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All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Active and Passive Radiative Transfer Modeling of the Olympic Mountains Experiment

Sensor forward models are an important tool for interpreting remote sensing observations of geophysical phenomena. By implementing a three-dimensional framework, we can simulate and analyze observations from various sensors on disparate platforms. To demonstrate our model framework, we simulate observations from the Olympic Mountains Experiment (OLYMPEX). The use of cloud model simulations allows us to understand sensor response to cloud ice, falling snow, and other processes and features, and the application of model tools to observations allows us to quantify precipitation.MIIST 3D Forward ModelThe Multi-Instrument Inverse Solver Testbed(MIIST) uses the Atmospheric Radiative TransferSimulator (ARTS) for solving the vector radiativetransfer (RT) equation in up to three spatialdimensions within a spherical geometry• Gas absorptiono Line-by-line calculationso Fast transmittance tables• Hydrometeor scattering solverso Discrete ordinateo RT4 (Evans, 1D)o Radar Single Scattering (1D or 3D)o Monte Carlo (3D)Scattering TablesHigh-fidelity hydrometeor scatteringtables are necessary for accurateand consistent forward modeling ofmulti-frequency observations• Requires full Stokes matriceso And absorption vector• Randomly oriented particleso Discrete Dipole Approximationo Characteristic Basis Function Method(coming soon)• Horizontally-oriented plateso Invariant Imbedding T-matrix MethodCloud Resolving SimulationsCloud resolving simulations (e.g.,NU-WRF) supply output consistentwith ARTS needs• Atmospheric Informationo Temperatureo Pressure / heighto Water vapor• Hydrometeor Profileso ARTS architecture ripe for explicit binmicrophysics• Examples use Morrison 2M schemeThe Olympic Mountains Experiment (OLYMPEX)Validation for GPM of mid-latitudefrontal systems approaching nearcoastalmountains from the ocean• Large collection of ground-based andairborne sensorso Radarso Radiometerso In situ• Contemporaneous with RADEXo Two sets of radar at same frequenciesRadiometer Simulation (3 km NUWRF, 20151203, 15:00)2018.12.14 7Simulate 166 GHz polarizationdifference• Corresponds to the presence of aligned icecrystals• Look at trends for both simulations andobservations• Simulations can tolerate lower resolutiono Larger domainSimulations from Observations: OLYMPEXSimulate sensor response usinggeophysical retrievals as input• Single frequency radar retrievals• Multiple scattering enhancementapparent at W band• Spatially dependent phenomenonModeling Application: 1D Retrievals03 December 2015• DC-8 and ER-2 flightso Focus on APR-3 (DC-8)• Citationo Stacked microphysics legso Qualitative comparisonso Range of frozen habitso Presence of supercooledliquid cloudsResults• Retrievals match probeso Good qualitative match• Bands of increasedreflectivity correspond tolarge Dm and highaggregate fraction• Significant amounts ofsupercooled liquid water

Adams, Ian S.↗
NASA NTRS2023

3D Printed Substrate

In preparation for long-term, manned, deep space missions, NASA requires a sustainable system for crop and food production. This system has a variety of benefits, including a fresh food supply, improvements in air quality, a lower need to resupply and psychological benefits for the gardeners. Specifically, NASA is attempting to improve and iterate their Vegetable Production System (VEGGIE), a plant growth unit currently aboard the International Space Station (ISS). The VEGGIE unit is highly dependent on a variety of factors, including passive water delivery, growth lights, rooting pillows and cabin conditions. While previous teams have improved and redesigned water reservoirs, the primary objective of the project was to create a new substrate unit to replace the current rooting pillow design. The current design consists of an electrostatic bag filled with arcillite and a slow-release fertilizer pellet. The prototype design retains the fertilizer pellet for nutrient consistency, however the outer bag and arcillite fillings have been replaced with a 3D printed lattice block. This lattice block has several key points that allow it to function in similar ways to the current design: 1. The lattice planes are porous, with each pore offset such that the overall porosity is the same as the arcillite filling. 2. The block demonstrates a wicking nature and is able to pull water upwards towards the roots. This minimizes time needed to integrate with the existing water reservoir. 3. The filament used is highly flexible and is able to pull apart to accommodate root growth. 4. The lattice planes are connected by microfibers left behind from the printing process. These fibers provide support for the growing roots and keep the lattice planes properly aligned. The substrate block design seeks to reduce the payload costs by being entirely 3D printed. While filament would still need to be provided to the ISS, it is far less expensive than shipping arcillite due to the significantly lower weight. The final design has iterated the lattice plane concept and utilizes vertically placed planes with pores running parallel to the water reservoir. This design has reliably shown water uptake and retention and has been successful in growing multiple romaine lettuce plants. Future work should include further growth testing using multiple plant species, compost and reusability testing, food safety testing and microgravity growth testing.

Affan Bhutta↗
NASA NTRS1983

The collapse of the local, Spitzer-Haerm formulation and a global-local generalization for heat flow in an inhomogeneous, fully ionized plasma

The breakdown of the classical (CBES) field aligned transport relations for electrons in an inhomogeneous, fully ionized plasma as a mathematical issue of radius of convergence is addressed, the finite Knudsen number conditions when CBES results are accurate is presented and a global-local (GL) way to describe the results of Coulomb physics moderated conduction that is more nearly appropriate for astrophysical plasmas are defined. This paper shows the relationship to and points of departure of the present work from the CBES approach. The CBES heat law in current use is shown to be an especially restrictive special case of the new, more general GL result. A preliminary evaluation of the dimensionless heat function, using analytic formulas, shows that the dimensionless heat function profiles versus density of the type necessary for a conduction supported high speed solar wind appear possible.

Scudder, J. D.↗
NASA NTRS1998

The prokaryote-to-eukaryote transition reflected in the evolution of the V/F/A-ATPase catalytic and proteolipid subunits

Changes in the primary and quarternary structure of vacuolar and archaeal type ATPases that accompany the prokaryote-to-eukaryote transition are analyzed. The gene encoding the vacuolar-type proteolipid of the V-ATPase from Giardia lamblia is reported. Giardia has a typical vacuolar ATPase as observed from the common motifs shared between its proteolipid subunit and other eukaryotic vacuolar ATPases, suggesting that the former enzyme works as a hydrolase in this primitive eukaryote. The phylogenetic analyses of the V-ATPase catalytic subunit and the front and back halves of the proteolipid subunit placed Giardia as the deepest branch within the eukaryotes. Our phylogenetic analysis indicated that at least two independent duplication and fusion events gave rise to the larger proteolipid type found in eukaryotes and in Methanococcus. The spatial distribution of the conserved residues among the vacuolar-type proteolipids suggest a zipper-type interaction among the transmembrane helices and surrounding subunits of the V-ATPase complex. Important residues involved in the function of the F-ATP synthase proteolipid have been replaced during evolution in the V-proteolipid, but in some cases retained in the archaeal A-ATPase. Their possible implication in the evolution of V/F/A-ATPases is discussed.

NASA Discipline Exobiology↗
NASA NTRS2024

Filament Wound Composite Analysis Using the NASA Multiscale Analysis Tool (NASMAT) and Finite Element Analysis

Fiber reinforced composite materials, owing to their tailorable thermomechanical and functional properties, allow one to produce a structure that is stronger, stiffer, and lighter than its metal counterpart while performing the same function, yielding a more efficient structure. This not only allows for the improvement of current technologies like aircraft structures, but also enables new technologies like gaseous hydrogen storage for mobility applications, which are otherwise impractical when manufactured using traditional metals due to weight and space restrictions or material embrittlement. However, the use of composites imposes greater design and manufacturing challenges on an engineer, since they are heterogenous, having a distinct structure across multiple length scale, behave generally anisotropically at the structural level and require complex manufacturing and processing methods. Capturing this complex behavior requires detailed numerical simulations, including the modeling of microstructural features like undulations, voids, and fiber alignment. In this paper, multiple repeating unit cells (RUCs), representing filament wound composites, are developed (via a script provided in the Appendix) and analyzed. The refinement of these RUCs is varied, and the analyses are performed using both the Abaqus finite element software and the NASA Multiscale Analysis Tool (NASMAT). A study is undertaken to compare the predicted effective elastic properties of the wound RUC to a laminate representation of the wound RUC, which neglects the undulations. Additionally, two different sets of periodic boundary conditions (PBCs) have been examined. One approximates the real boundary conditions using a standard approach and the other represents the PBCs exactly through the use of an offset. Lastly, a comparison of the local elastic stress fields is made among the models and approaches. Since wound structures are often approximated as laminated structures, it is important to understand the degree to which this assumption is valid, namely by first comparing the elastic constants and local elastic fields. This will provide, on the one hand, information concerning the bulk mechanical behavior and, on the other hand, insights concerning local load distributions and likely damage initiation sites.

Composites↗
NASA NTRS2008

Breadboard Signal Processor for Arraying DSN Antennas

A recently developed breadboard version of an advanced signal processor for arraying many antennas in NASA s Deep Space Network (DSN) can accept inputs in a 500-MHz-wide frequency band from six antennas. The next breadboard version is expected to accept inputs from 16 antennas, and a following developed version is expected to be designed according to an architecture that will be scalable to accept inputs from as many as 400 antennas. These and similar signal processors could also be used for combining multiple wide-band signals in non-DSN applications, including very-long-baseline interferometry and telecommunications. This signal processor performs functions of a wide-band FX correlator and a beam-forming signal combiner. [The term "FX" signifies that the digital samples of two given signals are fast Fourier transformed (F), then the fast Fourier transforms of the two signals are multiplied (X) prior to accumulation.] In this processor, the signals from the various antennas are broken up into channels in the frequency domain (see figure). In each frequency channel, the data from each antenna are correlated against the data from each other antenna; this is done for all antenna baselines (that is, for all antenna pairs). The results of the correlations are used to obtain calibration data to align the antenna signals in both phase and delay. Data from the various antenna frequency channels are also combined and calibration corrections are applied. The frequency-domain data thus combined are then synthesized back to the time domain for passing on to a telemetry receiver

Jongeling, Andre↗
NASA NTRSDate not supplied

Leveraging Nurse Informaticists for Development of the Impact Tool

The American Nurses Association (ANA) defines nursing informatics as the integration of “nursing science, computer science, and information science to manage and communicate data, information, knowledge, and wisdom in nursing practice. [1]” In additional to nursing education and clinical experience, this field requires additional education in areas of data analysis, database management, and clinical information systems. Nursing informaticists help bridge the communication gap between clinical and technical stakeholders which help align common goals. NASA is currently developing a new medical system trade analysis and decision support tool called IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces). The development team is comprised of multiple specialties including but not limited to clinicians (pharmacists, physicians, and nurse informaticists), software and program developers, human factors experts, and engineers. The nurse informaticists play a significant role in the development, operation, and results interpretation of IMPACT. Their expert knowledge and skills in both clinical nursing, information science, and database management place them in a unique position to collaborate and integrate with the clinical, engineering, and software development members of the team to achieve a cohesive, functional, and user-friendly model.

Lynn Boley↗
NASA NTRS1979

Proton-driven electromagnetic instabilities in high-speed solar wind streams

Electromagnetic instabilities of the field-aligned, right-hand circularly polarized magnetosonic wave and the left-hand circularly polarized Alfven wave driven by two drifted proton components are analyzed for model parameters determined from Imp 7 solar wind proton data measured during high-speed flow conditions. Growth rates calculated using bi-Lorentzian forms for the main and beam proton as well as core and halo electron velocity distributions do not differ significantly from those calculated using bi-Maxwellian forms. Using distribution parameters determined from 17 measured proton spectra, we show that considering the uncertainties the magnetosonic wave may be linearly stable and the Alfven wave is linearly unstable. Because proton velocity distribution function shapes are observed to persist for times long compared to the proton gyroperiod, the latter result suggests that linear stability theory fails for proton-driven ion cyclotron waves in the high-speed solar wind.

Abraham-Shrauner, B.↗
NASA NTRS1983

Ionospheric and Birkeland current distributions inferred from the MAGSAT magnetometer data

Ionospheric and field-aligned sheet current density distributions are presently inferred by means of MAGSAT vector magnetometer data, together with an accurate magnetic field model. By comparing Hall current densities inferred from the MAGSAT data and those inferred from simultaneously recorded ground based data acquired by the Scandinavian magnetometer array, it is determined that the former have previously been underestimated due to high damping of magnetic variations with high spatial wave numbers between the ionosphere and the MAGSAT orbit. Among important results of this study is noted the fact that the Birkeland and electrojet current systems are colocated. The analyses have shown a tendency for triangular rather than constant electrojet current distributions as a function of latitude, consistent with the statistical, uniform regions 1 and 2 Birkeland current patterns.

Zanetti, L. J.↗
NASA NTRSDate not supplied

Using Systems Engineering to Develop an Integrated Crew Health and Performance System to Mitigate Risk for Human Exploration Missions

New space exploration missions are currently being designed to take humanity beyond low Earth orbit (LEO) to cis-lunar space, the lunar surface, and eventually to Mars. These missions carry increased risks due to a number of factors, including distance from Earth, exposure to deep space hazards, reduced capacity and ability to resupply and evacuate, and increased communication delays. As distance from Earth grows and mission length increases, a growing proportion of mission risk can be attributed to the “human system.” Almost twenty years ago, the Institute of Medicine in the United States recommended the early and complete integration of the human system into the spacecraft and mission design process to mitigate this increased risk inherent in exploration missions. Exploration missions will require increasing levels of crew self-sufficiency that will challenge the current operational paradigms established in LEO. Enabling progressive Earth independence requires management of the increasingly complex interactions among spacecraft systems and integration of all the data and functions that affect human health and performance into one coordinated system –the Crew Health and Performance (CHP) system. This system is a critical spacecraft system that is analogous to other systems such as propulsion, guidance and navigation, or avionics. Design and integration of the CHP system requires the evidence-based merger of typically disparate disciplines such as medicine, human factors, and life support system design, using systems engineering (SE) practices. SE provides traceability of spacecraft requirements and enables reliable and repeatable trade space analysis of the many competing options for hardware and software to be included in the mission architecture. The approach described here enables spacecraft and mission designers to align the scope of a CHP system with mission specific requirements, decrease risk to the crew, and increase the probability of mission success.

Kerry McGuire↗
NASA NTRS1991

A grid-independent approximate Riemann solver with applications to the Euler and Navier-Stokes equations

A new two-dimensional approximate Riemann solver has been developed that obtains fluxes on grid faces via wave decomposition. By utilizing information propagation in the velocity-difference directions rather than in the grid-normal directions, this flux function more appropriately interprets and hence more sharply resolves shock and shear waves when they lie oblique to the grid. The model uses five waves to describe the difference in states at a grid face. Two acoustic waves, one shear wave, and one entropy wave propagate in the direction defined by the local velocity difference vector, while the fifth wave is a shear wave that propagates at a right angle to the other four. Test cases presented include a shock reflecting off a wall, a pure shear wave, supersonic flow over an airfoil, and viscous separated airfoil flow. Results using the new model give significantly sharper shock and shear contours than a grid-aligned solver. Navier-Stokes computations over an aifoil show reduced pressure distortions in the separated region as a result of the grid-independent upwinding.

Rumsey, Christopher L.↗
NASA NTRS1998

Auroral Microphysics Rocket (AMICIST) and Reflight of the Phaze Sounding Rocket

This grant was originally awarded for the flight of the AMICIST sounding rocket. However, upon launch failure of the PHAZE rocket, additional resources were placed in this grant to cover the launch of the PHAZE II rocket. AMICIST was successfully launched from the Poker Flat Range on February 24, 1995, and the PHAZE II was successfully launched also from the Poker Flat Range on February 10, 1997. The major objective of the AMICIST flight was to investigate the bursts of transverse ion acceleration occurring during aurora, commonly known as Lower Hybrid Solitary Structures, with the flight of two scientific payloads to unravel space from time effects. The data clearly showed that the structures of ion acceleration were a spatial phenomena having a scale size transverse to the local magnetic field of about 100 m. On the other hand, structures in the auroral electrons were generally observed on this flight to be temporal features that occurred at the same time at the two payloads separated by a few kilometers. The primary objective of the PHAZE rocket flight was to further study the temporal features of auroral electron precipitation having many electron detectors, some fixed in energy, that could study the distribution function of the auroral electrons on time scales of a fraction of a millisecond. A important paper on this topic has just been submitted for publication which uses the PHAZE data to show that the potential structure (electric field parallel to the magnetic field) that accelerates the auroral electrons within one Earth radius of the ground, is not static, but rather fluctuates with frequencies close to the local proton and hydrogen gyrofrequencies. The fluctuation appears to be an actual turning on and off of the electric field at these frequencies. When the potential is turned off, ambient electrons can enter the region and be accelerated along B when the potential is on creating field- aligned bursts which manifest themselves as flickering aurora seen from the ground. The on/off model can explain many of the dynamic features of the aurora which have been unexplained since man first looked up at the visual display. Much needs to be done yet to understand how ions couple into this process.

Arnoldy Roger L.↗
NASA NTRS2025

Enhancing Nasa Sounding Rocket Capabilities Through Composite Material Adoption

Sounding rockets are a suborbital research platform employed by NASA for heliophysics, astrophysics, and geospace science investigations, and for technology development. They follow semi-parabolic trajectories and are launched using surplus military, and commercial, solid-propellant rocket motors. NASA sounding rocket payloads are comprised of standard, modular subassemblies, designed to perform specific functions critical to achieving mission success criteria. Since the program’s inception, payload length and mass have trended upwards, limiting the capability of the platform to reach exospheric apogees and decreasing the time above critical altitudes to observe solar and celestial targets. To offset this trend, composite materials may be of use in payload and subsystem design to decrease payload mass. This investigation seeks to understand if there is a practical benefit to introducing composite materials on the NSRP by assessing mission specific impacts to those missions conducted in fiscal year 2024. To accurately estimate the mass of a composites-based payload, a standard subsystem (NIACS) underwent structural reconfiguration. Materials were selected that align with NSRP design, manufacturing, and testing standards. NIACS reconfiguration resulted in a mass reduction of 19.6% which was then applied to the payload system in entirety. Using vehicle performance carpet plots, delta apogee and time above the Kármán line were determined. Performance improvements were then evaluated against that mission’s success criteria to determine if that mission would have benefitted from using composite materials. On average, each mission would have gained 59.8 kilometers apogee and 62.9 seconds above the Kármán line. However, only nine of the seventeen missions would have benefitted from these performance improvements. Two of the missions could have used a lower-impulse launch vehicle to achieve mission success. Upleg stability met programmatic criteria; downleg instability and dynamic pressure improved, showing that ballast would not offset the mass reduction of using composite materials. Cost analysis showed that production costs will increase 39%. For the two missions that could have used a lower-impulse launch vehicle, the cost of the launch vehicle would have offset payload production costs. In summary, composite materials are not recommended for universal use on NASA sounding rocket payloads due to unclear programmatic benefits and added cost. However, they are justified for optical astrophysics and heliophysics missions, high-apogee (exosphere) requirements, or when they reduce payload costs versus higher impulse launch vehicles. Reflown, recoverable subsystems should use composites to enhance apogee and observation time.

Robert Henry Burth↗
NASA NTRS1992

Electrostatic waves due to field-aligned electron beams in the low-latitude boundary layer

Mass-resolved ion, electron, and plasma wave data obtained from several low-latitude boundary layer (LLBL) crossings by the AMPTE CCE satellite are analyzed. The data clearly separate the LLBL from the adjacent magnetosheath and magnetosphere. Attention was focused on wave-particle interactions involving electrons. Electron beams were found to be present in the LLBL during the southward interplanetary magnetic field, along with a simultaneous enhancement of electrostatic waves with parallel polarization. Linear theory analysis shows that for plasma conditions in the LLBL, electron beams are unstable to electrostatic waves that propagate parallel to the local magnetic field, in agreement with observations. A numerical simulation study of the beam-plasma interaction in the LLBL shows that the instability saturates by thermalization of the beam but that a beamlike structure can still remain in the electron distribution for certain initial parameters. It is suggested that peaks in the electron velocity distribution function may be found in the LLBL away from the beam source region.

Peroomian, V.↗
NASA NTRS1993

Two-dimensional spatiotemporal coding of linear acceleration in vestibular nuclei neurons

Response properties of vertical (VC) and horizontal (HC) canal/otolith-convergent vestibular nuclei neurons were studied in decerebrate rats during stimulation with sinusoidal linear accelerations (0.2-1.4 Hz) along different directions in the head horizontal plane. A novel characteristic of the majority of tested neurons was the nonzero response often elicited during stimulation along the "null" direction (i.e., the direction perpendicular to the maximum sensitivity vector, Smax). The tuning ratio (Smin gain/Smax gain), a measure of the two-dimensional spatial sensitivity, depended on stimulus frequency. For most vestibular nuclei neurons, the tuning ratio was small at the lowest stimulus frequencies and progressively increased with frequency. Specifically, HC neurons were characterized by a flat Smax gain and an approximately 10-fold increase of Smin gain per frequency decade. Thus, these neurons encode linear acceleration when stimulated along their maximum sensitivity direction, and the rate of change of linear acceleration (jerk) when stimulated along their minimum sensitivity direction. While the Smax vectors were distributed throughout the horizontal plane, the Smin vectors were concentrated mainly ipsilaterally with respect to head acceleration and clustered around the naso-occipital head axis. The properties of VC neurons were distinctly different from those of HC cells. The majority of VC cells showed decreasing Smax gains and small, relatively flat, Smin gains as a function of frequency. The Smax vectors were distributed ipsilaterally relative to the induced (apparent) head tilt. In type I anterior or posterior VC neurons, Smax vectors were clustered around the projection of the respective ipsilateral canal plane onto the horizontal head plane. These distinct spatial and temporal properties of HC and VC neurons during linear acceleration are compatible with the spatiotemporal organization of the horizontal and the vertical/torsional ocular responses, respectively, elicited in the rat during linear translation in the horizontal head plane. In addition, the data suggest a spatially and temporally specific and selective otolith/canal convergence. We propose that the central otolith system is organized in canal coordinates such that there is a close alignment between the plane of angular acceleration (canal) sensitivity and the plane of linear acceleration (otolith) sensitivity in otolith/canal-convergent vestibular nuclei neurons.

NASA Discipline Neuroscience↗
NASA NTRS2002

Hydrogen peroxide homeostasis: activation of plant catalase by calcium/calmodulin

Environmental stimuli such as UV, pathogen attack, and gravity can induce rapid changes in hydrogen peroxide (H(2)O(2)) levels, leading to a variety of physiological responses in plants. Catalase, which is involved in the degradation of H(2)O(2) into water and oxygen, is the major H(2)O(2)-scavenging enzyme in all aerobic organisms. A close interaction exists between intracellular H(2)O(2) and cytosolic calcium in response to biotic and abiotic stresses. Studies indicate that an increase in cytosolic calcium boosts the generation of H(2)O(2). Here we report that calmodulin (CaM), a ubiquitous calcium-binding protein, binds to and activates some plant catalases in the presence of calcium, but calcium/CaM does not have any effect on bacterial, fungal, bovine, or human catalase. These results document that calcium/CaM can down-regulate H(2)O(2) levels in plants by stimulating the catalytic activity of plant catalase. Furthermore, these results provide evidence indicating that calcium has dual functions in regulating H(2)O(2) homeostasis, which in turn influences redox signaling in response to environmental signals in plants.

NASA Discipline Plant Biology↗
NASA NTRS1986

Theoretical and material studies on thin-film electroluminescent devices

A theoretical study of resonant tunneling in multilayered heterostructures is presented based on an exact solution of the Schroedinger equation under the application of a constant electric field. By use of the transfer matrix approach, the transmissivity of the structure is determined as a function of the incident electron energy. The approach presented is easily extended to many layer structures where it is more accurate than other existing transfer matrix or WKB models. The transmission resonances are compared to the bound state energies calculated for a finite square well under bias using either an asymmetric square well model or the exact solution of an infinite square well under the application of an electric field. The results show good agreement with other existing models as well as with the bound state energies. The calculations were then applied to a new superlattice structure, the variablly spaced superlattice energy filter, (VSSEP) which is designed such that under bias the spatial quantization levels fully align. Based on these calculations, a new class of resonant tunneling superlattice devices can be designed.

Summers, C. J.↗
NASA NTRS1991

Singular control in minimum time spacecraft reorientation

Spacecraft reorientation is investigated numerically for an inertially symmetric rigid spacecraft with three bounded independent control torques aligned with the principal axes. The dynamical system of the spacecraft and the framework of the optimal-control problem are established in order to identify all of the potential strategies. The investigation lists bang-bang solutions and finite-order and infinite-order singular arcs, and the conditions for the finite-order singular arcs are given. Numerical examples are developed for all of the control-logic systems, and the suboptimality of the rest-to-rest maneuvers is proven for principal-axis rotations. The most efficient control technique is the singular control of infinite order, and the vector-valued singular control can be utilized in a derivative of the switching function.

Seywald, Hans↗