern both after GPA was applied individually to trajectories from a pair of experimental conditions and after GPA was applied to the same trajectories pooled together. For several subjects, joint trajectories but not finger trajectories were more curved in fast than slow movements. The curvature of both joint and finger trajectories of turn-and-reach movements was relatively unaffected by the vision conditions. Pooling across speed conditions significantly increased the discrepancy between joint but not finger trajectories for most subjects, indicating that subjects used different patterns of interjoint coordination in slow and fast movements while nevertheless preserving the shape of their finger trajectory. Higher movement speeds did not disrupt the arm joint rotations despite the larger interaction torques generated. Rather, subjects used the redundant degrees of freedom of the arm/trunk system to achieve similar finger trajectories with differing joint configurations. We examined finger movement patterns and velocity profiles to determine the frame of reference in which turn-and-reach movements could be most simply described. Finger trajectories of turn-and-reach movements had much larger curvatures and their velocity profiles were less smooth and less bell-like in trunk-based coordinates than in external coordinates. Taken together, these results support the conclusion that turn-and-reach movements are controlled in an external frame of reference.

NASA Discipline Neuroscience↗
NASA NTRS1998

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

Wood, William A.↗
NASA NTRS2004

Evidence from massive siderite beds for a CO2-rich atmosphere before approximately 1.8 billion years ago

It is generally thought that, in order to compensate for lower solar flux and maintain liquid oceans on the early Earth, methane must have been an important greenhouse gas before approximately 2.2 billion years (Gyr) ago. This is based upon a simple thermodynamic calculation that relates the absence of siderite (FeCO3) in some pre-2.2-Gyr palaeosols to atmospheric CO2 concentrations that would have been too low to have provided the necessary greenhouse effect. Using multi-dimensional thermodynamic analyses and geological evidence, we show here that the absence of siderite in palaeosols does not constrain atmospheric CO2 concentrations. Siderite is absent in many palaeosols (both pre- and post-2.2-Gyr in age) because the O2 concentrations and pH conditions in well-aerated soils have favoured the formation of ferric (Fe3+)-rich minerals, such as goethite, rather than siderite. Siderite, however, has formed throughout geological history in subsurface environments, such as euxinic seas, where anaerobic organisms created H2-rich conditions. The abundance of large, massive siderite-rich beds in pre-1.8-Gyr sedimentary sequences and their carbon isotope ratios indicate that the atmospheric CO2 concentration was more than 100 times greater than today, causing the rain and ocean waters to be more acidic than today. We therefore conclude that CO2 alone (without a significant contribution from methane) could have provided the necessary greenhouse effect to maintain liquid oceans on the early Earth.

Greenhouse Effect↗
NASA NTRS2004

Chemical Ionization Mass Spectrometry-Based Measurements of HO2 and RO2 During TRACE-P

The Transport and Chemical Evolution over the Pacific (TRACE-P) mission extends NASA's Global Tropospheric Experiment (GTE) series of campaigns. TRACE-P was an aircraft-based campaign that was part of a larger ground-based and aircraft-based program (APARE) under the auspices of the International Global Atmospheric Chemistry (IGAC) program. TRACE-P was designed to (1) determine the chemical composition of Asian outflow over the western Pacific, and to (2) determine the chemical evolution of the Asian outflow. These objectives were addressed through a variety of observations and numerical modeling exercises. In particular, the goals included sampling strategies that would improve understanding of the budgets of odd hydrogen species (OH and HO2), budgets of NOx (NO, NO2, and their reservoirs), and impacts of oxidants produced in the outflow on air quality in the United States. The NASA DC-8 and P-3B aircraft were deployed in the March and April, 2001 out of primary bases of operation in Hong Kong and Yokota Air Base in Japan. These two aircraft have complementary capabilities which allow high altitude and long range impacts, as well as low altitude, local impacts to be assessed. In order to quantify the composition and evolution of Asian outflow, it is important to quantify as many species as possible including photochemically active species (e.g. NO2, CH2O, O3, acetone, etc.), sources species (VOCs, CO, NOx, SO2, aerosols), reactive intermediates including free radicals (OH, HO2, RO2, and their reservoirs), and end products (nitric acid, sulfuric acid, secondary aerosols, etc.). The more complete the measurement suite, the more tightly constrained the numerical modeling can be (within the uncertainties of the measurements). The numerical models range in sophistication from simple steady state box models (as employed in this study) to multi-dimensional chemical transport models. Data were collected on approximately 20 flights of the DC-8 and 21 flights of the P-3B. Observations from both aircraft were used in the present analysis, but primarily focused on the P-3B flights since that was the platform on which the peroxy radical instrumentation was based.

Cantrell, Christopher A.↗
NASA NTRS2004

Overview 2003 of NASA Multi-D Stirling Convertor Development and DOE and NASA Stirling Regenerator R and D Efforts

This paper will report on (1) continuation through the 3rd year of a NASA grant for multi-dimensional Stirling CFD code development and validation, (2) continuation through the 3rd and final year of a Department of Energy, Golden Field Office (DOE) regenerator research effort. Results of the NASA multi-D code development effort and the DOE regenerator research efforts will be summarized. Early results and planning for the new regenerator microfabrication contract will also be discussed.

Twe, Roy↗
NASA NTRS2004

Advanced Technology Development for Stirling Convertors

A high-efficiency Stirling Radioisotope Generator (SRG) for use on potential NASA Space Science missions is being developed by the Department of Energy, Lockheed Martin, Stirling Technology Company, and NASA Glenn Research Center (GRC). These missions may include providing spacecraft onboard electric power for deep space missions or power for unmanned Mars rovers. GRC is also developing advanced technology for Stirling convertors, aimed at substantially improving the specific power and efficiency of the convertor and the overall power system. Performance and mass improvement goals have been established for second- and thirdgeneration Stirling radioisotope power systems. Multiple efforts are underway to achieve these goals, both in-house at GRC and under various grants and contracts. The status and results to date for these efforts will be discussed in this paper. Cleveland State University (CSU) is developing a multi-dimensional Stirling computational fluid dynamics code, capable of modeling complete convertors. A 2-D version of the code is now operational, and validation efforts at both CSU and the University of Minnesota are complementing the code development. A screening of advanced superalloy, refractory metal alloy, and ceramic materials has been completed, and materials have been selected for creep and joining characterization as part of developing a high-temperature heater head. A breadboard characterization is underway for an advanced controller using power electronics for active power factor control with a goal of eliminating the heavy tuning capacitors that are typically needed to achieve near unity power factors. Key Stirling developments just initiated under recent NRA (NASA Research Announcement) awards will also be discussed. These include a lightweight convertor to be developed by Sunpower Inc. and an advanced microfabricated regenerator to be done by CSU.

Thieme, Lanny G.↗
NASA NTRS2004

A Numerical Investigation of the Extinction of Low Strain Rate Diffusion Flames by an Agent in Microgravity

Our goal has been to investigate the influence of both dilution and radiation on the extinction process of nonpremixed flames at low strain rates. Simulations have been performed by using a counterflow code and three radiation models have been included in it, namely, the optically thin, the narrowband, and discrete ordinate models. The counterflow flame code OPPDIFF was modified to account for heat transfer losses by radiation from the hot gases. The discrete ordinate method (DOM) approximation was first suggested by Chandrasekhar for solving problems in interstellar atmospheres. Carlson and Lathrop developed the method for solving multi-dimensional problem in neutron transport. Only recently has the method received attention in the field of heat transfer. Due to the applicability of the discrete ordinate method for thermal radiation problems involving flames, the narrowband code RADCAL was modified to calculate the radiative properties of the gases. A non-premixed counterflow flame was simulated with the discrete ordinate method for radiative emissions. In comparison with two other models, it was found that the heat losses were comparable with the optically thin and simple narrowband model. The optically thin model had the highest heat losses followed by the DOM model and the narrow-band model.

Puri, Ishwar K.↗
NASA NTRS1995

Potential ligand-binding residues in rat olfactory receptors identified by correlated mutation analysis

A family of G-protein-coupled receptors is believed to mediate the recognition of odor molecules. In order to identify potential ligand-binding residues, we have applied correlated mutation analysis to receptor sequences from the rat. This method identifies pairs of sequence positions where residues remain conserved or mutate in tandem, thereby suggesting structural or functional importance. The analysis supported molecular modeling studies in suggesting several residues in positions that were consistent with ligand-binding function. Two of these positions, dominated by histidine residues, may play important roles in ligand binding and could confer broad specificity to mammalian odor receptors. The presence of positive (overdominant) selection at some of the identified positions provides additional evidence for roles in ligand binding. Higher-order groups of correlated residues were also observed. Each group may interact with an individual ligand determinant, and combinations of these groups may provide a multi-dimensional mechanism for receptor diversity.

NASA Discipline Neuroscience↗
NASA NTRS2005

Supporting Development for the Stirling Radioisotope Generator and Advanced Stirling Technology Development at NASA Glenn

A high-efficiency, 110-W(sub e) (watts electric) Stirling Radioisotope Generator (SRG110) for possible use on future NASA Space Science missions is being developed by the Department of Energy, Lockheed Martin, Stirling Technology Company (STC), and NASA Glenn Research Center (GRC). Potential mission use includes providing spacecraft onboard electric power for deep space missions and power for unmanned Mars rovers. GRC is conducting an in-house supporting technology project to assist in SRG110 development. One-, three-, and six-month heater head structural benchmark tests have been completed in support of a heater head life assessment. Testing is underway to evaluate the key epoxy bond of the permanent magnets to the linear alternator stator lamination stack. GRC has completed over 10,000 hours of extended duration testing of the Stirling convertors for the SRG110, and a three-year test of two Stirling convertors in a thermal vacuum environment will be starting shortly. GRC is also developing advanced technology for Stirling convertors, aimed at substantially improving the specific power and efficiency of the convertor and the overall generator. Sunpower, Inc. has begun the development of a lightweight Stirling convertor, under a NASA Research Announcement (NRA) award, that has the potential to double the system specific power to about 8 W(sub e) per kilogram. GRC has performed random vibration testing of a lowerpower version of this convertor to evaluate robustness for surviving launch vibrations. STC has also completed the initial design of a lightweight convertor. Status of the development of a multi-dimensional computational fluid dynamics code and high-temperature materials work on advanced superalloys, refractory metal alloys, and ceramics are also discussed.

Thieme, Lanny G.↗
NASA NTRS2005

Applications and Improvement of a Coupled, Global and Cloud-Resolving Modeling System

Recently Grabowski (2001) and Khairoutdinov and Randall (2001) have proposed the use of 2D CFWs as a "super parameterization" [or multi-scale modeling framework (MMF)] to represent cloud processes within atmospheric general circulation models (GCMs). In the MMF, a fine-resolution 2D CRM takes the place of the single-column parameterization used in conventional GCMs. A prototype Goddard MMF based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM) is now being developed. The prototype includes the fvGCM run at 2.50 x 20 horizontal resolution with 32 vertical layers from the surface to 1 mb and the 2D (x-z) GCE using 64 horizontal and 32 vertical grid points with 4 km horizontal resolution and a cyclic lateral boundary. The time step for the 2D GCE would be 15 seconds, and the fvGCM-GCE coupling frequency would be 30 minutes (i.e. the fvGCM physical time step). We have successfully developed an fvGCM-GCE coupler for this prototype. Because the vertical coordinate of the fvGCM (a terrain-following floating Lagrangian coordinate) is different from that of the GCE (a z coordinate), vertical interpolations between the two coordinates are needed in the coupler. In interpolating fields from the GCE to fvGCM, we use an existing fvGCM finite- volume piecewise parabolic mapping (PPM) algorithm, which conserves the mass, momentum, and total energy. A new finite-volume PPM algorithm, which conserves the mass, momentum and moist static energy in the z coordinate, is being developed for interpolating fields from the fvGCM to the GCE. In the meeting, we will discuss the major differences between the two MMFs (i.e., the CSU MMF and the Goddard MMF). We will also present performance and critical issues related to the MMFs. In addition, we will present multi-dimensional cloud datasets (i.e., a cloud data library) generated by the Goddard MMF that will be provided to the global modeling community to help improve the representation and performance of moist processes in climate models and to improve our understanding of cloud processes globally (the software tools needed to produce cloud statistics and to identify various types of clouds and cloud systems from both high-resolution satellite and model data will be also presented).

Tao, W.-K.↗
NASA NTRS2005

Using CFD as a Rocket Injector Design Tool: Recent Progress at Marshall Space Flight Center

New programs are forcing American propulsion system designers into unfamiliar territory. For instance, industry s answer to the cost and reliability goals set out by the Next Generation Launch Technology Program are engine concepts based on the Oxygen- Rich Staged Combustion Cycle. Historical injector design tools are not well suited for this new task. The empirical correlations do not apply directly to the injector concepts associated with the ORSC cycle. These legacy tools focus primarily on performance with environment evaluation a secondary objective. Additionally, the environmental capability of these tools is usually one-dimensional while the actual environments are at least two- and often three-dimensional. CFD has the potential to calculate performance and multi-dimensional environments but its use in the injector design process has been retarded by long solution turnaround times and insufficient demonstrated accuracy. This paper has documented the parallel paths of program support and technology development currently employed at Marshall Space Flight Center in an effort to move CFD to the forefront of injector design. MSFC has established a long-term goal for use of CFD for combustion devices design. The work on injector design is the heart of that vision and the Combustion Devices CFD Simulation Capability Roadmap that focuses the vision. The SRL concept, combining solution fidelity, robustness and accuracy, has been established as a quantitative gauge of current and desired capability. Three examples of current injector analysis for program support have been presented and discussed. These examples are used to establish the current capability at MSFC for these problems. Shortcomings identified from this experience are being used as inputs to the Roadmap process. The SRL evaluation identified lack of demonstrated solution accuracy as a major issue. Accordingly, the MSFC view of code validation and current MSFC-funded validation efforts were discussed in some detail. The objectives of each effort were noted. Issues relative to code validation for injector design were discussed in some detail. The requirement for CFD support during the design of the experiment was noted and discussed in terms of instrumentation placement and experimental rig uncertainty. In conclusion, MSFC has made significant progress in the last two years in advancing CFD toward the goal of application to injector design. A parallel effort focused on program support and technology development via the SCIT Task have enabled the progress.

Tucker, Kevin↗
NASA NTRS1996

Quantifying Transport Between the Tropical and Mid-Latitude Lower Stratosphere

Because exchange with the tropics is slower than multi-dimensional models generally assume, ozone at mid-latitudes apears to be more sensitive to elevated levels of industrial chlorine than currently predicted. Nevertheless, approximately 45% of air in the tropical ascent region at 21 km has been entrained from mid-latitudes, implying that emissions from supersonic aircraft could deplete ozone in the middle stratosphere.

stratosphere↗
NASA NTRS2003

Approaches to Cycle Analysis and Performance Metrics

The following notes were prepared as part of an American Institute of Aeronautics and Astronautics (AIAA) sponsored short course entitled Air Breathing Pulse Detonation Engine (PDE) Technology. The course was presented in January of 2003, and again in July of 2004 at two different AIAA meetings. It was taught by seven instructors, each of whom provided information on particular areas of PDE research. These notes cover two areas. The first is titled Approaches to Cycle Analysis and Performance Metrics. Here, the various methods of cycle analysis are introduced. These range from algebraic, thermodynamic equations, to single and multi-dimensional Computational Fluid Dynamic (CFD) solutions. Also discussed are the various means by which performance is measured, and how these are applied in a device which is fundamentally unsteady. The second topic covered is titled PDE Hybrid Applications. Here the concept of coupling a PDE to a conventional turbomachinery based engine is explored. Motivation for such a configuration is provided in the form of potential thermodynamic benefits. This is accompanied by a discussion of challenges to the technology.

Parson, Daniel E.↗
NASA NTRS1997

Guidance of Nonlinear Systems

The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.

Meyer, George↗