Search NASA⌕ Search

SEARCH · Search NASA

Results for “JORDAN FORM”

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 NTRS1973

An algorithm for calculation of the Jordan canonical form of a matrix

Jordan canonical forms are used extensively in the literature on control systems. However, very few methods are available to compute them numerically. Most numerical methods compute a set of basis vectors in terms of which the given matrix is diagonalized when such a change of basis is possible. Here, a simple and efficient method is suggested for computing the Jordan canonical form and the corresponding transformation matrix. The method is based on the definition of a generalized eigenvector, and a natural extension of Gauss elimination techniques.

Sridhar, B.↗
NASA NTRS1974

On the use and computation of the Jordan canonical form in system theory

This paper investigates various aspects of the application of the Jordan canonical form of a matrix in system theory and develops a computational approach to determining the Jordan form for a given matrix. Applications include pole placement, controllability and observability studies, serving as an intermediate step in yielding other canonical forms, and theorem proving. The computational method developed in this paper is both simple and efficient. The method is based on the definition of a generalized eigenvector and a natural extension of Gauss elimination techniques. Examples are included for demonstration purposes.

Sridhar, B.↗
NASA NTRS1990

State-variable models of structures having rigid-body modes

In cases where the equations of motion of a structure having rigid-body freedom are cast in state-variable form, generalized state rigid-body modes may be needed. It is possible to find a linearly-independent set of generalized vectors which transform an n x n matrix into the almost-diagonal Jordan form. Attention is presently given to equations governing these generalized eigenvectors, together with illustrative examples of the damped and undamped structure cases.

Craig, Roy R., Jr.↗
NASA NTRS1989

Numerically efficient algorithm for model development of high-order systems

A technique for estimating transfer functions in partial fraction expansion form from frequency response data for a high-order system is presented. The problem formulation avoids many of the numerical difficulties associated with high-order polynomials and has the advantage of having the option to fix the camping and frequency of a mode, if known, during the estimation process. The resulting transfer function(s) may be converted to Jordan-Form time domain equations directly. During the implementation of this technique, a frequency and amplitude normalizing window was developed that maximized the efficiency of the optimization algorithm. The combination of estimating the transfer function in factored form, the ability to fix preciously determined parameters and the effectiveness of the normalizing window led to a progressive approach to synthesizing transfer functions from frequency response data for high-order systems.

Parada, L. O.↗
NASA NTRS1979

Gust alleviation using direct turbulence measurements

The research reported upon in this paper describes an effective method of gust alleviation using direct measurements of atmospheric turbulence to drive the aircraft control surfaces in a way that attempts to directly counter or cancel those forces and moments produced on the aircraft by gusts. The method yields a feedforward or open loop control law, simple to mechanize and relatively insensitive to changes in flight condition. When applied directly, the resulting control law effectively gust-alleviates in the low frequency phugoid and short period range but has a tendency to amplify structural mode vehicle motions due to the phase lag of the actuators. A method of design based upon the use of a diagonal or Jordan form of the equations of motion enables the designer to avoid this problem of structural mode excitation.

Rynaski, E. G.↗
NASA NTRS1983

Population Control of Self-Replicating Systems: Option C

From the conception and development of the theory of self-replicating automata by John von Neumann, others have expanded on his theories. In 1980, Georg von Tiesenhausen and Wesley A. Darbro developed a report which is a "first' in presenting the theories in a conceptualized engineering setting. In that report several options involving self-replicating systems are presented. One of the options allows each primary to generate n replicas, one in each sequential time frame after its own generation. Each replica is limited to a maximum of m ancestors. This study involves determining the state vector of the replicas in an efficient manner. The problem is cast in matrix notation, where F = fij is a non-diagonalizable matrix. Any element fij represents the number of elements of type j = (c,d) in time frame k+1 generated from type i = (a,b) in time frame k. It is then shown that the state vector is: bar F(k)=bar F (non-zero) X F sub K = bar F (non-zero) xmx J sub kx m sub-1 where J is a matrix in Jordan form having the same eigenvalues as F. M is a matrix composed of the eigenvectors and the generalized eigenvectors of F.

Mccord, R. L.↗
NASA NTRS1975

Relaxation methods in fluid mechanics

The present work considers the iterative solution of a coupled set of difference equations and examines methods that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. Methods are studied with regard to their efficiency and economy of computer resources. The basic principles of classical relaxation are set forth, with attention confined to linear elliptic equations. This discussion involves the evaluation of the spectral radius that is the magnitude of the eigenvalue with largest modulus. The subject of relaxation is then related to the study of ordinary differential equations and hyperbolic partial differential equations. Problems that occur when linearly dependent eigenvectors appear in the relaxation matrix are discussed, leading to multiply connected eigenvalues in the Jordan canonical form. Finally, a brief survey of relaxation methods used in aerodynamics is given.

Lomax, H.↗
NASA NTRS1990

Reliable algorithm for modal decomposition

This paper describes a reliable, general algorithm for modal decomposition in real arithmetic and its use in analyzing and synthesizing control logic for linear dynamic systems. The numerical difficulties are described associated with computing the Jordan canonical form when the system has repeated, or nearly repeated, eigenvalues. A new algorithm is described that satisfactorily solves these numerical difficulties. The relation and extension to related numerical analysis research are discussed to clarify the reliability of the techniques. Finally, its implementation as a practical modal decomposition method for efficiently computing the matrix exponential, transfer functions, and frequency response is also described.

Walker, Robert A.↗
NASA NTRS1990

Mueller-Lyer decrement: practice or prolonged inspection?

Noting the similarity between the illusion decrement and selective adaptation paradigms, Long has challenged the view that illusion decrement effects reflect a strategic--as opposed to a structural--underlying mechanism, and has called for further research on this issue. To investigate the confound between prolonged free inspection and repeated trials in the standard decrement procedure, the effects of three inspection conditions (continuous, intermittent, and immediate) on the magnitude of the overestimation Mueller-Lyer illusion have been assessed under two levels of trials (a total of two or six judgments). Significant illusion decline was found only under conditions of repeated trials, with either continuous or intermittent inspection. These findings do not support the predictions of purely structural theories (including neural adaptation and efferent readiness theories), according to which degree of decrement should be determined solely by viewing time. Instead, the data demonstrate that illusion decrement is a product of practice, providing converging evidence for the view of decrement as involving a cognitive 'recalibration' or learning process.

Form Perception↗
NASA NTRS1991

Shared versus distributed memory multiprocessors

The question of whether multiprocessors should have shared or distributed memory has attracted a great deal of attention. Some researchers argue strongly for building distributed memory machines, while others argue just as strongly for programming shared memory multiprocessors. A great deal of research is underway on both types of parallel systems. Special emphasis is placed on systems with a very large number of processors for computation intensive tasks and considers research and implementation trends. It appears that the two types of systems will likely converge to a common form for large scale multiprocessors.

Jordan, Harry F.↗
NASA NTRS1987

Cosmic ray heavy ion LET mapping for aluminum, silicon, and tissue targets

Linear energy transfer (LET) values in aluminum, silicon, and tissue targets have been calculated for 31 galactic cosmic ray ion species in eight different units. The values are described for single event upset (SEU) effect assessments or radiobiological evaluations. The data are presented in graphical and tabular form.

Stassinopoulos, E. G.↗
NASA NTRS2007

Overview of Umbilical Extravehicular Activity (EVA) Interfaces in Life Support Systems on Spacecraft Vehicles and Applications for the Crew Exploration Vehicle (CEV)

Extravehicular Activities (EVAs) for manned spacecraft vehicles have been performed for contingencies and nominal operations numerous times throughout history. This paper will investigate how previous U.S. manned spacecraft vehicles provided life support to crewmembers performing the EVA. Specifically defined are umbilical interfaces with respect to crewmember cooling, drinking water, air (or oxygen), humidity control, and carbon dioxide removal. As historical data is available, the need for planned versus contingency EVAs in previous vehicles as well as details for a nominal EVA day versus a contingency EVA day will be discussed. The hardware used to provide the cooling, drinking water, air (or oxygen), humidity control, and carbon dioxide removal, and the general functions of that hardware, will also be detailed, as information is available. The Crew Exploration Vehicle (CEV or Orion) EVA interfaces will be generically discussed to provide a glimpse of how similar they are to the EVA interfaces in previous vehicles. Conclusions on strategies that should be used for CEV based on previous spacecraft EVA interfaces will be made in the form of questions and recommendations.

Peterson, Laurie J.↗