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NASA NTRS2007

NASA Tech Briefs, January 2007

Topics covered include: Flexible Skins Containing Integrated Sensors and Circuitry; Artificial Hair Cells for Sensing Flows; Video Guidance Sensor and Time-of-Flight Rangefinder; Optical Beam-Shear Sensors; Multiple-Agent Air/Ground Autonomous Exploration Systems; A 640 512-Pixel Portable Long-Wavelength Infrared Camera; An Array of Optical Receivers for Deep-Space Communications; Microstrip Antenna Arrays on Multilayer LCP Substrates; Applications for Subvocal Speech; Multiloop Rapid-Rise/Rapid Fall High-Voltage Power Supply; The PICWidget; Fusing Symbolic and Numerical Diagnostic Computations; Probabilistic Reasoning for Robustness in Automated Planning; Short-Term Forecasting of Radiation Belt and Ring Current; JMS Proxy and C/C++ Client SDK; XML Flight/Ground Data Dictionary Management; Cross-Compiler for Modeling Space-Flight Systems; Composite Elastic Skins for Shape-Changing Structures; Glass/Ceramic Composites for Sealing Solid Oxide Fuel Cells; Aligning Optical Fibers by Means of Actuated MEMS Wedges; Manufacturing Large Membrane Mirrors at Low Cost; Double-Vacuum-Bag Process for Making Resin- Matrix Composites; Surface Bacterial-Spore Assay Using Tb3+/DPA Luminescence; Simplified Microarray Technique for Identifying mRNA in Rare Samples; High-Resolution, Wide-Field-of-View Scanning Telescope; Multispectral Imager With Improved Filter Wheel and Optics; Integral Radiator and Storage Tank; Compensation for Phase Anisotropy of a Metal Reflector; Optical Characterization of Molecular Contaminant Films; Integrated Hardware and Software for No-Loss Computing; Decision-Tree Formulation With Order-1 Lateral Execution; GIS Methodology for Planning Planetary-Rover Operations; Optimal Calibration of the Spitzer Space Telescope; Automated Detection of Events of Scientific Interest; Representation-Independent Iteration of Sparse Data Arrays; Mission Operations of the Mars Exploration Rovers; and More About Software for No-Loss Computing.

Source record↗

DOE OSTI2023

Adaptation to climate change through strategic integration of long fallow into cropping system in a dryland Mediterranean-type environment

The crop-growing region of Western Australia characterized by a Mediterranean-type climate is projected to become warmer and drier. Appropriate selection of crop sequences will be of importance to cope with these climatic changes for this largest grain-producing region of Australia. Through linking a widely used crop model (APSIM), 26 General Circulation Models (GCMs) with one Shared Socioeconomic Pathway (SSP585) and economic analysis, we explored how the climate change would affect dryland wheat cropping and whether/how long fallow (the practice of leaving a field out of production for an entire growing season) could be integrated into wheat cropping system in Western Australia. The potential adaptation of long fallow into wheat system was assessed with four fixed rotations (fallow-wheat, fallow-wheat-wheat, fallow-wheat-wheat-wheat, and fallow-wheat-wheat-wheat-wheat) and four flexible sowing rule-based rotations (the land was fallowed if sowing rule was not met), compared with continuous wheat. The simulation results at four representing locations show that climate change would have negative impacts on both yield and economic return of continuous wheat cropping in Western Australia. Wheat after fallow out-yielded and out-profited wheat after wheat under future climate. But integrating fallow into wheat cropping systems with the above fixed rotations would lead to yield and economic loss. By contrast, cropping systems in which fallowing took place when sowing condition could not be met at a certain time would achieve comparable yield and economic return to continuous wheat, with wheat yield being only 5% less than continuous wheat and the gross margin being $12ha -1 more than continuous wheat averaged across locations. We highlight strategic integration of long fallow into cropping system in a dryland Mediterranean-type environment would have a great potential to cope with future climate change. These findings can be extended into other Mediterranean-type cropping regions in Australia and beyond.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Seasonality and longer-term development generate temporal dynamics in the Populus microbiome

ABSTRACT Temporal variation in community composition is central to our understanding of the assembly and functioning of microbial communities, yet the controls over temporal dynamics for microbiomes of long-lived plants, such as trees, remain unclear. Temporal variation in tree microbiomes could arise primarily from seasonal (i.e., intra-annual) fluctuations in community composition or from longer-term changes across years as host plants age. To test these alternatives, we experimentally isolated temporal variation in plant microbiome composition using a common garden and clonally propagated plants, and we used amplicon sequencing to characterize bacterial/archaeal and fungal communities in the leaf endosphere, root endosphere, and rhizosphere of two Populus spp. over four seasons across two consecutive years. Microbial community composition differed among seasons and years (which accounted for up to 21% of the variation in microbial community composition) and was correlated with seasonal dissimilarity in climatic conditions. However, microbial community dissimilarity was also positively correlated with time, reflecting longer-term compositional shifts as host trees aged. Together, our findings demonstrate that temporal patterns in tree microbiomes arise from both seasonal fluctuations and longer-term changes, which interact to generate unique seasonal patterns each year. In addition to shedding light on two important controls over the assembly of plant microbiomes, our results also suggest future studies of tree microbiomes should account for background temporal dynamics when testing the drivers of spatial patterns in microbial community composition and temporal responses of plant microbiomes to environmental change. IMPORTANCE Microbiomes are integral to the health of host plants, but we have a limited understanding of the factors that control how the composition of plant microbiomes changes over time. Especially little is known about the microbiome of long-lived trees, relative to annual and non-woody plants. We tested how tree microbiomes changed between seasons and years in poplar (genus Populus ), which are widespread and ecologically important tree species that also serve as important biofuel feedstocks. We found the composition of bacterial, archaeal, and fungal communities differed among seasons, but these seasonal differences depended on year. This dependence was driven by longer-term changes in microbial composition as host trees developed across consecutive years. Our findings suggest that temporal variation in tree microbiomes is driven by both seasonal fluctuations and longer-term (i.e., multiyear) development.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2017

Novel End-to-End Molecular Biology Approach for Direct Nanopore 1D cDNA Sequencing of Reverse Transcribed mRNAs Purified from Cell Cultures by the NASA ISS WetLab2 SPM

Continued space bioscience research onboard the International Space Station (ISS) and future long-duration flight missions to the Moon or Mars will require the ability to conduct on-orbit molecular analysis of biological samples independently from Earth. In the last year two new molecular analytic technologies have been installed and the technologies demonstrated onboard the ISS: The Sample Prep Module (SPM) WetLab-2 (WL2) qRT-PCR toolbox and the Oxford Nanopore MinIon Biomolecule Sequencer. Here we describe protocol development and integration into existing ISS technology for end-to-end on-orbit biological sample processing and molecular analysis with real time results generated utilizing only field offline analytic software. For this experiment we isolated primary cells from bone marrow flushes of wild type B6129SF2 mice (Jackson Labs) long bones. The cell isolate was then processed using the SPM to produce total 147nanograms of RNA. The total RNA was purified to only messenger RNA (mRNA) and transferred to Smartcycler Thermocycle ISS kit consumable tube using Eppendorf gel loading pipette tips for further processing. Complementary first strand cDNA was synthesized using OLIGO dT priming followed by addition of SuperScript II Reverse Transcriptase and thermal cycling as per manufacturers instruction. All thermal cycling was conducted using the ISS WetLab-2 Cephid Smarcycler real time thermal cycler. Our protocol takes advantage of mRNAs native poly(A) tail, synthesized in vivo to protect the mRNA from degradation by endonucleases, to eliminate end-prep for adapter ligation. The adapted library is purified using MyOne C1 Streptavidin beads before elution in buffer. The pre-sequencing library is diluted in the loading buffer and injected into the MinIon sample port, drawn into the nanopore window by capillary action, and sequenced using the MinKnown software with local basecalling. The sequencing read produced 34.5 million events and local basecalling produced 117,301 successful reads. NCBI Blast of the data for the mouse genome resulted in 2,462 successful nucleotide collection matches (gene sequences) exceeding 70 homology. These results demonstrate the viability of this novel flight ready end-to-end sample analytic methodology and provide a real time homolog for flight experimentation utilizing supply kits and technologies that have already been demonstrated on ISS.

MinIon↗

DOE OSTI2024

A new method for solving the linearized 1D Vlasov–Poisson system yielding a new class of solutions

We describe a new method for solving the linearized 1D Vlasov–Poisson system by using properties of Cauchy-type integrals. Our method remedies critical flaws of the two standard methods, reveals a previously unrecognized Gaussian-in-time-like decay, and can also account for an externally applied electric field. The Landau approximation involves deforming the Bromwich contour around the poles closest to the real axis due to the analytically continued dielectric function, finding the long-time behavior for a stable system: Landau damping. Jackson's generalization encircles all poles while sending the contour to infinity, assuming its contribution vanishes, which is not true in general. This gives incorrect solutions for physically reasonable configurations and can exhibit pathological behavior, of which we show examples. The van Kampen method expresses the solution for a stable equilibrium as a continuous superposition of waves, resulting in an opaque integral. Case's generalization includes unstable systems and predicts a decaying discrete mode for each growing discrete mode, an apparent contradiction to both the Jackson solution and ours. We show, without imposing additional constraints, that the decaying modes are never present in the time evolution due to an exact cancellation with part of the continuum. Our solution is free of integral expressions, is obtained using algebra and Laurent series expansions, does not rely on analytic continuations, and results in a correct asymptotically convergent form in the case of infinite sums. The analysis used can be readily applied in higher-dimensional, electromagnetic systems and also provides a new technique for evaluating certain inverse Laplace transforms.

Physics↗

DOE OSTI2021

Accelerating phase-field-based microstructure evolution predictions via surrogate models trained by machine learning methods

Abstract The phase-field method is a powerful and versatile computational approach for modeling the evolution of microstructures and associated properties for a wide variety of physical, chemical, and biological systems. However, existing high-fidelity phase-field models are inherently computationally expensive, requiring high-performance computing resources and sophisticated numerical integration schemes to achieve a useful degree of accuracy. In this paper, we present a computationally inexpensive, accurate, data-driven surrogate model that directly learns the microstructural evolution of targeted systems by combining phase-field and history-dependent machine-learning techniques. We integrate a statistically representative, low-dimensional description of the microstructure, obtained directly from phase-field simulations, with either a time-series multivariate adaptive regression splines autoregressive algorithm or a long short-term memory neural network. The neural-network-trained surrogate model shows the best performance and accurately predicts the nonlinear microstructure evolution of a two-phase mixture during spinodal decomposition in seconds, without the need for “on-the-fly” solutions of the phase-field equations of motion. We also show that the predictions from our machine-learned surrogate model can be fed directly as an input into a classical high-fidelity phase-field model in order to accelerate the high-fidelity phase-field simulations by leaping in time. Such machine-learned phase-field framework opens a promising path forward to use accelerated phase-field simulations for discovering, understanding, and predicting processing–microstructure–performance relationships.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Development of Building Design Optimization Methodology: Residential Building Applications

Building design optimization is a highly complex problem, requiring long computational running processes because of the many options that exist when a building is being designed. This paper introduces an integrated approach through which to perform this optimization within an acceptable time frame. The approach includes the methods of variable selection, model simplification, and a sequential optimization process. Using singular value decomposition, a large number of design variables is reduced to a smaller subset that can be solved more quickly through the optimization algorithm. To expedite the variable selection process, a modeling approach that quickly simulates annual energy consumption was developed to replace full annual energy simulations. The developed methodology was applied to two residential buildings in the US, and the results are discussed herein. To assess the accuracy of the integrated optimization methodology, the optimized life cycle costs are compaa variables demonstrating the strongest contributions in the optimization study were identified. The proposed methodology significantly shortened the time requirements for the optimization processes of the two case studies by 74% and 84%; the optimized life cycle costs were within 0.05% and 0.06%, respectively, of the optimum point.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS1995

A far-field non-reflecting boundary condition for two-dimensional wake flows

Far-field boundary conditions for external flow problems have been developed based upon long-wave perturbations of linearized flow equations about a steady state far field solution. The boundary improves convergence to steady state in single-grid temporal integration schemes using both regular-time-stepping and local-time-stepping. The far-field boundary may be near the trailing edge of the body which significantly reduces the number of grid points, and therefore the computational time, in the numerical calculation. In addition the solution produced is smoother in the far-field than when using extrapolation conditions. The boundary condition maintains the convergence rate to steady state in schemes utilizing multigrid acceleration.

Danowitz, Jeffrey S.↗

NASA NTRS2014

Integration and Testing of LCS Software

Kennedy Space Center is in the midst of developing a command and control system for the launch of the next generation manned space vehicle. The Space Launch System (SLS) will launch using the new Spaceport Command and Control System (SCCS). As a member of the Software Integration and Test (SWIT) Team, command scripts, and bash scripts were written to assist in integration and testing of the Launch Control System (LCS), which is a component of SCCS. The short term and midterm tasks are for the most part completed. The long term tasks if time permits will require a presentation and demonstration.

Command Script↗

NASA NTRS2020

Ellicott City Disasters II - Building a Real-Time Predictive Flood Model for Improving Early Warning Systems in Ellicott City, Maryland

As flood events in the United States grow in frequency and intensity, the uses of applied remote sensing analyses are increasingly necessary for effective flood monitoring and warning systems. The NASA DEVELOP Ellicott City Disasters III project investigated the use of machine learning for applications in flood risk detection to support the improvement of early warning systems in Ellicott City, Maryland. To strengthen the efforts of the Howard County Office of Emergency Management (OEM) in building a more robust flood monitoring system, this term built on the predictive capability of the long-short term memory (LSTM) model created by the second term of this DEVELOP project to create a Sequentially Trained Real-time EstimAted Model (STREAM). Enhancements to the model included the integration of both real-time and predicted weather products from the National Weather Service to increase predictive capacity. These weather products were supplemented by stream gauge data from the OEM as well as real-time radar products. The resultant flood risk model was trained to evaluate input variables and predict stage height in Ellicott City in real time. The model, upgraded to predict stage height up to 8 hours in advance, was incorporated into an online dashboard in a user-friendly interface. The project demonstrated the potential for integration of open data and NASA Earth observations into a flood risk forecasting tool capable of informing real-time decision-making.

Erika Munshi↗

NASA NTRS2020

Ellicott City Disasters III: Building a Real-Time Statistical Flood Model for Improving Early Warning Systems in Ellicott City, Maryland

Erika Munshi↗

NASA NTRSDate not supplied

An Examination of Autumn Southern Polar Ozone Tendencies and the Residual Circulation in MERRA-2 Products

Changes in lower stratospheric ozone caused by dynamical transport can be difficult to characterize and thus are sometimes difficult to distinguish from chemical losses. Correlations between ozone changes and various dynamical proxies (e.g., the eddy heat flux) from year to year can be of interest, but they do little in themselves to explain the ozone transport mechanisms behind such correlations. In this study, we use products from the Modern-Era Retrospective analysis for Research and Applications Version 2 (MERRA-2) to calculate the ozone mass flux, integrating it in space and time over the upper tropospheric/lower stratospheric Southern polar cap during periods when little chemical loss is expected. The ozone mass flux is expressed in terms of components of the residual circulation of the Transformed Eulerian Mean (TEM, i.e., 𝑣𝑣̅ ∗and 𝑤𝑤(∗) as well as eddy mixing terms. We relate these terms to the local ozone mass tendency ("#! "$ ), similarly integrated, and we find that the interannual variability of the ozone changes are strongly related to the residual meridional circulation and the meridional eddy mixing terms. These directly calculated dynamical transport terms provide clearer ozone proxies. Removing these advective terms from a long-term ozone time series can more effectively reveal ozone variations and long-term trends, specifically those caused by photochemical production and losses (e.g., human-produced ozone depletion).

Ozone↗

DOE OSTI2022

Modeling of streamflow in a 30 km long reach spanning 5 years using OpenFOAM 5.x

Abstract. Developing accurate and efficient modeling techniques for streamflow at the tens-of-kilometers spatial scale and multi-year temporal scale is critical for evaluating and predicting the impact of climate- and human-induced discharge variations on river hydrodynamics. However, achieving such a goal is challenging because of limited surveys of streambed hydraulic roughness, uncertain boundary condition specifications, and high computational costs. We demonstrate that accurate and efficient three-dimensional (3-D) hydrodynamic modeling of natural rivers at 30 km and 5-year scales is feasible using the following three techniques within OpenFOAM, an open-source computational fluid dynamics platform: (1) generating a distributed hydraulic roughness field for the streambed by integrating water-stage observation data, a rough wall theory, and a local roughness optimization and adjustment strategy; (2) prescribing the boundary condition for the inflow and outflow by integrating precomputed results of a one-dimensional (1-D) hydraulic model with the 3-D model; and (3) reducing computational time using multiple parallel runs constrained by 1-D inflow and outflow boundary conditions. Streamflow modeling for a 30 km long reach in the Columbia River (CR) over 58 months can be achieved in less than 6 d using 1.1 million CPU hours. The mean error between the modeled and the observed water stages for our simulated CR reach ranges from −16 to 9 cm (equivalent to approximately ±7 % relative to the average water depth) at seven locations during most of the years between 2011 and 2019. We can reproduce the velocity distribution measured by the acoustic Doppler current profiler (ADCP). The correlation coefficients of the depth-averaged velocity between the model and ADCP measurements are in the range between 0.71 and 0.83 at 75 % of the survey cross sections. With the validated model, we further show that the relative importance of dynamic pressure versus hydrostatic pressure varies with discharge variations and topography heterogeneity. Given the model's high accuracy and computational efficiency, the model framework provides a generic approach to evaluate and predict the impacts of climate- and human-induced discharge variations on river hydrodynamics at tens-of-kilometers and decadal scales.

58 GEOSCIENCES↗

NASA NTRSDate not supplied

Deep Learning-Based Negotiation Strategy Selection for Cooperative Conflict Resolution in Urban Air Mobility

This paper presents a collaborative conflict resolution technique using deep neural network-based intelligent search of the solution space. This approach offers a rapid convergence to a mutually acceptable solution for real-time conflict resolution, suitable for urban air mobility operations. Furthermore, the presented technique allows operational flexibility to the urban air mobility agents where these agents can collaboratively devise the solution via integrative negotiation, based on their local utility functions, as long as such a solution does not violate the global safety thresholds. The presented machine-to-machine negotiation method is built on our prior work on holistic assessment of the airspace and potential conflict detection implemented at-the-edge, onboard the unmanned aircraft systems. This paper extends the prior work to augment decision-making at-the-edge, thereby, promising a true distributed control architecture for urban air mobility. In this approach, each agent (a) builds a potential in-flight conflict map, (b) identifies the conflicting agents, (c) dynamically prepares a list of alternatives based on its current utility functions, (d) negotiates with the conflicting agents to pick one of these alternatives, and (e) implements the negotiated alternative to mutually resolve the conflict. Note that such an approach does not require a contingency plan to be made pre-flight, as the conflict resolution strategies are decided and negotiated in real time based on the present state of the agent. The contingency plan, if available, can serve as an input to the real-time conflict resolution strategy formulation, and also can be used as a fallback plan in case the negotiation fails and the impacted agents need to switch to a rule-based/supervisory resolution mode from the discussed distributed resolution mode. The presented collaborative negotiation-based conflict resolution technique incorporates a time-dependent reward function to catalyze collaborative resolution by incentivizing the agents with local and global rewards beneficial to their business operations.

Advanced Air Mobility↗

NASA NTRS1994

UV laser long-path absorption spectroscopy

Long path Differential Optical Absorption Spectroscopy (DOAS) using a picosecond UV laser as a light source was developed in our institute. Tropospheric OH radicals are measured by their rotational absorption lines around 308 nm. The spectra are obtained using a high resolution spectrograph. The detection system has been improved over the formerly used optomechanical scanning device by application of a photodiode array which increased the observed spectral range by a factor of 6 and which utilizes the light much more effectively leading to a considerable reduction of the measurement time. This technique provides direct measurements of OH because the signal is given by the product of the absorption coefficient and the OH concentration along the light path according to Lambert-Beers law. No calibration is needed. Since the integrated absorption coefficient is well known the accuracy of the measurement essentially depends on the extent to which the OH absorption pattern can be detected in the spectra. No interference by self generated OH radicals in the detection lightpath has been observed. The large bandwidth (greater than 0.15 nm) and the high spectral resolution (1.5 pm) allows absolute determination of interferences by other trace gas absorptions. The measurement error is directly accessible from the absorption-signal to baseline-noise ratio in the spectra. The applicability of the method strongly depends on visibility. Elevated concentrations of aerosols lead to considerable attenuation of the laser light which reduces the S/N-ratio. In the moderately polluted air of Julich, where we performed a number of OH measurement spectra. In addition absorption features of unidentified species were frequently detected. A quantitative deconvolution even of the known species is not easy to achieve and can leave residual structures in the spectra. Thus interferences usually increase the noise and deteriorate the OH detection sensitivity. Using diode arrays for sensitive absorption measurements some specific problems of those detectors have to be solved experimentally (i.e. fixed pattern noise, dark signal noise, nonuniform efficiency of individual elements, spatial sensitivity variations). In order to improve the low spatial resolution we performed laboratory studies using a multiple reflection cell to convert the long path technique to a real in situ point measurement. Under the conditions of field experiments in Julich residual absorbance signals at present are about 1.5x10(exp -4) corresponding to an OH detection sensitivity of 2x10(exp 6) OH/cm(exp 3) using a light path of 5.8 km. Total integration times for one measurement point vary between a few minutes and an hour.

Dorn, Hans-Peter↗

DOE OSTI2023

A Vision for Coupling Operation of US Fusion Facilities with HPC Systems and the Implications for Workflows and Data Management

The operation of large US Department of Energy (DOE) research facilities, like the DIII-D National Fusion Facility, results in the collection of complex multi-dimensional scientific datasets, both experimental and model-generated. In the future, it is envisioned that integrated data analysis coupled with large-scale high performance computing (HPC) simulations will be used to improve experimental planning and operation. Practically, massive data sets from these simulations provide the physics basis for generation of both reduced semi-analytic and machine-learning-based models. Storage of both HPC simulation datasets (generated from US DOE leadership computing facilities) and experimental datasets presents significant challenges. In this paper, we present a vision for a DOE-wide data management workflow that integrates US DOE fusion facilities with leadership computing facilities. Data persistence and long-term availability beyond the length of allocated projects is essential, particularly for verification and recalibration of artificial intelligence and machine learning (AI/ML) models. Because these data sets are often generated and shared among hundreds of users across multiple leadership computing facility centers, they would benefit from cross-platform accessibility, persistent identifiers (e.g. DOI, or digital object identifier), and provenance tracking. Here, the ability to handle different data access patterns suggests that a combination of low cost, high latency (e.g. for storing ML training sets) and high cost, low latency systems (e.g. for real-time, integrated machine control feedback) may be needed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Autonomous Aerosol and Plasma Co‐Jet Printing of Metallic Devices at Ambient Temperature

Abstract Additive manufacturing of metallic materials holds the potential to revolutionize the fabrication of functional devices unattainable via traditional methods. Despite recent advancements, printing metallic materials typically requires thermal processing at elevated temperatures to form dense structures with desired properties, which presents a major challenge for direct printing and integration with temperature‐sensitive materials. Herein, a unique co‐jet printing (CJP) method is reported integrating an aerosol jet and a non‐thermal, atmospheric pressure plasma jet to enable concurrent aerosol deposition of metal nanoparticle inks and in situ sintering at ambient temperature. A machine learning algorithm is integrated with the CJP to perform real‐time defect detection and autonomous correction, enhancing the yield of printed films with high electrical conductivity from 44% to 94%. Concurrent printing and sintering eliminate the need for post‐printing processing, reducing the overall manufacturing time by multiple folds depending on product size. CJP enables direct printing of functional devices on a variety of temperature‐sensitive materials including biological materials. Direct printing of hydration sensors on living plant leaves is demonstrated for long‐duration monitoring of hydration level in the plant. The versatile CJP method opens tremendous opportunities to harmoniously integrate abiotic and biotic materials for emerging applications in wearable/implantable devices and biohybrid systems.

Du, Yipu [Department of Aerospace and Mechanical E↗

NASA NTRS1991

Elimination of secular terms from the differential equations for the elements of perturbed two-body motion

In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.

Bond, Victor R.↗