Results for “ORTHOGONAL TRANSFORMATIONS” — Page 10

NASA NTRS1971

Attitude stability of spinning flexible spacecraft

The stability of spinning flexible satellites in a force-free environment was analyzed. The satellite was modeled as a rigid core having attached to it a flexible appendage idealized as a collection of particles (point masses) interconnected by springs. Both Liapunov and Routh-Hurwitz stability procedures are used. In the former, the Hamiltonian of the system, constrained through the angular momentum integral so as to admit complete damping, is used as a testing function. Equations of motion are written using the hybrid coordinate formulation, which readily accepts a modal coordinate transformation ultimately allowing truncation to a level amenable to literal stability analysis. Closed form stability criteria are generated for the first mode of a restricted appendage model lying in a plane containing the system center of mass and orthogonal to the spin axis. The effects of spin on flexible bodies are discussed by considering a very elementary particle model. Control of passively unstable spacecraft is briefly considered.

Likins, P. W.↗

NASA NTRS1993

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution. Appendix 7

Because of the interesting science which can be performed using a satellite attached by a very long tether to a mother vehicle in orbit, such as the Space Shuttle, NASA will deploy TSS-1 (Tethered Satellite System) in 1992. A very long tether (20 km in this case) has the possibility of undergoing oscillations of several different types, or modes, and higher harmonics of these modes. The purpose of this document is to describe a method for detecting the amplitude, frequency, and phase (and predicting future motion in the steady state) of these modes, in particular, the skiprope mode, using tethered satellite dynamics measurements. Specifically the rotation rate data about two orthogonal axes, calculated from output from satellite gyroscopes, are used. The data of interest are the satellite pitch and roll rate measurements. NASA has determined to use two methods to diagnose skiprope properties and predict future values. One of these, a Fourier transform domain approach, is the subject of this notebook. The main program and all subroutines are described along with the test plan for evaluating the Frequency Domain Skiprope Observer.

Ioup, George E.↗

NASA NTRS1984

An analytic solution for the orbital perturbations of the Venus Radar Mapper due to gravitational harmonics

Hill's variational equations are solved analytically for the orbital perturbations of a spacecraft nominally in an elliptic orbit around a non-spherical body. The rotation of the central planet about its spin-axis is not considered in the analysis. The perturbations are restricted to the planetary gravitational harmonics only. An extremely simple algorithm is derived to transform the spherical harmonic potentials to the orbital coordinate system, and the resulting accelerations are shown to be simply trigonometric functions of the true anomaly. With the principal matrix solution for the differential equations of the adjoint system given in closed form, the orthogonality of the trigonometric functions makes it possible to obtain an analytic solution for the non-homogeneous problem, at intervals of 2 pi in true anomaly. The solution for orbital perturbations can be extended over several revolutions by applying well-known results from Floquet's theory. The technique is demonstrated with results presented on the spacecraft periapsis altitude for the forthcoming Venus Radar Mapper Mission.

Vijayaraghavan, A.↗

NASA NTRS1972

Charged particle motion in the vicinity of a neutral plane

The motion of a charged particle in a 2-dimensional neutral sheet with linear magnetic field variation is analyzed by Hamiltonian methods. From the basic Hamiltonian formulation, results of Sonnerup are recovered and given intuitive interpretation. The transformed Hamiltonian is used to derive the correct frequency of oscillation and serves as the basis of analytical treatment of perturbed versions of the motion, e.g. with electric field added. For 2-dimensional fields with slightly differing configurations - in particular, with added small field component orthogonal to the sheet, with an X-type null or with a chain of null points - two alternative methods are developed, reducing the problem either to motion in a 2-dimensional potential or to a pair of coupled oscillators.

Stern, D.↗

NASA NTRS1995

Time-Domain Computation Of Electromagnetic Fields In MMICs

Maxwell's equations solved on three-dimensional, conformed orthogonal grids by finite-difference techniques. Method of computing frequency-dependent electrical parameters of monolithic microwave integrated circuit (MMIC) involves time-domain computation of propagation of electromagnetic field in response to excitation by single pulse at input terminal, followed by computation of Fourier transforms to obtain frequency-domain response from time-domain response. Parameters computed include electric and magnetic fields, voltages, currents, impedances, scattering parameters, and effective dielectric constants. Powerful and efficient means for analyzing performance of even complicated MMIC.

Lansing, Faiza S.↗

NASA NTRS2000

A Dual Polarized Quasi-Optical SIS Mixer at 550-GHz

We describe the design, fabrication, and the performance of a low-noise dual-polarized quasi-optical superconductor insulator superconductor (SIS) mixer at 550 GHz. The mixer utilizes a novel cross-slot antenna on a hyperhemispherical substrate lens, two junction tuning circuits, niobium trilayer junctions, and an IF circuit containing a lumped element 180 deg hybrid. The antenna consists of an orthogonal pair of twin-slot antennas, and has four feed points, two for each polarization. Each feed point is coupled to a two-junction SIS mixer. The 180 deg IF hybrid is implemented using a lumped element/microstrip circuit located inside the mixer block. Fourier transform spectrometer (FTS) measurements of the mixer frequency response show good agreement with computer simulations. The measured co-polarized and cross-polarized patterns for both polarizations also agree with the theoretical predictions. The noise performance of the dual-polarized mixer is excellent, giving uncorrected receiver noise temperature of better than 115 K (DSB) at 528 GHz for both the polarizations.

Chattopadhyay, Goutam↗

DOE OSTI2026

Improving Chirped Fiber Bragg Grating Resolution for Position-Sensitive Sensors in Shock- and Detonation-Driven Experiments

Chirped fiber Bragg gratings (CFBGs) are robust diagnostic sensors that are widely used to track detonation-driven and shock wave propagation. CFBGs are inscribed with a linearly chirped periodic index of refraction changes that alter the Bragg wavelength along the length of the probe. The light return of each individual Bragg element is captured by a detector at a unique time to map the full reflected spectrum. The CFBG spectrum is measured with a dispersive Fourier transform of the reflected light that temporally stretches the spectrum to increase spatial resolution and make a one-to-one map of the wavelength on a time axis. Here, we propose an improvement of CFBG temporal resolution by incorporating two co-linear laser pulses with orthogonal polarization states and a 5 ns time offset. The two separate signals were split and tracked by two separate detectors. An oscilloscope captured good separation in the signals, and two separate spectrograms were generated and interleaved in the post-processing of the data. This novel technique doubled the CFBG temporal resolution and led to a doubled location resolution. As a proof-of-concept of this technique, the resolution improvement was compared between standard CFBG measurements and the two polarization states method on a position-sensitive CFBG sensor. CFBG resolution doubling will advance sensor capabilities and will have a direct impact on improving capture and analysis in dynamic, high-explosive experiments.

42 ENGINEERING↗

NASA NTRS1982

Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Thompson, J. F.↗

NASA NTRS1988

Incompressible and anelastic flow simulations on numerically generated grids

In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property of orthogonality has been preserved. Flow equations in general curvilinear coordinates maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible models, using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.

Sharman, R. D.↗

DOE OSTI2021

Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes

Uncertainty propagation in complex engineering systems often poses significant computational challenges related to modeling and quantifying probability distributions of model outputs, as those emerge as the result of various sources of uncertainty that are inherent in the system under investigation. Gaussian Processes regression (GPs) is a robust meta-modeling technique that allows for fast model prediction and exploration of response surfaces. Multi-fidelity variations of GPs further leverage information from cheap and low fidelity model simulations in order to improve their predictive performance on the high fidelity model. In order to cope with the high volume of data required to train GPs in high dimensional design spaces, a common practice is to introduce latent design variables that are typically projections of the original input space to a lower dimensional subspace, and therefore substitute the problem of learning the initial high dimensional mapping, with that of training a GP on a low dimensional space. Here in this paper, we present a Bayesian approach to identify optimal transformations that map the input points to low dimensional latent variables. The \projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters, conditioned on the available training data. The proposed Bayesian inference scheme relies on a two-step iterative algorithm that samples from the marginal posteriors of the GP parameters and the projection matrix respectively, both using Markov Chain Monte Carlo (MCMC) sampling. In order to take into account the orthogonality constraints imposed on the orthonormal projection matrix, a Geodesic Monte Carlo sampling algorithm is employed, that is suitable for exploiting probability measures on manifolds. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. We validate our framework on three synthetic problems with a known lower-dimensional subspace. The benefits of our proposed framework, are illustrated on the computationally challenging aerodynamic optimization of a last-stage blade for an industrial gas turbine, where we study the effect of an 85-dimensional shape parameterization of a three-dimensional airfoil on two output quantities of interest, specifically on the aerodynamic efficiency and the degree of reaction

42 ENGINEERING↗

NASA NTRS1978

A procedure for calculating laminar, transitional and/or turbulent three-dimensional boundary layers including surface curvature effects about arbitrary blunt-nosed bodies

The governing equations for laminar, transitional and/or turbulent, incompressible, three-dimensional boundary layers are solved numerically. The equations are developed in terms of an orthogonal surface coordinate system and include surface curvature effects. The coordinates are generated numerically, while the inviscid flow is obtained from a general potential flow procedure. The only restrictions on body geometry are that it possess a blunt nose and a plane of symmetry. The boundary-layer equations, after being transformed into similarity type variables, are solved using the implicit finite-difference Krause scheme. Various test cases are presented to establish the accuracy of the resulting computer program.

Dwoyer, D. L.↗

NASA NTRS2014

TPSAS-NF1676L-18357-DND

High-spectral resolution measurements (in the IR region) from space born infrared sensors can provide sufficient spectral information about cloud properties like cloud top pressure, cloud particle size and cloud optical thickness. Empirical orthogonal function (EOF) based regression scheme was used to retrieve cloud properties along with atmospheric state profiles. A channel based physical inversion scheme was also tried on cloud-contaminated radiances to improve retrieval accuracy achieved by regression scheme. Recently developed principle component (PC) based physical retrieval algorithm utilized the EOF transformation to compress both hyperspectral radiance spectra and atmospherical profiles into PC scores to greatly boost the computational speed while maintaining the information content. The accuracy of the (PC) based radiation transfer model (PCRTM) to simulate top-of the atmosphere(TOA) high-spectral resolution radiance spectra for both clear and cloudy sky conditions has been well tested by comparing with the other line-by-line radiation transfer model and using the observation data. The application of the PCRTM based physical inversion method on simulated IASI radiance under 'cloudy' conditions will be a good integrity test for the new algorithm.

X Liu↗

NASA NTRSDate not supplied

Derivation of Integrated Load Distributions from Resampled Computational Data

Principal component analysis (PCA) has been the center of many surrogate models used to characterize fluid flows in recent years. However, little work has been done to character- ize the uncertainty in the PCA transform itself and its effect on derived surrogate models. To explore the uncertainty, a typical interpolated surrogate model is constructed for a represen- tative aerodynamic body from computational data. The computational data is then resampled to explore the robustness of the PCA transformation. The variations of the model predictions during this resampling are analyzed to get a measure of confidence in the PCA transformation, which is then applied to the interpolated surrogate model to get uncertainty on integrated force predictions. An initial test case has been explored with promising results.

Principal Component Analysis↗

NASA NTRSDate not supplied

Derivation of Integrated Load Distributions from Resampled Computational Data

Principal component analysis (PCA) has been the center of many surrogate models used to characterize fluid flows in recent years. However, little work has been done to character- ize the uncertainty in the PCA transform itself and its effect on derived surrogate models. To explore the uncertainty, a typical interpolated surrogate model is constructed for a represen- tative aerodynamic body from computational data. The computational data is then resampled to explore the robustness of the PCA transformation. The variations of the model predictions during this resampling are analyzed to get a measure of confidence in the PCA transformation, which is then applied to the interpolated surrogate model to get uncertainty on integrated force predictions. An initial test case has been explored with promising results.

Computational Fluid Dynamics↗

NASA NTRS2015

9+ Years of CALIPSO PSC Observations: An Evolving Climatology

Polar stratospheric clouds (PSCs) play a crucial role in the springtime chemical depletion of ozone at high latitudes. PSC particles (primarily supercooled ternary solution, or STS droplets) provide sites for heterogeneous chemical reactions that transform stable chlorine and bromine reservoir species into highly reactive ozone-destructive forms. Furthermore, large nitric acid trihydrate (NAT) PSC particles can irreversibly redistribute odd nitrogen through gravitational sedimentation (a process commonly known as denitrification), which prolongs the ozone depletion process by slowing the reformation of the stable chlorine reservoirs. Spaceborne observations from the CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) lidar on the CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) satellite are providing a rich new dataset for studying PSCs. CALIPSO is an excellent platform for studying polar processes with CALIOP acquiring, on average, over 300,000 backscatter profiles daily at latitudes between 55o and 82o in both hemispheres. PSCs are detected in the CALIOP backscatter profiles using a successive horizontal averaging scheme that enables detection of strongly scattering PSCs (e.g., ice) at the finest possible spatial resolution (5 km), while enhancing the detection of very tenuous PSCs (e.g., low number density NAT) at larger spatial scales (up to 135 km). CALIOP PSCs are separated into composition classes (STS; liquid/NAT mixtures; and ice) based on the ensemble 532-nm scattering ratio (the ratio of total-to-molecular backscatter) and 532-nm particulate depolarization ratio (which is sensitive to the presence of non-spherical, i.e. NAT and ice particles). In this paper, we will provide an overview of the CALIOP PSC detection and composition classification algorithm and then examine the vertical and spatial distribution of PSCs in the Arctic and Antarctic on vortex-wide scales for entire PSC seasons over the more than nine-year data record from 2006- 2015.

Pitts, Michael C.↗

NASA NTRS2015

CALIPSO Polar Stratospheric Cloud Observations from 2006-2015

Polar stratospheric clouds (PSCs) play a crucial role in the springtime chemical depletion of ozone at high latitudes. PSC particles (primarily supercooled ternary solution, or STS droplets) provide sites for heterogeneous chemical reactions that transform stable chlorine and bromine reservoir species into highly reactive ozone-destructive forms. Furthermore, large nitric acid trihydrate (NAT) PSC particles can irreversibly redistribute odd nitrogen through gravitational sedimentation (a process commonly known as denitrification), which prolongs the ozone depletion process by slowing the reformation of the stable chlorine reservoirs. Spaceborne observations from the CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) lidar on the CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) satellite are providing a rich new dataset for studying PSCs. CALIPSO is an excellent platform for studying polar processes with CALIOP acquiring, on average, over 300,000 backscatter profiles daily at latitudes between 55o and 82o in both hemispheres. PSCs are detected in the CALIOP backscatter profiles using a successive horizontal averaging scheme that enables detection of strongly scattering PSCs (e.g., ice) at the finest possible spatial resolution (5 km), while enhancing the detection of very tenuous PSCs (e.g., low number density NAT) at larger spatial scales (up to 135 km). CALIOP PSCs are separated into composition classes (STS; liquid/NAT mixtures; and ice) based on the ensemble 532-nm scattering ratio (the ratio of total-to-molecular backscatter) and 532-nm particulate depolarization ratio (which is sensitive to the presence of non-spherical, i.e. NAT and ice particles). In this paper, we will provide an overview of the CALIOP PSC detection and composition classification algorithm and then examine the vertical and spatial distribution of PSCs in the Arctic and Antarctic on vortex-wide scales for entire PSC seasons over the more than nine-year data record from 2006- 2015.

Pitts, Michael C.↗

NASA NTRSDate not supplied

TPSAS-NF1676L-20076-DND

Polar stratospheric clouds (PSCs) play a crucial role in the springtime chemical depletion of ozone at high latitudes. PSC particles (primarily supercooled ternary solution, or STS droplets) provide sites for heterogeneous chemical reactions that transform stable chlorine and bromine reservoir species into highly reactive ozone-destructive forms. Furthermore, large nitric acid trihydrate (NAT) PSC particles can irreversibly redistribute odd nitrogen through gravitational sedimentation (a process commonly known as denitrification), which prolongs the ozone depletion process by slowing the reformation of the stable chlorine reservoirs. Spaceborne observations from the CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) lidar on the CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) satellite are providing a rich new dataset for studying PSCs. CALIPSO is an excellent platform for studying polar processes with CALIOP acquiring, on average, over 300,000 backscatter profiles daily at latitudes between 55o and 82o in both hemispheres. PSCs are detected in the CALIOP backscatter profiles using a successive horizontal averaging scheme that enables detection of strongly scattering PSCs (e.g., ice) at the finest possible spatial resolution (5 km), while enhancing the detection of very tenuous PSCs (e.g., low number density NAT) at larger spatial scales (up to 135 km). CALIOP PSCs are separated into composition classes (STS; liquid/NAT mixtures; and ice) based on the ensemble 532-nm scattering ratio (the ratio of total-to-molecular backscatter) and 532-nm particulate depolarization ratio (which is sensitive to the presence of non-spherical, i.e. NAT and ice particles). In this paper, we will provide an overview of the CALIOP PSC detection and composition classification algorithm and then examine the vertical and spatial distribution of PSCs in the Arctic and Antarctic on vortex-wide scales for entire PSC seasons over the more than eight-year data record.

Michael C Pitts↗

NASA NTRSDate not supplied

A Synopsis of the 8+ Year CALIOP Polar Stratospheric Cloud Data Record

Polar stratospheric clouds (PSCs) play a crucial role in the springtime chemical depletion of ozone at high latitudes. PSC particles (primarily supercooled ternary solution, or STS droplets) provide sites for heterogeneous chemical reactions that transform stable chlorine and bromine reservoir species into highly reactive ozone-destructive forms. Furthermore, large nitric acid trihydrate (NAT) PSC particles can irreversibly redistribute odd nitrogen through gravitational sedimentation (a process commonly known as denitrification), which prolongs the ozone depletion process by slowing the reformation of the stable chlorine reservoirs. Spaceborne observations from the CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) lidar on the CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) satellite are providing a rich new dataset for studying PSCs. CALIPSO is an excellent platform for studying polar processes with CALIOP acquiring, on average, over 300,000 backscatter profiles daily at latitudes between 55o and 82o in both hemispheres. PSCs are detected in the CALIOP backscatter profiles using a successive horizontal averaging scheme that enables detection of strongly scattering PSCs (e.g., ice) at the finest possible spatial resolution (5 km), while enhancing the detection of very tenuous PSCs (e.g., low number density NAT) at larger spatial scales (up to 135 km). CALIOP PSCs are separated into composition classes (STS; liquid/NAT mixtures; and ice) based on the ensemble 532-nm scattering ratio (the ratio of total-to-molecular backscatter) and 532-nm particulate depolarization ratio (which is sensitive to the presence of non-spherical, i.e. NAT and ice particles). In this paper, we will provide an overview of the CALIOP PSC detection and composition classification algorithm and then examine the vertical and spatial distribution of PSCs in the Arctic and Antarctic on vortex-wide scales for entire PSC seasons over the more than eight-year data record.

Michael C Pitts↗