Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “MULTIPLICITY”

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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Multiple zeros of polynomials

For polynomials of higher degree, iterative numerical methods must be used. Four iterative methods are presented for approximating the zeros of a polynomial using a digital computer. Newton's method and Muller's method are two well known iterative methods which are presented. They extract the zeros of a polynomial by generating a sequence of approximations converging to each zero. However, both of these methods are very unstable when used on a polynomial which has multiple zeros. That is, either they fail to converge to some or all of the zeros, or they converge to very bad approximations of the polynomial's zeros. This material introduces two new methods, the greatest common divisor (G.C.D.) method and the repeated greatest common divisor (repeated G.C.D.) method, which are superior methods for numerically approximating the zeros of a polynomial having multiple zeros. These methods were programmed in FORTRAN 4 and comparisons in time and accuracy are given.

Wood, C. A.↗
NASA NTRS1973

SERT II hollow cathode multiple restarts in space

Future missions, both station keeping and primary electric propulsion, will require multiple thruster restarts after periods of inactivity from a few hours to over one year. Although not a part of the original SERT II (Space Electric Rocket Test) flight objective, the opportunity to demonstrate multiple cathode restarts in space became available following completion of thruster running. Both neutralizer and main cathodes of each flight thruster have been restarted repeatedly following storage periods up to 490 days. No deterioration of cathode heaters has been noted nor has any change been required in starting voltages or currents.

Kerslake, W. R.↗
NASA NTRS1973

Modeling a particular class of multiple-input/multiple-output black boxes with stochastic integral equations and identifying the required parameters

A method is given for obtaining a mathematical model of a class of black boxes having multiple inputs and multiple outputs in terms of Ito stochastic integral equations. This method is applicable to the class of black boxes having ergodic correlation functions when there is zero applied input. The point of view adopted in this paper is phenomenological in that it is desired that calculations made using the mathematical model should be close to what is actually observed at the output of the black box. How close is defined in the problem statement.

Eyman, E. D.↗
NASA NTRS1974

Multiple scattering from finite inhomogeneous media

Utilizing the characteristic information concerning the apparent phase constant difference between the electric and magnetic fields propagating in an inhomogeneous medium, a theoretical analysis of the multiple scattering of electromagnetic waves in finite inhomogeneous media is presented. The solution is obtained by first approximating the coefficients of a pair of exact coupled first-order differential equations and then solving the equations by first-order iteration. The present first-order approximate solution with multiple scattering considerations is shown to be more accurate than the WKB solution. Methods to improve the accuracy of the first-order solution further are discussed. Application of the solution to slowly varying finite media with periodic properties demonstrates the validity of the solution. The same approach can be extended to frequencies in the optical region by retaining additional terms in the coefficients of the coupled differential equations.

Tang, C. C. H.↗
NASA NTRS1974

Multiplex imaging with multiple-pinhole cameras

When making photographs in X rays or gamma rays with a multiple-pinhole camera, the individual images of an extended object such as the sun may be allowed to overlap. Then the situation is in many ways analogous to that in a multiplexing device such as a Fourier spectroscope. Some advantages and problems arising with such use of the camera are discussed, and expressions are derived to describe the relative efficacy of three exposure/postprocessing schemes using multiple-pinhole cameras.

Brown, C.↗
NASA NTRS1974

Effects of multiple scattering on scintillation of transionospheric radio signals

Recent development in the optical scintillation theory has been adapted to the ionospheric geometry in order to study the ionospheric scintillation phenomenon in the presence of multiple scattering. Under approximations well satisfied in typical ionospheres for a frequency above about 20 MHz, the first through fourth moment equations have been derived and some analytic solutions given. The fourth moment equation has also been solved numerically. The numerical results show clearly the occurrence of focusing and saturation phenomena. The new multiple-scatter effects are emphasized.

Liu, C. H.↗
NASA NTRS1974

Multiple pure tone noise generated by fans at supersonic tip speeds

The existence of clusters of pure tones at integral multiples of shaft speed has been noted for supersonic-tip-speed operation of fans and compressors. A continuing program to explore this phenomenon, often called combination-tone noise, has been in effect for several years. This paper reviews the research program, which involves a wide range of engines, compressor rigs, and special apparatus. Elements of the aerodynamics of the blade-associated shock waves are outlined and causes of blade-to-blade shock inequalities, responsible for the multiple tones, are described.

Sofrin, T. G.↗
NASA NTRS1974

Multiple IMU system test plan, volume 4

Operating procedures for this redundant system are described. A test plan is developed with two objectives. First, performance of the hardware and software delivered is demonstrated. Second, applicability of multiple IMU systems to the space shuttle mission is shown through detailed experiments with FDI algorithms and other multiple IMU software: gyrocompassing, calibration, and navigation. Gimbal flip is examined in light of its possible detrimental effects on FDI and navigation. For Vol. 3, see N74-10296.

Landey, M.↗
NASA NTRS1975

A multiple thruster array for 30-cm thrusters

A 3.0 m diameter chamber of the 7.6 m diameter by 21.4 m long vacuum tank was modified to permit testing of an array of up to six 30-cm thrusters with a variety of laboratory and thermal vacuum breadboard power systems. A primary objective of the Multiple Thruster Array (MTA) program is to assess the impact of multiple thruster operation on individual thruster and power processor requirements. The areas of thruster startup, steady-state operation, throttling, high voltage recycle, thrust vectoring, and shutdown are of special concern. The results of initial tests are reported.

Rawlin, V. K.↗
NASA NTRS1974

Stability analysis of nonlinear systems by multiple time scaling

The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.

Morino, L.↗
NASA NTRS1975

On eigenvectors of multiple eigenvalues obtained in NASTRAN

In the case of nonmultiple eigenvalues, each of the three real eigenvalue extraction methods available in NASTRAN will, for a given type of normalization, give essentially the same eigenvectors, but this is not so in the case of multiple eigenvalues. This discrepancy is explained and illustrated by considering the example of a NASTRAN demonstration problem that has both multiple and nonmultiple eigenvalues.

Pamidi, P. R.↗
NASA NTRS1975

A multiple thruster array for 30-cm thrusters

The 3.0-m diameter chamber of the 7.6-m diameter by 21.4-m long vacuum tank at NASA LeRC was modified to permit testing of an array of up to six 30-cm thrusters with a variety of laboratory and thermal vacuum bread-board power systems. A primary objective of the Multiple Thruster Array (MTA) program is to assess the impact of multiple thruster operation on individual thruster and power processor requirements. The areas of thruster startup, steady-state operation, throttling, high voltage recycle, thrust vectoring, and shutdown are of special concern. The results of initial tests are reported.

Rawlin, V. K.↗
NASA NTRS1975

Satellite attitude prediction by multiple time scales method

An investigation is made of the problem of predicting the attitude of satellites under the influence of external disturbing torques. The attitude dynamics are first expressed in a perturbation formulation which is then solved by the multiple scales approach. The independent variable, time, is extended into new scales, fast, slow, etc., and the integration is carried out separately in the new variables. The theory is applied to two different satellite configurations, rigid body and dual spin, each of which may have an asymmetric mass distribution. The disturbing torques considered are gravity gradient and geomagnetic. Finally, as multiple time scales approach separates slow and fast behaviors of satellite attitude motion, this property is used for the design of an attitude control device. A nutation damping control loop, using the geomagnetic torque for an earth pointing dual spin satellite, is designed in terms of the slow equation.

Tao, Y. C.↗
NASA NTRS1976

Active control technology and the use of multiple control surfaces

Needed criteria for active control technology applications in commercial transports are lacking. Criteria for redundancy requirements, believed to be consistent with certification philosophy, are postulated to afford a discussion of the relative value of multiple control surfaces. The control power and frequency bandpass requirements of various active control technology applications are shown to be such that multiple control surfaces offer advantages in minimizing the hydraulic or auxiliary power for the control surface actuators.

Hart, J. E.↗
NASA NTRS1976

An investigation of high-multiplicity gamma events in pp collisions with c.m. energies between 22 and 62 GeV

An experiment was conducted at the CERN intersecting storage rings using colliding proton beams to investigate high-multiplicity gamma-ray events. The objective of the study was to reveal certain features of multiple pion production as well as other possible mechanisms of gamma-ray production. The detector system consisted of ten planes of spark chambers, three scintillation counter hodoscopes and two arrays of lead-glass Cerenkov counters, the first array containing 16 counters and the second, 60 counters. The event trigger was obtained from the Cerenkov counters, and the energies in all the Cerenkov counters after trigger, as well as the information on all the charged particles given by the scintillation counters and spark chambers were recorded on magnetic tape. The relationship between the number of gamma-rays per event and the number of Cerenkov counters triggered by a neutral secondary was established by means of a Monte Carlo calculation.

Dell, G. F.↗
NASA NTRS1977

Multiple curved descending approaches and the air traffic control problem

A terminal area air traffic control simulation was designed to study ways of accommodating increased air traffic density. The concepts that were investigated assumed the availability of the microwave landing system and data link and included: (1) multiple curved descending final approaches; (2) parallel runways certified for independent and simultaneous operation under IFR conditions; (3) closer spacing between successive aircraft; and (4) a distributed management system between the air and ground. Three groups each consisting of three pilots and two air traffic controllers flew a combined total of 350 approaches. Piloted simulators were supplied with computer generated traffic situation displays and flight instruments. The controllers were supplied with a terminal area map and digital status information. Pilots and controllers also reported that the distributed management procedure was somewhat more safe and orderly than the centralized management procedure. Flying precision increased as the amount of turn required to intersect the outer mark decreased. Pilots reported that they preferred the alternative of multiple curved descending approaches with wider spacing between aircraft to closer spacing on single, straight in finals while controllers preferred the latter option. Both pilots and controllers felt that parallel runways are an acceptable way to accommodate increased traffic density safely and expeditiously.

Hart, S. G.↗
NASA NTRS1976

Effect of multiple path approach procedures on runway landing capacity

When using the Instrument Landing System (ILS) all aircraft must follow a straight line approach path before landing. The Microwave Landing System (MLS) will allow use of differing curved approach paths. The objective of this research is to find out whether the introduction of MLS and consequently multiple approach paths can bring an increase in runway landing capacity. A model is developed which is capable of computing the expected ultimate landing runway capacity, under ILS and MLS conditions, when aircraft population characteristics and Air Traffic Control separation rules are given. This model can be applied in situations when only a horizontal separation between aircraft approaching a runway is allowed, as well as when both vertical and horizontal separations are possible. Results suggest that an increase in runway landing capacity, caused by introducing the MLS-described multiple approach paths, is to be expected only when an aircraft population consists of aircraft with significantly differing approach velocities and particularly in situations when a vertical separation can be applied.

Tosic, V.↗