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Workshop on Advances in NASA-Relevant, Minimally Invasive Instrumentation

The purpose of this meeting is to highlight those advances in instrumentation and methodology that can be applied to the medical problems that will be encountered as the duration of manned space missions is extended. Information on work that is presently being done by NASA as well as other approaches in which NASA is not participating will be exchanged. The NASA-sponsored efforts that will be discussed are part of the overall Space Medicine Program that has been undertaken by NASA to address the medical problems of manned spaceflight. These problems include those that have been observed in the past as well as those which are anticipated as missions become longer, traverse different orbits, or are in any way different. This conference is arranged in order to address the types of instrumentation that might be used in several major medical problem areas. Instrumentation that will help in the cardiovascular, musculoskeletal, and psychological areas, among others will be presented. Interest lies in identifying instrumentation which will help in learning more about ourselves through experiments performed directly on humans. Great emphasis is placed on non-invasive approaches, although every substantial program basic to animal research will be needed in the foreseeable future. Space Medicine is a rather small affair in what is primarily an engineering organization. Space Medicine is conducted throughout NASA by a very small skeleton staff at the headquarters office in Washington and by our various field centers. These centers include the Johnson Space Center in Houston, Texas, the Ames Research Center in Moffett Field, California, the Jet Propulsion Laboratory in Pasadena, California, the Kennedy Space Center in Florida, and the Langley Research Center in Hampton, Virginia. Throughout these various centers, work is conducted in-house by NASA's own staff scientists, physicians, and engineers. In addition, various universities, industries, and other government laboratories perform research that cannot be effectively carried out in-house. At the moment, approximately 50% of the work is performed in-house and 50% is extramural. The area of bioinstrumentation pervades every one of our problem areas. In each, equipment or procedures are being developed that will allow more clinical work to be done in a ground-based or spacecraft setting. Although work of this kind goes on throughout the NASA organization and through its grants and contracts in the community at large, the major thrust of it is concentrated at the Jet Propulsion Laboratory which plays a lead role in this type of research and acts as the lead center in bioinstrumentation for NASA. It is recognized that there is much additional research being pursued in this area which would be potentially valuable to NASA and could, with some stimulation from, be made more applicable to NASA's needs. It is hoped, therefore, that the proceedings of this conference will be used as the basis for developing research strategies to be used as a road map to point the way in which NASA's own sponsored program should proceed over the course of the next three years. Additionally, it is hoped that the conference will highlight additional areas in which NASA should be involved either in-house or through the sponsorship of non-NASA scientists. NASA would also like to get an idea of which areas should be emphasized or perhaps de-emphasized among those that it is currently pursuing. In considering these questions, the discussion should concern itself not so much with whether a particular procedure or piece of equipment would work in a spacecraft, but rather, with whether the procedures that are advocated are at the state-of-the-art or beyond the state-of-the-art and whether they hold promise of giving additional insight into the problems to be confronted as humans venture into space for longer and longer periods of time.

Source record

Taking three-dimensional x-ray diffraction (3DXRD) from the synchrotron to the laboratory scale

Three-dimensional x-ray diffraction (3DXRD), a rotating x-ray diffraction technique, is a powerful tool for studying the micromechanical behavior of polycrystalline materials, capable of measuring the volume, position, orientation, and strain of thousands of grains simultaneously. However, its application has been historically limited to synchrotron facilities. Here, we present the first demonstration of laboratory-scale 3DXRD (Lab-3DXRD) using a liquid-metal-jet source. Lab-3DXRD achieves accuracy comparable to synchrotron-based 3DXRD, as validated against laboratory diffraction contrast tomography (LabDCT) and synchrotron-3DXRD. Over 96% of the grains detected with Lab-3DXRD are cross-validated, particularly for coarse grains (> ~60 μm), while the results suggest that finer grains should be accessible by taking advantage of high-efficiency detectors. We further demonstrate that its sensitivity to finer grains is enhanced by incorporating pre-characterization into the analysis. This study establishes Lab-3DXRD as a practical alternative to synchrotron techniques, making 3DXRD accessible to a wider range of academic and industrial researchers.

characterization and analytical techniques

Thermal Design

An essential phase of the Explorer XIII development was a thermal study and design to provide an acceptable temperature environment for the electronics components and external surfaces of the satellite during ascent and in orbit. It was necessary to establish by preflight analysis and tests that tolerable temperatures could be maintained in three regimes of flight. In the first regime (from launch until release of the heat shield) the satellite was subjected to radiative and conductive heat from the shield. In the second regime, after release of the shield at 350,000 feet, the satellite was heated by free molecular flow. In the third regime - the orbit phase - it was necessary that temperatures within limits for a 1-year lifetime be established. In addition to these three regimes, a study was made to investigate the effect of elevated rocket-motor temperatures during launch and after burnout. This chapter will deal with some pertinent preflight estimates and correlation of these estimates with flight data.

Explorer XIII Satellite

Glenn Research Center Propulsion Systems Laboratory 2026 Customer Guide

This guide describes the Propulsion Systems Laboratory (PSL) at the NASA Glenn Research Center. It was written to help customers understand the various components involved in conducting a test program within the PSL. The PSL complex supports two large-engine test cells that simulate altitude flight conditions for a wide range of research and experimental tests. These test cells operate at altitudes up to 90,000 ft and speeds from subsonic to above supersonic. Test points such as pressure, temperature, and Mach number can be set at the engine or test article inlet based on customer requirements. The facility’s support systems include the heated and cooled combustion air systems; altitude exhaust system; hydraulic system; nitrogen, oxygen, and hydrogen systems; thrust measurement system, which includes the facility’s single- and multi-axis thrust stands; inlet system; and electrical systems. In addition to providing a detailed description of PSL systems and capabilities, this guide discusses the facility’s history and past tests and addresses facility safety procedures, pretest requirements, and test operation standards.

Engine Icing Test Facility

The Future of Oaks in the Santa Monica Mountains: A Case Study in Using Remote Sensing Data for Species Distributions Models

The Woolsey Fire began on November 8, 2018, and lasted for almost two weeks, during which it burned almost 100,000 acres of valuable landscape and habitat, including a vast area of woodland. The persistence of key woodland species provides aesthetic, monetary, and ecological value to the landscape through carbon sequestration, air temperature moderation, and erosion mitigation, among other ecosystem services. This study investigated the impact of the Woolsey Fire on native woodland species distributions and identified areas suitable for restoration within the Santa Monica Mountains National Recreation Area. The team partnered with the Resource Conservation District of the Santa Monica Mountains; National Park Service, Santa Monica Mountains National Recreation Area; California Department of Parks and Recreation, Los Angeles County Division; County of Los Angeles Fire Department, Prevention Services Bureau, Forestry Division; County of Los Angeles Department of Regional Planning; and the University of Montana. The Earth observations used include data from Landsat 8 Operational Land Imager, NASA ER-2 Jet Airborne Visible InfraRed Imaging Spectrometer, Shuttle Radar Topography Mission, and RapidEye. The team produced maps of burn severity from the Woolsey Fire, its impact on plant species distributions, and habitat suitability projections for 2050 and 2099 to assist partners in prioritizing areas for restoration. A plant community classification was successfully created using Multiple Endmember Spectral Mixture Analysis (MESMA). Overall accuracy was assessed at 90.54% by comparing the classification to validation pixels derived from ground truth information provided by our partners.

Roger Ly

Safe, High Power/Voltage Battery Module Design Challenges

NASA seeks to demonstrate a path for achieving safe, high power, and high performing Li-ion battery designs for the purpose of establishing design guidelines for our aeronautic and spacecraft applications. Safe means passively resistant to thermal runaway propagation of any single cell catastrophic thermal runaway. High power means capable of 3C continuous discharge without overheating. High performing means achieving > 160 Wh/kg, 200 Wh/L. The biggest challenge has been balancing a high flux light weight path for cell heat dissipation during the high rate discharge that minimizes thermal gradients between cells and also protects adjacent cells from the heat load of thermal runaway cell. Our solution includes an oscillating heat pipe spine that contacts every 18650 cell in the pack and careful cell design selection to maximize the range of initial temperatures conditions where the battery can safely complete the 3C discharge.

Thermal runaway

Design and Analysis of Battery Thermal Management Systems

Thermal management of battery cell packs is a critically needed technology. The purpose of this work is to design new and improved Battery Thermal Management Systems (BTMS) for use in electric airplanes. The BTMS should be 3D printable and hold twelve to sixteen 18650 batteries. To minimize aircraft’s weight, an actively air-cooled battery pack was chosen to avoid the excess weight of water-cooled and phase change material (PCM) cooled packs. As a result, significant changes were made to remove all metal in the pack and replace it with lower density polymer matrix composites (PMCs) which can be additively manufactured. Two air cooled battery pack configurations (traditional propeller fans & bladeless fans) were designed, modeled, and compared. These packs were first modeled in SolidWorks 2021 3D CAD, then imported into COMSOL MultiPhysics to be studied using the “Heat Transfer in Solids and Fluids” module. The design with the bladeless fans eliminated the need to use high conductivity heavy metal to remove unwanted thermal energy. These bladeless fans were designed entirely out of PMCs. This thermal pack design weighs 0.04 kg less than that of the traditional propeller fans design and has increased the battery pack energy density by 8.25 Wh/kg.

Thermal Management System for Battery Packs

Internally Catalyzed Hydrogen Atom Transfer (I-CHAT)—A New Class of Reactions in Combustion Chemistry

The current paradigm of low-T combustion and autoignition of hydrocarbons is based on the sequential two-step oxygenation of fuel radicals. The key chain-branching occurs when the second oxygenation adduct (OOQOOH) is isomerized releasing an OH radical and a key ketohydroperoxide (KHP) intermediate. The subsequent homolytic dissociation of relatively weak O–O bonds in KHP generates two more radicals in the oxidation chain leading to ignition. Based on the recently introduced intramolecular “catalytic hydrogen atom transfer” mechanism (J. Phys. Chem. 2024, 128, 2169), abbreviated here as I-CHAT, we have identified a novel unimolecular decomposition channel for KHPs to form their classical isomers—enol hydroperoxides (EHP). The uncertainty in the contribution of enols is typically due to the high computed barriers for conventional (“direct”) keto–enol tautomerization. Remarkably, the I-CHAT dramatically reduces such barriers. The novel mechanism can be regarded as an intramolecular version of the intermolecular relay transfer of H-atoms mediated by an external molecule following the general classification of such processes (Catal. Rev.-Sci. Eng. 2014, 56, 403). Here, we present a detailed mechanistic and kinetic analysis of the I-CHAT-facilitated pathways applied to n-hexane, n-heptane, and n-pentane models as prototype molecules for gasoline, diesel, and hybrid rocket fuels. We particularly examined the formation kinetics and subsequent dissociation of the γ-enol-hydroperoxide isomer of the most abundant pentane-derived isomer γ-C5-KHP observed experimentally. To gain molecular-level insight into the I-CHAT catalysis, we have also explored the role of the internal catalyst moieties using truncated models. All applied models demonstrated a significant reduction in the isomerization barriers, primarily due to the decreased ring strain in transition states. In addition, the longer-range and sequential H-migration processes were also identified and illustrated via a combined double keto–enol conversion of heptane-2,6-diketo-4-hydroperoxide as a potential chain-branching model. To assess the possible impact of the I-CHAT channels on global fuel combustion characteristics, we performed a detailed kinetic analysis of the isomerization and decomposition of γ-C5-KHP comparing I-CHAT with key alternative reactions—direct dissociation and Korcek channels. Calculated rate parameters were implemented into a modified version of the n-pentane kinetic model developed earlier using RMG automated model generation tools (ACS Omega, 2023, 8, 4908). Simulations of ignition delay times revealed the significant effect of the new pathways, suggesting an important role of the I-CHAT pathways in the low-T combustion of large alkanes.

Biochemistry & Molecular Biology

Microstructural Evolution and Mechanical Properties of LP-DED NASA HR-1 – A Hydrogen Resistant AM Superalloy for Space Propulsion Applications

The National Aeronautics and Space Administration (NASA) has actively pursued metal additive manufacturing (AM) technologies for spaceflight applications since the late 2000s. AM offers transformative advantages in cost, schedule, part consolidation, and design flexibility. Among the various AM techniques, laser powder directed energy deposition (LP-DED) is particularly well suited for fabricating complex geometries with fine feature resolution. In propulsion systems that utilize high-pressure gaseous hydrogen—such as liquid hydrogen rocket engines—hydrogen environment embrittlement (HEE) presents a serious threat to material performance 1,2 . Mechanical property degradation under these conditions can compromise component reliability, especially under cyclic loading. To address this challenge, NASA developed NASA HR-1 (Hydrogen Resistant-1) as a solution for liquid rocket engine components operating in hydrogen-rich environments, using the LP-DED technique 3-9 . A key component in a liquid rocket engine is the exhaust nozzle, which is typically regeneratively cooled (regen) due to the high heat flux. NASA HR-1 was specifically developed for regen nozzle applications using hydrogen as a propellant, providing resistance to HEE, a critical issue for many materials. The AM version of NASA HR-1 was also formulated to achieve high ultimate tensile strength, along with high yield strength and ductility in this environment 5,6 . Low-cycle fatigue (LCF) is another important consideration in nozzle design, as components are expected to endure multiple starts and missions. Additionally, the LP-DED version of the alloy exhibits improved thermal conductivity compared to its wrought counterpart, which benefits nozzle cooling. Overall, NASA HR-1 offers an excellent balance of high strength, HEE resistance, LCF performance, thermal conductivity, and ductility to meet the demanding requirements of channel-cooled nozzles and other components used with hydrogen and other propellants. The LP-DED–processed NASA HR-1 requires several post-processing heat treatment steps to achieve the material properties desirable for its intended application 6 . These steps include stress relief, homogenization, solution annealing, and aging for precipitation hardening. The stress relief treatment mitigates residual stresses accumulated during the LP-DED process and minimizes the potential for distortion. Homogenization, a common step for AM materials, reduces elemental segregation and promotes recrystallization to develop a more equiaxed grain structure. The subsequent solution annealing treatment heats the part to a solid solution temperature to dissolve the undesirable η-phase that forms during cooling from homogenization, followed by rapid cooling to retain an η-phase–free microstructure. Finally, aging promotes precipitation of the strengthening γ′ phase in the alloy. The integration of compositional design and optimized thermal processing enables high-quality LP-DED NASA HR-1 components with excellent microstructural and mechanical stability. Improved chemical and microstructure homogeneity enhances ductility and fatigue resistance—both critical for safe and reliable operation in high-pressure hydrogen environments. NASA has successfully fabricated and hot-fire tested multiple subscale and full-scale channel wall nozzles using LP-DED NASA HR-1 5,6, 9-14 . These efforts included process refinements to support thin-wall construction and various channel geometries. Throughout development, several key observations emerged. After homogenization, the as-built columnar grain structure transforms into a fully equiaxed microstructure. However, subsequent treatments—such as solution annealing and aging—result in changes that are more difficult to track. The grain structure remains largely unchanged, and the γ′ precipitates, typically 5–10 nm in diameter, are beyond the resolution of scanning electron microscopy (SEM). While transmission electron microscopy (TEM) can resolve these fine precipitates, TEM sample preparation is time-consuming and difficult for LP-DED material. As an alternative, differential scanning calorimetry (DSC) offers a useful, qualitative approach to monitor precipitate evolution throughout different stages of heat treatment. The overall goal is to improve the understanding of how heat treatment affects the microstructure and mechanical performance of LP-DED NASA HR-1. This paper presents heat treatment design considerations, microstructural characterization, mechanical testing – including tensile and LCF testing in both air and hydrogen environments.

Superalloy

A Case Study of View-Factor Rectification Procedures for Diffuse-Gray Radiation Enclosure Computations

The view factors which are used in diffuse-gray radiation enclosure calculations are often computed by approximate numerical integrations. These approximately calculated view factors will usually not satisfy the important physical constraints of reciprocity and closure. In this paper several view-factor rectification algorithms are reviewed and a rectification algorithm based on a least-squares numerical filtering scheme is proposed with both weighted and unweighted classes. A Monte-Carlo investigation is undertaken to study the propagation of view-factor and surface-area uncertainties into the heat transfer results of the diffuse-gray enclosure calculations. It is found that the weighted least-squares algorithm is vastly superior to the other rectification schemes for the reduction of the heat-flux sensitivities to view-factor uncertainties. In a sample problem, which has proven to be very sensitive to uncertainties in view factor, the heat transfer calculations with weighted least-squares rectified view factors are very good with an original view-factor matrix computed to only one-digit accuracy. All of the algorithms had roughly equivalent effects on the reduction in sensitivity to area uncertainty in this case study.

Robert P Taylor

Model Correlation and Thermal Analysis of xEMU Boot at Lunar South Pole Temperatures

The National Aeronautics and Space Administration (NASA) Artemis program plans to send astronauts to the lunar south pole, a region of the moon that is colder than previous lunar missions and low earth orbit operations. The spacesuit boots that will be used on these missions will be directly impacted by these extremely cold temperatures (down to ~50 K). To assess the performance of the Exploration Extravehicular Mobility Unit (xEMU) lunar boot in these extreme temperatures, the boot was tested at the Jet Propulsion Lab (JPL) in the Cryogenic Ice Transfer, Acquisition Development, and Excavation Laboratory (CITADEL) thermal vacuum (TVAC) chamber. This data was used to correlate thermal models to predict operational performance of the boots on the lunar south pole. This paper documents the data analysis, thermal boot model correlation, and operational predictions conducted using data from the xEMU TVAC test. Data from the test series was used to determine expected thermal conductances within the boot and between the boot and environment. These conductances were used to correlate a Thermal Desktop model of the xEMU boot across 10 different test points which varied external temperature, internal boot ventilation flowrate, and contact pressure. The correlated model was then used to predict operational performance in the lunar south pole. While the predictions indicate promising evidence for performance of the boots at the 100K test point, there is still substantial uncertainty in performance, particularly at the 48K test point. The results of this test series and model correlation stress the importance of improved testing for characterizing the expected thermal resistance between the outside of the boot and the lunar surface.

xEMU

Power and Propulsion Element Steerable High Gain Antenna Lunar Transit Thermal Analysis Tracking Methodology

The Power and Propulsion Element (PPE) is an ion thruster propulsion spacecraft developed as an element of Space Reactor (SR-1) Freedom to provide propulsion, communications and power for the spacecraft. PPE was originally being developed for the use with the lunar orbiting space station Gateway as one of the first two planned elements. PPE was to be launched with the Habitation and Logistics Outpost (HALO) element in a configuration called the Co-Manifested Vehicle (CMV) that would arrive at a Near-Rectilinear Halo Orbit (NRHO) around the Moon via a lunar transit spiral trajectory phase. The PPE communication system is equipped with two Steerable High Gain Antennas (SHGA) each steered by a two-axis gimbal (TAG) mechanism. A thermal analysis was conducted during the near-Earth spiral phase of the mission using Thermal Desktop (TD). This analysis utilized multiple axis Earth tracking articulators in combination with SINDA system internal environmental heating symbols to produce accurate Earth ground station tracking communication system temperatures. This presentation provides an overview of the communication system thermal model and the analysis methodology.

Thermal Analysis

Model Correlation and Thermal Analysis of xEMU Boot at Lunar South Pole Temperatures

The National Aeronautics and Space Administration (NASA) Artemis program plans to send astronauts to the lunar south pole, a region of the moon that is colder than previous lunar missions and low earth orbit operations. The spacesuit boots that will be used on these missions will be directly impacted by these extremely cold temperatures (down to ~50 K). To assess the performance of the Exploration Extravehicular Mobility Unit (xEMU) lunar boot in these extreme temperatures, the boot was tested at the Jet Propulsion Lab (JPL) in the Cryogenic Ice Transfer, Acquisition Development, and Excavation Laboratory (CITADEL) thermal vacuum (TVAC) chamber. This data was used to correlate thermal models to predict operational performance of the boots on the lunar south pole. This paper documents the data analysis, thermal boot model correlation, and operational predictions conducted using data from the xEMU TVAC test. Data from the test series was used to determine expected thermal conductances within the boot and between the boot and environment. These conductances were used to correlate a Thermal Desktop model of the xEMU boot across 10 different test points which varied external temperature, internal boot ventilation flowrate, and contact pressure. The correlated model was then used to predict operational performance in the lunar south pole. While the predictions indicate promising evidence for performance of the boots at the 100K test point, there is still substantial uncertainty in performance, particularly at the 48K test point. The results of this test series and model correlation stress the importance of improved testing for characterizing the expected thermal resistance between the outside of the boot and the lunar surface.

thermal analysis

Compatibility of Type 304H Stainless Steel in Static Molten FLiBe for Inertial Confinement Fusion Reactors: Role of Impurities and Redox Control

Molten fluoride salts, such as FLiBe (LiF-BeF2), are promising candidates for tritium breeding and heat transfer in fusion reactors, but corrosion of structural materials remains a major challenge. This study investigates the corrosion behavior of austenitic stainless steel 304H in purified and NiF2-containing FLiBe at 500°C and 600°C, focusing on the effects of impurities and redox control. Exposure to purified FLiBe resulted in the concurrent depletion of Cr, Mn, and Fe, with corrosion at 500 °C dominated by the combined oxide formation and elemental dissolution, while at 600°C elemental depletion was predominant. The addition of a controlled NiF2 impurity significantly accelerated corrosion at both temperatures, demonstrating the sensitivity of 304H to the salt redox state. Beryllium additions were effective in mitigating corrosion for both baseline and NiF2-containing FLiBe; minimal depletion of Cr, Mn, and Fe occurred with Be additions as low as 2.5 mg (147 wppm), and no NiBe intermetallics formed at 5 mg (294 wppm), indicating that small Be inventories can provide substantial protection without deleterious phase formation. Thermodynamic equilibrium and coupled thermodynamic-kinetic analyses at the salt-alloy interface suggested low corrosion rates in systems with limited hydrogen fluoride (HF) generation, highlighting the importance of salt redox control. Estimates for a Be addition rate were calculated for the HYLIFE-II fusion reactor that can mitigate corrosion-induced degradation, assuming complete conversion of tritium to tritium fluoride (TF). Overall, 304H shows reasonable compatibility with FLiBe under optimized redox conditions. These results provide quantitative guidance for material selection and salt management in fusion blanket and heat exchanger systems and motivate validation under flowing, nonisothermal, and irradiated conditions.

Pillai, Rishi [ORNL] (ORCID:0000000243688197)

Thrust Chamber Thermal Barrier Coating Techniques

Methods for applying thermal barrier coatings to the hot-gas side wall of rocket thrust chambers in order to significantly reduce the heat transfer in high heat flux regions has been the focus of technology efforts for many years. A successful technique developed by NASA-Lewis that starts with the coating on a mandrel and then builds the thrust chamber around it by electroforming appropriate materials is described. This results in a smooth coating with exceptional adherence, as was demonstrated in hot fire rig tests. The low cycle fatigue life of chambers with coatings applied in this manner was increased dramatically compared to uncoated chambers.

Richard J Quentmeyer

Skylab Experiment M552: Exothermic Brazing

The M552 Skylab experiment reveals that brazing in space is feasible. It successfully demonstrated the ability to retain molten metal within a braze tube joint system. Surface energy was the dominant operative force system controlling liquid metal for this experiment. The zero gravity environment for brazing resulted in several differences; increased solubility, increased liquid spreading, more uniform menisci (liquid/vapor interface) and a reduction of braze alloy shrinkage defects. The residual radioactive intensity and location of the redistributed isotope was interpreted to provide a sequential history of braze alloy movement during the melt-flow-solidification stages of the process. Convection theory applied to M552 was validated but some results were not explainable by it, i.e., increased nickel transport and the radial mixing of the silver isotope on samples SLN-2 and SLN-4. All characteristics of thermal analysis appeared to react as expected but heat conduction rates increased because of increased extent, rate and uniformity of braze alloy spreading.

J R Williams

Technoeconomic Analysis Round Robin of a Retrofit of the Ivanpah Concentrating Solar Plant with a Molten-Salt System with Thermal Energy Storage

While the fidelity of technoeconomic analysis (TEA) models for concentrating solar thermal systems has improved in recent years, there is a lack of consensus on the specific inputs used to forecast performance of a newly built tower system due to a lack of validations and post-mortems available to the public. This effort is a joint initiative between multiple international organizations to validate and compare their TEA models. The specific case study is a proposed retrofit of one unit of the Ivanpah Solar Energy Generating System to include molten-salt storage, replacing the steam generation system with a molten-salt receiver, salt-to-steam heat exchanger train, and new balance of plant while keeping the existing steam turbine, solar field, and interconnection in place, using plant data for calibration. This manuscript discusses several of the agreed-upon assumptions for this study as well as a preliminary analysis from prior work that motivates the study.

14 SOLAR ENERGY

Computation of Optimal Interplanetary Low-Thrust Trajectories With Bounded Thrust Magnitude By Means of the Generalized Newton-Raphson Method

The generalized Newton-Raphson method, an iterative procedure for solving nonlinear operator equations, has been extended in application to variational problems with bounded control variables. A minimum fuel interplanetary low thrust orbital transfer problem is worked out in detail to demonstrate the practical aspects of the algorithm as well as its computational effectiveness. The control variables are the thrust magnitude, limited from zero to some prescribed maximum value, and the thrust steering angle.

Computation