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At least 1,009 records · Page 56

Evolution of Astrodynamics for Multibody Environments, Numerical Precision and Dynamical Understanding

The innovative nature of dynamical systems theory and its applications in trajectory design enabled many recent missions by opening up new transfer and capture opportunities to meet mission requirements, reduce fuel costs, and address various launch constraints and contingencies. With a combination of proven numerical methods and an advanced understanding of the dynamics, an ‘experienced’ user can rapidly design multibody and cislunar missions such as Lunar IceCube and Artemis/Themis and relatively quickly conceive trajectory concepts for Sun-Earth mission orbits, such as the Space Weather Follow On-L1 Lissajous orbit—one that can be achieved and maintained.

Dynamical Systems↗

Energetic Particles in Geospace: Origin, Dynamics, and Modeling

This presentation explores the origins and dynamics of energetic particles—specifically solar energetic particles (SEPs) and galactic cosmic rays (GCRs) - within the heliosphere and Earth's magnetosphere. We will discuss the fundamental physical processes governing their transport and acceleration in the heliosphere, including interactions with the solar wind and the interplanetary magnetic field. The penetration of these particles into Earth's magnetosphere is examined, emphasizing how the geomagnetic field influences their propagation across the magnetosphere. Key phenomena such as the temporal trapping of SEPs in geospace, reductions in rigidity cutoff during geomagnetic storms, and the enhancement of atmospheric NOx and HOx concentrations - which affect the ozone balance through catalytic reactions—are discussed. The presentation also outlines contemporary numerical modeling techniques used to simulate SEPs and GCRs, providing insights into their complex behaviors under varying geomagnetic conditions.

solar energetic particles↗

The Space Weather Follow On – Lagrange 1 Mission

The Space Weather Follow On – Lagrange 1 (SWFO-L1) Observatory will be situated in a Sun-Earth L1 Lissajous orbit with the goal of providing continuous measurements of the space environment and observations of the Sun’s outer atmosphere, and contributing to accurate forecasts of space weather disturbances. Unique to the SWFO-L1 mission are challenges of a rideshare launch, immoderate momentum management delta-V residuals, and spacecraft maneuver design considerations, resulting in specialized operational approach, management, and support.

cislunar↗

The Space Weather Follow On – Lagrange 1 Mission

The Space Weather Follow On – Lagrange 1 (SWFO-L1) Observatory will be situated in a Sun-Earth L1 Lissajous orbit with the goal of providing continuous measurements of the space environment and observations of the Sun’s outer atmosphere, and contributing to accurate forecasts of space weather disturbances. Unique to the SWFO-L1 mission are challenges of a rideshare launch, immoderate momentum management delta-V residuals, and spacecraft maneuver design considerations, resulting in specialized operational approach, management, and support.

Dynamical Systems↗

Impact Testing of 410 Stainless Steel for Material Impact Model Development

A project is underway to develop a consistent set of material properties, impact test data, and failure analysis for a variety of metallic aircraft materials that can be used to develop improved impact failure and deformation models. This project is jointly funded by the NASA Glenn Research Center and the Federal Aviation Administration William J. Hughes Technical Center. Particular features of this set of data are that all material property and impact test data are obtained using traceable material, the test methods and procedures are extensively documented, and all the raw data are available. Four parallel efforts are currently underway: measurement of material deformation and failure response over a wide range of strain rates and temperatures, failure analysis of material property specimens and impact test articles, development of improved numerical modeling techniques for deformation and failure, and impact testing of flat panels and substructures for model validation. This report describes impact testing performed on 410 stainless steel sheet and plate samples of different thicknesses with two different types of projectiles, one a regular cylinder and one with a more complex geometry incorporating features representative of a jet engine fan blade. Data from this testing will be used in validating material models developed under this program. The material tests and the material models developed in this program will be published in separate reports.

410 Stainless Steel↗

Mathematical Tools for the Analysis of Periodic and Aperiodic Grid Signals

Numerous sensing techniques and instrumentation are used in determining the state of the electric grid. Coupled with such measurements are the methods and analysis tools used. The parameters of interest result in both periodic and aperiodic signals. An examination of appropriate analysis tools is presented

97 MATHEMATICS AND COMPUTING↗

A generalized-capacity-matrix technique for computing aerodynamic flows

A numerical generalized-capacity-matrix technique is developed for application to aerodynamic flow computations. This technique allows the very fast direct (noniterative) numerical elliptic solvers to be used in problems with arbitrary internal boundaries and with a wide class of boundary conditions, including numerical application of the Kutta condition on an airfoil without iteration. Accuracy, speed, and usefulness of the technique are demonstrated with linear problems for potential flows over airfoil shapes. The method's main advantages, however, can be exploited within iterative procedures for a variety of complex flow problems governed by systems of equations not necessarily elliptic or linear.

Martin, E. D.↗

Particle-mesh techniques

This is an introduction to numerical Particle-Mesh techniques, which are commonly used to model plasmas, gravitational N-body systems, and both compressible and incompressible fluids. The theory behind this approach is presented, and its practical implementation, both for serial and parallel machines, is discussed. This document is based on a four-hour lecture course presented by the author at the NASA Summer School for High Performance Computational Physics, held at Goddard Space Flight Center.

Macneice, Peter↗

Estimation of geopotential from satellite-to-satellite range rate data: Numerical results

A technique for high-resolution geopotential field estimation by recovering the harmonic coefficients from satellite-to-satellite range rate data is presented and tested against both a controlled analytical simulation of a one-day satellite mission (maximum degree and order 8) and then against a Cowell method simulation of a 32-day mission (maximum degree and order 180). Innovations include: (1) a new frequency-domain observation equation based on kinetic energy perturbations which avoids much of the complication of the usual Keplerian element perturbation approaches; (2) a new method for computing the normalized inclination functions which unlike previous methods is both efficient and numerically stable even for large harmonic degrees and orders; (3) the application of a mass storage FFT to the entire mission range rate history; (4) the exploitation of newly discovered symmetries in the block diagonal observation matrix which reduce each block to the product of (a) a real diagonal matrix factor, (b) a real trapezoidal factor with half the number of rows as before, and (c) a complex diagonal factor; (5) a block-by-block least-squares solution of the observation equation by means of a custom-designed Givens orthogonal rotation method which is both numerically stable and tailored to the trapezoidal matrix structure for fast execution.

Thobe, Glenn E.↗

Viscosity measurements at high temperature and high pressure: A novel technique

The extensive numerical modelling of transport phenomena was performed for the melt growth of mercury cadmium telluride. To increase the fidelity of modelling the kinematic viscosity of liquid Hg(1-x)Cd(x)Te was determined at various compositions in the range of x between 0 and 0.2 and at temperatures around and below the respective melting point. The phase diagram of Hg(1-x)Cd(x)Te shows that for this range the melting point varies from 670 C for pure HgTe to 790 C at x=0.2. The vapor pressure above the melt varies correspondingly from 15 to about 40 atm. Hence, the measurement of viscosities in this system requires a technique that allows for combinations of high temperatures and pressures. In addition, a closed isothermal system is required. The high pressure melt container must also be inert to molten Hg(1-x)Cd(x)Te to avoid possible errors from contamination of the liquid. A novel technique that largely circumvents the above experimental problems is described. Its theory is also presented.

Jin, Wei-Qing↗

Analysis and design of three dimensional supersonic nozzles. Volume 2: Numerical program for analysis of nozzle-exhaust flow fields

The FORTRAN IV Program developed to analyze the flow field associated with scramjet exhaust systems is presented. The instructions for preparing input and interpreting output are described. The program analyzes steady three dimensional supersonic flow by the reference plane characteristic technique. The governing equations and numerical techniques employed are presented in Volume 1 of this report.

Kalben, P.↗

Prediction of blade-vortex interaction noise using airloads generated by a finite-difference technique

The present numerical finite-difference scheme for helicopter blade-load prediction during realistic, self-generated three-dimensional blade-vortex interactions (BVI) derives the velocity field through a nonlinear superposition of the rotor flow-field yielded by the full potential rotor flow solver RFS2 for BVI, on the one hand, over the rotational vortex flow field computed with the Biot-Savart law. Despite the accurate prediction of the acoustic waveforms, peak amplitudes are found to have been persistently underpredicted. The inclusion of BVI noise source in the acoustic analysis significantly improved the perceived noise level-corrected tone prediction.

Tadghighi, Hormoz↗

Application of artificial intelligence to impulsive orbital transfers

A generalized technique for the numerical solution of any given class of problems is presented. The technique requires the analytic (or numerical) solution of every applicable equation for all variables that appear in the problem. Conditional blocks are employed to rapidly expand the set of known variables from a minimum of input. The method is illustrated via the use of the Hohmann transfer problem from orbital mechanics.

Burns, Rowland E.↗

Accuracy and resolution of Earth Radiation Budget Estimates

A numerical filter inversion technique that reduces wide-angle satellite measurements to top-of-the-atmosphere radiant exitances has been proposed for the Earth Radiation Budget Experiment (ERBE). The matrix formulation of this technique is presented, and the design of the numerical filter is discussed. The filter is smoothed with a singular value decomposition. The inversion process is simulated by generating synthetic measurements from a 24 degree spherical harmonic radiation field derived from Nimbus 6 ERB data. The numerical filter is applied to these measurements after they are corrupted with instrument error. The results are curves of expected error versus resolution area.

Green, R. N.↗

A differential delay equation arising from the sieve of Eratosthenes

Consideration is given to the differential delay equation introduced by Buchstab (1937) in connection with an asymptotic formula for the uncanceled terms in the sieve of Eratosthenes. Maier (1985) used this result to show there is unexpected irreqularity in the distribution of primes in short intervals. The function omega(u) is studied in this paper using numerical and analytical techniques. The results are applied to give some numerical constants in Maier's theorem.

Cheer, A. Y.↗