Search NASA⌕ Search

SEARCH · Search NASA

Results for “VECTOR SPACE”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Vector space methods of photometric analysis - Applications to O stars and interstellar reddening

A multivariate vector-space formulation of photometry is developed which accounts for error propagation. An analysis of uvby and H-beta photometry of O stars is presented, with attention given to observational errors, reddening, general uvby photometry, early stars, and models of O stars. The number of observable parameters in O-star continua is investigated, the way these quantities compare with model-atmosphere predictions is considered, and an interstellar reddening law is derived. It is suggested that photospheric expansion affects the formation of the continuum in at least some O stars.

Massa, D.↗
NASA NTRS2009

Discrete Fourier Transform Analysis in a Complex Vector Space

Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

Dean, Bruce H.↗
NASA NTRS2010

How to Maneuver Around in Eccentricity Vector Space

The GRAIL mission to the Moon will be the first time that two separate robotic orbiters will be placed into formation in orbit around a body other than Earth. The need to design an efficient series of maneuvers to shape the orbits and phasing of the two orbiters after arrival presents a significant challenge to mission designers. This paper presents a simple geometric method for relating in-plane impulsive maneuvers to changes in the eccentricity vector, which determines the shape and orientation of an orbit in the orbit plane. Examples then show how such maneuvers can accommodate desired changes to other orbital elements such as period, incination, and longitude of the ascending node.

orbit maneuvers↗
NASA NTRS1980

Vector space methods of photometric analysis. II - Refinement of the MK grid for B stars. III - The two components of ultraviolet reddening

This paper discusses systematic errors which arise from exclusive use of the MK system to determine reddening. It is found that implementation of uvby, beta photometry to refine the qualitative MK grid substantially reduces stellar mismatch error. A working definition of 'identical' ubvy, beta types is investigated and the relationship of uvby to B-V color excesses is determined. A comparison is also made of the hydrogen based uvby, beta types with the MK system based on He and metal lines. A small core correlated effective temperature luminosity error in the MK system for the early B stars is observed along with a breakdown of the MK luminosity criteria for the late B stars. The second part investigates the wavelength dependence of interstellar extinction in the ultraviolet wavelength range observed with the TD-1 satellite. In this study the sets of identical stars employed to find reddening are determined more precisely than in previous studies and consist only of normal, nonsupergiant stars. A multivariate analysis of variance techniques in an unbiased coordinate system is used for determining the wavelength dependence of reddening.

Massa, D.↗
NASA NTRS2003

Robot Acquisition of Active Maps Through Teleoperation and Vector Space Analysis

The work performed under this contract was in the area of intelligent robotics. The problem being studied was the acquisition of intelligent behaviors by a robot. The method was to acquire action maps that describe tasks as sequences of reflexive behaviors. Action maps (a.k.a. topological maps) are graphs whose nodes represent sensorimotor states and whose edges represent the motor actions that cause the robot to proceed from one state to the next. The maps were acquired by the robot after being teleoperated or otherwise guided by a person through a task several times. During a guided task, the robot records all its sensorimotor signals. The signals from several task trials are partitioned into episodes of static behavior. The corresponding episodes from each trial are averaged to produce a task description as a sequence of characteristic episodes. The sensorimotor states that indicate episode boundaries become the nodes, and the static behaviors, the edges. It was demonstrated that if compound maps are constructed from a set of tasks then the robot can perform new tasks in which it was never explicitly trained.

Peters, Richard Alan, II↗
NASA NTRS2015

Discrete Fourier Transform in a Complex Vector Space

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Dean, Bruce H.↗
NASA NTRS1983

On orthogonal expansions of the space of vector functions which are square-summable over a given domain and the vector analysis operators

The Hilbert space L2(omega) of vector functions is studied. A breakdown of L2(omega) into orthogonal subspaces is discussed and the properties of the operators for projection onto these subspaces are investigated from the standpoint of preserving the differential properties of the vectors being projected. Finally, the properties of the operators are examined.

Bykhovskiy, E. B.↗
NASA NTRS1972

Distribution of error in least-squares solution of an overdetermined system of linear simultaneous equations

Probability density functions were derived for errors in the evaluation of unknowns by the least squares method in system of nonhomogeneous linear equations. Coefficients of the unknowns were assumed correct and computational precision were also assumed. A vector space was used, with number of dimensions equal to the number of equations. An error vector was defined and assumed to have uniform distribution of orientation throughout the vector space. The density functions are shown to be insensitive to the biasing effects of the source of the system of equations.

Miller, C. D.↗
NASA NTRS1974

The saturation spectrum of parametric instabilities

Recent calculations on the nonlinear saturation spectrum of the parametric decay instability are described. The initial calculations did not use the correct expression for the spontaneous emission term and were aimed at obtaining the distribution of spectral energy in the unstable part of wave vector space. Results of those initial calculations are combined here with the correct expression for the spontaneous emission term to obtain the distribution of spectral energy in the stable part of wave vector space. These latter calculations are believed to be relevant to the interpretation of the so called plasma line spectra obtained in ionospheric heating experiments at Arecibo, Puerto Rico.

Fejer, J. A.↗
NASA NTRS1988

Automatic calibration of space based manipulators and mechanisms

Four tasks in manipulator kinematic calibration are summarized. Calibration of a seven degree of freedom manipulator was simulated. A calibration model is presented that can be applied on a closed-loop robot. It is an expansion of open-loop kinematic calibration algorithms subject to constraints. A closed-loop robot with a five-bar linkage transmission was tested. Results show that the algorithm converges within a few iterations. The concept of model differences is formalized. Differences are categorized as structural and numerical, with emphasis on the structural. The work demonstrates that geometric manipulators can be visualized as points in a vector space with the dimension of the space depending solely on the number and type of manipulator joint. Visualizing parameters in a kinematic model as the coordinates locating the manipulator in vector space enables a standard evaluation of the models. Key results include a derivation of the maximum number of parameters necessary for models, a formal discussion on the inclusion of extra parameters, and a method to predetermine a minimum model structure for a kinematic manipulator. A technique is presented that enables single point sensors to gather sufficient information to complete a calibration.

Everett, Louis J.↗
NASA NTRS2019

Powder Bed Fusion Additive Manufacturing of JBK-75

JBK-75 is an iron-nickel derivative alloy of A-286 that has been of interest to NASA’s propulsion community for use in fuel injectors and other components that are used in hot, corrosive environments. To enable the rapid production of these components in JBK-75, Marshall Space Flight Center has developed parameters for manufacturing fully dense JBK-75 components using powder bed fusion additive manufacturing (PBFAM). These parameters were developed in a two-step development. First, the depth of laser penetration in the powdered material was measured across a spectrum of laser powers to determine the optimal power necessary for generating the desired meltpool depth. The parameter set’s vector-to-vector spacing was then then tailored to guarantee the full densification of the desired area. The results of this development was a readily implementable parameter that produced 99.6% dense material when using a 147W power running at 600mm/s with a 85μm(32%) vector-to-vector spacing.

Jones, Z. C.↗
NASA NTRS1988

The SAMEX Vector Magnetograph: A Design Study for a Space-Based Solar Vector Magnetograph

This report presents the results of a pre-phase A study performed by the Marshall Space Flight Center (MSFC) for the Air Force Geophysics Laboratory (AFGL) to develop a design concept for a space-based solar vector magnetograph and hydrogen-alpha telescope. These are two of the core instruments for a proposed Air Force mission, the Solar Activities Measurement Experiments (SAMEX). This mission is designed to study the processes which give rise to activity in the solar atmosphere and to develop techniques for predicting solar activity and its effects on the terrestrial environment.

Hagyard, M. J.↗
NASA NTRS2006

A New Look at Some Solar Wind Turbulence Puzzles

Some aspects of solar wind turbulence have defied explanation. While it seems likely that the evolution of Alfvenicity and power spectra are largely explained by the shearing of an initial population of solar-generated Alfvenic fluctuations, the evolution of the anisotropies of the turbulence does not fit into the model so far. A two-component model, consisting of slab waves and quasi-two-dimensional fluctuations, offers some ideas, but does not account for the turning of both wave-vector-space power anisotropies and minimum variance directions in the fluctuating vectors as the Parker spiral turns. We will show observations that indicate that the minimum variance evolution is likely not due to traditional turbulence mechanisms, and offer arguments that the idea of two-component turbulence is at best a local approximation that is of little help in explaining the evolution of the fluctuations. Finally, time-permitting, we will discuss some observations that suggest that the low Alfvenicity of many regions of the solar wind in the inner heliosphere is not due to turbulent evolution, but rather to the existence of convected structures, including mini-clouds and other twisted flux tubes, that were formed with low Alfvenicity. There is still a role for turbulence in the above picture, but it is highly modified from the traditional views.

Roberts, Aaron↗
NASA NTRS2002

Control of Initialized Fractional-Order Systems

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex Airplane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex Airplane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Hartly, Tom T.↗
NASA NTRS2002

Control of Initialized Fractional-Order Systems

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex w-plane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex w-plane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Hartley, Tom T.↗