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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Continued Development of Meandering Winding Magnetometer (MWM (Register Trademark)) Eddy Current Sensors for the Health Monitoring, Modeling and Damage Detection of Composite Overwrapped Pressure Vessels

Composite Overwrapped Pressure Vessels (COPVs) are used in essentially all NASA spacecraft, launch. vehicles and payloads to contain high-pressure fluids for propulsion, life support systems and science experiments. Failure of any COPV either in flight or during ground processing would result in catastrophic damage to the spacecraft or payload, and could lead to loss of life. Therefore, NASA continues to investigate new methods to non-destructively inspect (NDE) COPVs for structural anomalies and to provide a means for in-situ structural health monitoring (SHM) during operational service. Partnering with JENTEK Sensors, engineers at NASA, Kennedy Space Center have successfully conducted a proof-of-concept study to develop Meandering Winding Magnetometer (MWM) eddy current sensors designed to make direct measurements of the stresses of the internal layers of a carbon fiber composite wrapped COPV. During this study three different MWM sensors were tested at three orientations to demonstrate the ability of the technology to measure stresses at various fiber orientations and depths. These results showed good correlation with actual surface strain gage measurements. MWM-Array technology for scanning COPVs can reliably be used to image and detect mechanical damage. To validate this conclusion, several COPVs were scanned to obtain a baseline, and then each COPV was impacted at varying energy levels and then rescanned. The baseline subtracted images were used to demonstrate damage detection. These scans were performed with two different MWM-Arrays. with different geometries for near-surface and deeper penetration imaging at multiple frequencies and in multiple orientations of the linear MWM drive. This presentation will include a review of micromechanical models that relate measured sensor responses to composite material constituent properties, validated by the proof of concept study, as the basis for SHM and NDE data analysis as well as potential improvements including design changes to miniaturize and make the sensors durable in the vacuum of space

Russell, Richard↗
DOE OSTI2023

A practical method for modeling temporally-averaged ocean wave frequency-directional spectra for characterizing wave energy climates

Wave energy resource characterization investigations have been hindered because frequency-directional wave spectra are not broadly available for many coastal regions due to the insufficient spatial coverage of buoy observation networks and spectral wave model hindcast outputs. We address this problem by developing and validating a practical method for approximating temporally-averaged frequency-directional wave spectra averaged over periods of months or years from bulk wave parameters, which are available at a much greater coverage and resolution than frequency-directional wave spectra. While the temporally averaged frequency-directional wave spectrum over these periods cannot be used for analyzing a single sea state, it aggregates multiple sea states, identifies dominant wave energy systems representing wave climate, and resolves their spectral characteristics. Therefore, modelling temporally averaged frequency-directional wave spectra is of great value for planning and designing wave energy projects, e.g., resource characterization, site assessment, and conceptual design of wave energy converters. Temporally-averaged frequency-directional wave spectra and related important wave energy parameters approximated using this method are found to be more accurate than commonly used parametric wave spectrum models. This method can be applied to a wide range of wave climates given its universality and high accuracy. Also, the availability of bulk wave parameters from multi-decade high-resolution wave model hindcasts is increasing.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

RELAP5-3D Capabilities for High-Temperature Gas-Cooled Reactor Analysis

RELAP5-3D is the premier systems thermal-hydraulic code in the world. The code has been used significantly for high-temperature gas-cooled reactor (HTGR) analyses over the last 10 years, but there has not been a comprehensive summary of RELAP5-3D capabilities and methods for HTGR modeling. In this paper, we provide a guide for how novice users can build models for prismatic HTGRs. This guide includes best practices for developing heat structures and setting up radiation and conduction heat transfer. We also provide a summary of relevant validation studies. These studies are divided into three categories: separate effects tests, integral effects tests, and nuclear reactor studies. We present a comprehensive review of RELAP5-3D HTGR applications for reactor modeling over the last 10 years. These applications include work for the Modular High-Temperature Gas-Cooled Reactor benchmark, design activities for a prismatic HTGR as part of the U.S. Department of Energy’s Advanced Demonstration and Test Reactor Options Study, and studies performed to design gas-cooled microreactors. Following the comprehensive literature review, we present a gap analysis highlighting capabilities of RELAP5-3D that are available and missing for a complete analysis of HTGR thermal hydraulics. We also discuss the limitations of existing code capabilities and potential improvements that could improve analyses. Current research efforts have yet to fully validate RELAP5-3D for a prismatic HTGR analysis; however, some of this is attributable to confounding factors in the available experimental data as opposed to code capabilities. In conclusion, this paper presents the most comprehensive review to date on RELAP5-3D capabilities, limitations, and applications for HTGR analysis.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

LLNL Explosives Anisotropy Research

Lawrence Livermore National Laboratory scientists and engineers led a multi-institutional team in executing a series of high explosives tests that successfully demonstrated fundamental principles of anisotropy, a possible enabler for improved weapon and munition safety. Working under snowy and frigid conditions on Idaho’s Snake River Plain, a 13-member team from LLNL carried out 52 explosives shots over four days in mid-November at the Idaho National Laboratory’s (INL) National Security Test Range (NSTR) to complete the study. The broader anisotropy (ANISO) team included high explosives handlers and volunteers from INL, Los Alamos National Laboratory, Marine Raiders from the Marine Special Operations Command and members of the U.S. Special Operations Command. The purpose of the study was to explore theoretical methods of creating anisotropic explosives — explosives that perform differently depending on the direction the detonation wave moves through the explosive — by engineering certain physical features in the charges and obtaining basic data from testing. The work is part of an overall effort by the Lab to develop anisotropic explosives that could be used in munitions to reduce the severity and lethality of an unintended detonation without sacrificing performance. The data gathered from the study will be used to design and construct follow-on experiments at LLNL’s High Explosives Applications Facility (HEAF) and validate computer models for future anisotropic assemblies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2012

NASA Tech Briefs, March 2012

The topics include: 1) Spectral Profiler Probe for In Situ Snow Grain Size and Composition Stratigraphy; 2) Portable Fourier Transform Spectroscopy for Analysis of Surface Contamination and Quality Control; 3) In Situ Geochemical Analysis and Age Dating of Rocks Using Laser Ablation-Miniature Mass Spectrometer; 4) Physics Mining of Multi-Source Data Sets; 5) Photogrammetry Tool for Forensic Analysis; 6) Connect Global Positioning System RF Module; 7) Simple Cell Balance Circuit; 8) Miniature EVA Software Defined Radio; 9) Remotely Accessible Testbed for Software Defined Radio Development; 10) System-of-Systems Technology-Portfolio-Analysis Tool; 11) VESGEN Software for Mapping and Quantification of Vascular Regulators; 12) Constructing a Database From Multiple 2D Images for Camera Pose Estimation and Robot Localization; 13) Adaption of G-TAG Software for Validating Touch and Go Asteroid Sample Return Design Methodology; 14) 3D Visualization for Phoenix Mars Lander Science Operations; 15) RxGen General Optical Model Prescription Generator; 16) Carbon Nanotube Bonding Strength Enhancement Using Metal Wicking Process; 17) Multi-Layer Far-Infrared Component Technology; 18) Germanium Lift-Off Masks for Thin Metal Film Patterning; 19) Sealing Materials for Use in Vacuum at High Temperatures; 20) Radiation Shielding System Using a Composite of Carbon Nanotubes Loaded With Electropolymers; 21) Nano Sponges for Drug Delivery and Medicinal Applications; 22) Molecular Technique to Understand Deep Microbial Diversity; 23) Methods and Compositions Based on Culturing Microorganisms in Low Sedimental Fluid Shear Conditions; 24) Secure Peer-to-Peer Networks for Scientific Information Sharing; 25) Multiplexer/Demultiplexer Loading Tool (MDMLT); 26) High-Rate Data-Capture for an Airborne Lidar System; 27) Wavefront Sensing Analysis of Grazing Incidence Optical Systems; 28) Foam-on-Tile Damage Model; 29) Instrument Package Manipulation Through the Generation and Use of an Attenuated-Fluent Gas Fold; 30) Multicolor Detectors for Ultrasensitive Long-Wave Imaging Cameras; 31) Lunar Reconnaissance Orbiter (LRO) Command and Data Handling Flight Electronics Subsystem; and 32) Electro-Optic Segment-Segment Sensors for Radio and Optical Telescopes.

Source record↗
NASA NTRS2013

Swept-Wing Ice Accretion Characterization and Aerodynamics

NASA, FAA, ONERA, the University of Illinois and Boeing have embarked on a significant, collaborative research effort to address the technical challenges associated with icing on large-scale, three-dimensional swept wings. The overall goal is to improve the fidelity of experimental and computational simulation methods for swept-wing ice accretion formation and resulting aerodynamic effect. A seven-phase research effort has been designed that incorporates ice-accretion and aerodynamic experiments and computational simulations. As the baseline, full-scale, swept-wing-reference geometry, this research will utilize the 65% scale Common Research Model configuration. Ice-accretion testing will be conducted in the NASA Icing Research Tunnel for three hybrid swept-wing models representing the 20%, 64% and 83% semispan stations of the baseline-reference wing. Three-dimensional measurement techniques are being developed and validated to document the experimental ice-accretion geometries. Artificial ice shapes of varying geometric fidelity will be developed for aerodynamic testing over a large Reynolds number range in the ONERA F1 pressurized wind tunnel and in a smaller-scale atmospheric wind tunnel. Concurrent research will be conducted to explore and further develop the use of computational simulation tools for ice accretion and aerodynamics on swept wings. The combined results of this research effort will result in an improved understanding of the ice formation and aerodynamic effects on swept wings. The purpose of this paper is to describe this research effort in more detail and report on the current results and status to date. 1

Broeren, Andy P.↗
NASA NTRS2013

Swept-Wing Ice Accretion Characterization and Aerodynamics

NASA, FAA, ONERA, the University of Illinois and Boeing have embarked on a significant, collaborative research effort to address the technical challenges associated with icing on large-scale, three-dimensional swept wings. The overall goal is to improve the fidelity of experimental and computational simulation methods for swept-wing ice accretion formation and resulting aerodynamic effect. A seven-phase research effort has been designed that incorporates ice-accretion and aerodynamic experiments and computational simulations. As the baseline, full-scale, swept-wing-reference geometry, this research will utilize the 65 percent scale Common Research Model configuration. Ice-accretion testing will be conducted in the NASA Icing Research Tunnel for three hybrid swept-wing models representing the 20, 64 and 83 percent semispan stations of the baseline-reference wing. Threedimensional measurement techniques are being developed and validated to document the experimental ice-accretion geometries. Artificial ice shapes of varying geometric fidelity will be developed for aerodynamic testing over a large Reynolds number range in the ONERA F1 pressurized wind tunnel and in a smaller-scale atmospheric wind tunnel. Concurrent research will be conducted to explore and further develop the use of computational simulation tools for ice accretion and aerodynamics on swept wings. The combined results of this research effort will result in an improved understanding of the ice formation and aerodynamic effects on swept wings. The purpose of this paper is to describe this research effort in more detail and report on the current results and status to date.

Broeren, Andy P.↗
NASA NTRS2020

An Overview of NASA’s Learn-to-Fly Technology Development

“Learn-to-Fly” (L2F) is an advanced technology development effort within the Modeling and Control for Agile Aircraft Development (MCAAD) group, a part of the NASA Transformative Aeronautics Concepts Program’s (TACP) Transformational Tools and Technologies (TTT) project. The goal of L2F is to develop technologies for enabling self-learning flight vehicles, using both ground- and flight-test approaches. Specifically, research has been conducted to demonstrate the potential to merge two enabling technologies, real-time aerodynamic modeling and adaptive flight controls, to substantially reduce the typical ground- and flight-testing time requirements for air vehicle design. This effort involved development of real-time, on-board algorithms to demonstrate key L2F technologies including aerodynamic modeling and control for an aircraft with minimal a priori knowledge. This research included both ground-based wind tunnel experiments utilizing modern design of experiments (DOE) techniques, as well as a flight test campaign, and was intended to rapidly advance these technologies and demonstrate key capabilities of the L2F approach. This paper presents the overview of the methods used to develop L2F technologies in NASA Langley Research Center’s 12-Foot Low Speed Tunnel, as well as in flight experiments. These methods include efficient wind tunnel data collection, real-time global nonlinear aerodynamic modeling in both the time and frequency domains, and the integration of the modeling techniques with adaptive flight controls, all of which were demonstrated using experimental validation.

Stephen E Riddick↗
DOE OSTI2023

Neutron Absorber Plate Characterization Plan for Criticality Experiments Design [Slides]

The goal of this presentation is to show the feasibility of performing a critical experiment with a B 4 C/Aluminum alloy neutron absorber plate. The motivation of this experiment is to provide integral data on modern neutron absorber product “Boralcan” by Rio Tinto. In 2020, used in about 20% of spent fuel pools in the US, and in casks for storage and transportation in the US and in Europe. The added value of this experiment: Neutron absorber plate modeling method verification: homogeneous or not, a lot of potential savings by relaxing boron loading credit limits. No available critical benchmark involving Boralcan, other boron-related experiments are relatively old. Nuclear data validation for B, C, and Al in the form of B 4 C in Al matrix.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Q1 Report for FY25 Theory and Simulation Performance Target: Development of an integrated modeling framework for fusion reactor design and assessment

This report describes the work and activities carried out towards the completion of each of the following milestones in FY25 Q1: 1. Demonstrate workflow for generating self-consistent CESOL plasma profiles + first wall and divertor loading prediction and generate the CAT plasma and neutron loading needed for further engineering analysis: $/circ$ Initially run CESOL with SOLPS and map heat flux using simple HEAT method: ▪ Generate SOLPS grid for CAT reference case, ▪ Implement and apply ‘lower’ fidelity method of using HEAT-like analytic method to map SOLPS heat flux from charged particles to first wall, and ▪ Provide initial heat flux + neutron loading for further engineering analysis. 2. Demonstrate multiphysics magnet analysis: $/circ$ Demonstrate validation of the Elmer workflow by comparing induced stresses due to EM forces generated by TF coils using multiple codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion

Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation method for nonlocal diffusion models with Dirichlet boundary condition. The numerical scheme is shown to be convergent to both nonlocal diffusion and its corresponding local limit as nonlocal interaction vanishes. The analysis is carried out on a special family of rectilinear Cartesian grids for a linear RK method with designed kernel support. The key idea for the stability of the RK collocation scheme is to compare the collocation scheme with the standard Galerkin scheme, which is stable. In addition, assembling the stiffness matrix of the nonlocal problem requires costly computational resources because high-order Gaussian quadrature is necessary to evaluate the integral. We thus provide a remedy to the problem by introducing a quasi-discrete nonlocal diffusion operator for which no numerical quadrature is further needed after applying the RK collocation scheme. The quasi-discrete nonlocal diffusion operator combined with RK collocation is shown to be convergent to the correct local diffusion problem by taking the limits of nonlocal interaction and spatial resolution simultaneously. The theoretical results are then validated with numerical experiments. We additionally illustrate a connection between the proposed technique and an existing optimization based approach based on generalized moving least squares.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Experiment and computational fluid dynamics investigation of biochar elutriation in fluidized bed

Here, in fluidized bed biomass fast pyrolysis, the biomass is converted to biochar and elutriated. The elutriation rate is a key parameter in reactor designs and operations. This research presents a video-based continuous measurement of biochar elutriation rate in a fluidized bed with sands and biomass as bed materials. The fluidized bed is simulated with the Computational Fluid Dynamics - Coarse-Grained Discrete Element Method (CFD-CGDEM) in MFiX. The fluidization behavior of non-spherical sands can be more accurately captured when a rolling friction model is used. The predicted elutriation rate is close to the experimental measurement when the particle size distributions are considered and the filtered drag with a shape correction is used. These results validated the accuracy of the MFiX based CFD framework for the prediction of biochar elutriations in the fluidized bed biomass fast pyrolysis reactor.

09 BIOMASS FUELS↗
DOE OSTI2020

Kinetic modeling of microbial growth, enzyme activity, and gene deletions: An integrated model of β-glucosidase function in Cellvibrio japonicus

Understanding the complex growth and metabolic dynamics in microorganisms requires advanced kinetic models containing both metabolic reactions and enzymatic regulation to predict phenotypic behaviors under different conditions and perturbations. Most current kinetic models lack gene expression dynamics and are separately calibrated to distinct media, which consequently makes them unable to account for genetic perturbations or multiple substrates. This challenge limits our ability to gain a comprehensive understanding of microbial processes towards advanced metabolic optimizations that are desired for many biotechnology applications. Here, we present an integrated computational and experimental approach for the development and optimization of mechanistic kinetic models for microbial growth and metabolic and enzymatic dynamics. Our approach integrates growth dynamics, gene expression, protein secretion, and gene-deletion phenotypes. We applied this methodology to build a dynamic model of the growth kinetics in batch culture of the bacterium Cellvibrio japonicus grown using either cellobiose or glucose media. The model parameters were inferred from an experimental data set using an evolutionary computation method. The resulting model was able to explain the growth dynamics of C. japonicus using either cellobiose or glucose media and was also able to accurately predict the metabolite concentrations in the wild-type strain as well as in β-glucosidase gene deletion mutant strains. We validated the model by correctly predicting the non-diauxic growth and metabolite consumptions of the wild-type strain in a mixed medium containing both cellobiose and glucose, made further predictions of mutant strains growth phenotypes when using cellobiose and glucose media, and demonstrated the utility of the model for designing industrially-useful strains. Importantly, the model is able to explain the role of the different β-glucosidases and their behavior under genetic perturbations. Here, this integrated approach can be extended to other metabolic pathways to produce mechanistic models for the comprehensive understanding of enzymatic functions in multiple substrates.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Direct Feed High-Level Waste APPS Model Glass Testing (DFHLW APPS) Matrix

This report summarizes the data collected during the batching and melting of the Direct Feed High-Level Waste APPS Model Glass Matrix (DFHLW APPS) to serve as a quality-assured validation of the Aspen Process Performance Simulation (APPS) formulation method. Of 15 glasses tested, 12 satisfied all target property constraints. Two glasses, APPS-05 and -06, formed nepheline on canister centerline cooling heat-treatment and failed the Product Consistency Test response limits. Glass APPS-07-2 formed unacceptably high concentrations of crystals (primarily Na3Nd(PO4)2) when heat treated at 950 °C. All other glasses were found to be satisfactory. The measured property values were compared to predicted values from a set of current models. In many cases the current models were found to be inadequate for design of DFHLW glasses. These models are being adjusted to correct for mispredictions. Other models, e.g., density, toxicity characteristic leaching procedure, and sulfur solubility, are adequate for formulation of DFHLW glasses.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1981

An experimental study of transmission, reflection and scattering of sound in a free jet flight simulation facility and comparison with theory

When a free jet (or open jet) is used as a wind tunnel to simulate the effects of flight on model noise sources, it is necessary to calibrate out the effects of the free jet shear layer on the transmitted sound, since the shear layer is absent in the real flight case. In this paper, a theoretical calibration procedure for this purpose is first summarized; following this, the results of an experimental program, designed to test the validity of the various components of the calibration procedure, are described. The experiments are conducted by using a point sound source located at various axial positions within the free jet potential core. By using broadband excitation and cross-correlation methods, the angle changes associated with ray paths across the shear layer are first established. Measurements are then made simultaneously inside and outside the free jet along the proper ray paths to determine the amplitude changes across the shear layer. It is shown that both the angle and amplitude changes can be predicted accurately by theory. It is also found that internal reflection at the shear layer is significant only for large ray angles in the forward quadrant where total internal reflection occurs. Finally, the effects of sound absorption and scattering by the shear layer turbulence are also examined experimentally.

Ahuja, K. K.↗
NASA NTRS1999

Unstructured Grid Euler Method Assessment for Longitudinal and Lateral/Directional Aerodynamic Performance Analysis of the HSR Technology Concept Airplane at Supersonic Cruise Speed

Unstructured grid Euler computations, performed at supersonic cruise speed, are presented for a High Speed Civil Transport (HSCT) configuration, designated as the Technology Concept Airplane (TCA) within the High Speed Research (HSR) Program. The numerical results are obtained for the complete TCA cruise configuration which includes the wing, fuselage, empennage, diverters, and flow through nacelles at M (sub infinity) = 2.4 for a range of angles-of-attack and sideslip. Although all the present computations are performed for the complete TCA configuration, appropriate assumptions derived from the fundamental supersonic aerodynamic principles have been made to extract aerodynamic predictions to complement the experimental data obtained from a 1.675%-scaled truncated (aft fuselage/empennage components removed) TCA model. The validity of the computational results, derived from the latter assumptions, are thoroughly addressed and discussed in detail. The computed surface and off-surface flow characteristics are analyzed and the pressure coefficient contours on the wing lower surface are shown to correlate reasonably well with the available pressure sensitive paint results, particularly, for the complex flow structures around the nacelles. The predicted longitudinal and lateral/directional performance characteristics for the truncated TCA configuration are shown to correlate very well with the corresponding wind-tunnel data across the examined range of angles-of-attack and sideslip. The complementary computational results for the longitudinal and lateral/directional performance characteristics for the complete TCA configuration are also presented along with the aerodynamic effects due to empennage components. Results are also presented to assess the computational method performance, solution sensitivity to grid refinement, and solution convergence characteristics.

Ghaffari, Farhad↗
DOE OSTI2023

A fast Monte Carlo cell-by-cell simulation for radiobiological effects in targeted radionuclide therapy using pre-calculated single-particle track standard DNA damage data

Introduction: We developed a new method that drastically speeds up radiobiological Monte Carlo radiation-track-structure (MC-RTS) calculations on a cell-by-cell basis. Methods: The technique is based on random sampling and superposition of single-particle track (SPT) standard DNA damage (SDD) files from a “pre-calculated” data library, constructed using the RTS code TOPAS-nBio, with “time stamps” manually added to incorporate dose-rate effects. This time-stamped SDD file can then be input into MEDRAS, a mechanistic kinetic model that calculates various radiation-induced biological endpoints, such as DNA double-strand breaks (DSBs), misrepairs and chromosomal aberrations, and cell death. As a benchmark validation of the approach, we calculated the predicted energy-dependent DSB yield and the ratio of direct-to-total DNA damage, both of which agreed with published in vitro experimental data. We subsequently applied the method to perform a superfast cell-by-cell simulation of an experimental in vitro system consisting of neuroendocrine tumor cells uniformly incubated with 177 Lu. Results and discussion: The results for residual DSBs, both at 24 and 48 h post-irradiation, are in line with the published literature values. Our work serves as a proof-of-concept demonstration of the feasibility of a cost-effective “in silico clonogenic cell survival assay” for the computational design and development of radiopharmaceuticals and novel radiotherapy treatments more generally.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2020

Bounded motion design in the Earth zonal problem using differential algebra based normal form methods

Establishing long-term relative bounded motion between orbits in perturbed dynamics is a key challenge in astrodynamics to enable cluster flight with minimum propellant expenditure. Herein, we present an approach that allows for the design of long-term relative bounded motion considering a zonal gravitational model. Entire sets of orbits are obtained via high-order Taylor expansions of Poincarè return maps about reference fixed points. The high-order normal form algorithm is used to determine a change in expansion variables of the map into normal form space, in which the phase space behavior is circular and can be easily parameterized by action–angle coordinates. The action–angle representation of the normal form coordinates is then used to parameterize the original Poincarè return map and average it over a full phase space revolution by a path integral along the angle parameterization. As a result, the averaged nodal period and drift in the ascending node are obtained, for which the bounded motion conditions are straightforwardly imposed. Sets of highly accurate bounded orbits are obtained, extending over several thousand kilometers, and valid for decades.

79 ASTRONOMY AND ASTROPHYSICS↗