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At least 1,027 records · Page 57

Local behavior of autonomous neutral functional differential equations.

Basic problems for a special class of neutral functional differential equations (NFDE) are formulated, and some contributions to a general qualitative theory in the neighborhood of an equilibrium point are indicated. The properties of a NFDE (G,f) are examined to determine in what sense these properties are insensitive to small changes in (G,f) in the topology G x F. The special class of equations that is introduced includes retarded functional differential equations and difference equations.

Hale, J. K.↗

Liapunov functions for non-linear difference equation stability analysis.

Liapunov functions to determine the stability of non-linear autonomous difference equations can be developed through the use of auxiliary exact difference equations. For this purpose definitions are introduced for the gradient of an implicit function of a discrete variable, a principal sum, a definite sum and an exact difference equation, and a theorem for exactness of a difference form is proved. Examples illustrate the procedure.

Park, K. E.↗

Energy-ratio function for center-of-gravity feedback.

An energy-ratio function is introduced which greatly facilitates analysis and signal design for center-of-gravity feedback communication schemes. Using this function, we show that center-of-gravity feedback using regular-simplex signals achieves Shannon's lower bound on average energy per transmission for zero error probability if M, the number of messages, is 3, 4, or 5 and there is no constraint on system bandwidth.

Fang, T.-T.↗

TLC determination of functionality in prepolymers

Application of thin-layer chromatographics provides rapid qualitative determination of functional distribution in experimental prepolymer. Functionality distribution is of fundamental importance for it determines; (1) manner in which given carboxyl-terminated prepolymer will cure and (2) physical properties of resulting product.

Potts, J. E., Jr.↗

Logical-function generator

Apparatus and technique for generating logical functions and circuits have been developed. They provide aid in designing and constructing hardware to generate logic circuits, by defining circuit connections required to generate these functions. With this method, it is possible quickly and automatically to design logic, while eliminating involved and time-consuming mathematical manipulations.

Sivertson, W. E., Jr.↗

Space shuttle orbiter guidance, naviagation and control software functional requirements: Horizontal flight operations

The shuttle GN&C software functions for horizontal flight operations are defined. Software functional requirements are grouped into two categories: first horizontal flight requirements and full mission horizontal flight requirements. The document privides the intial step in the shuttle GN&C software design process. It also serves as a management tool to identify analyses which are required to define requirements.

Source record↗

Binder model system to be used for determination of prepolymer functionality

Development of a method for determining the functionality distribution of prepolymers used for rocket binders is discussed. Research has been concerned with accurately determining the gel point of a model polyester system containing a single trifunctional crosslinker, and the application of these methods to more complicated model systems containing a second trifunctional crosslinker, monofunctional ingredients, or a higher functionality crosslinker. Correlations of observed with theoretical gel points for these systems would allow the methods to be applied directly to prepolymers.

Martinelli, F. J.↗

Function generator for synthesizing complex vibration mode patterns

A simple highly flexible device for synthesizing complex vibration mode patterns is described. These mode patterns can be used to identify vibration mode data. This device sums selected sine and cosine functions and then plots the sum against a linear function.

Naumann, E. C.↗

The minitrack tracking function description, volume 1

The treatment of tracking data by the Minitrack system is described from the transmission of the nominal 136-MHz radio beacon energy from a satellite and the reception of this signal by the interferometer network through the ultimate derivation of the direction cosines (the angular coordinates of the vector from the tracking station to the spacecraft) as a function of time. Descriptions of some of the lesser-known functions operating on the system, such as the computer preprocessing program, are included. A large part of the report is devoted to the preprocessor, which provides for the data compression, smoothing, calibration correction, and ambiguity resolution of the raw interferometer phase tracking measurements teletyped from each of the worldwide Minitrack tracking stations to the central computer facility at Goddard Space Flight Center. An extensive bibliography of Minitrack hardware and theory is presented.

Englar, T. S., Jr.↗

Relation of the diffuse reflectance remission function to the fundamental optical parameters.

The Kubelka-Munk equations describing the diffuse reflectance of a powdered sample were compared to equations obtained using a uniformly-sized rough-surfaced spherical particle model. The comparison resulted in equations relating the remission function and the Kubelka-Munk constants to the index of refraction, the absorption coefficient, and the average particle diameter of a powdered sample. Published experimental results were used to test the equation relating to the remission function to the fundamental optical parameters.

Simmons, E. L.↗

A class of neutral functional differential equations.

Formulation and study of the initial value problem for neutral functional differential equations. The existence, uniqueness, and continuation of solutions to this problem are investigated, and an analysis is made of the dependence of the solutions on the initial conditions and parameters, resulting in the derivation of a continuous dependence theorem in which the fundamental mathematical principles underlying the continuous dependence problem for a very general system of nonlinear neutral functional differential equations are separated out.

Melvin, W. R.↗

New thermodynamic functions for the C3 molecule.

When graphite is used as ablation material in heat shields, very often a prominent carbon species vaporized into the stream is C3. The thermodynamic properties of the C3 molecule are, therefore, important in calculating transport phenomena in the ablation flow field. The nature of the C3 thermodynamic functions has been in doubt because of the uncertain contribution of the bending mode vibrations to the total internal energy of the molecule. An approach for overcoming these difficulties is considered. The results of the computations are presented in the form of graphs and approximating functions.

Pearson, W. E.↗

The state space and transfer function approaches in practical linear multivariable systems design.

A procedure using transfer function formalism for stabilizing a multivariable feedback system with significant plant uncertainty is presented. The method shapes nominal loop functions and decreases their magnitudes with frequency in such a manner that the system remains stable throughout the plant uncertainty range. An example illustrates the application of the described procedure.

Shaked, U.↗

Functional requirements for onboard management of space shuttle consumables, volume 2.

A study was conducted to develop the functional requirements for onboard management of space shuttle consumables. A specific consumables management concept for the space shuttle vehicle was developed and the functional requirements for the onboard portion of the concept were generated. Consumables management is the process of controlling or influencing the usage of expendable materials involved in vehicle subsystem operation. The subsystems considered in the study are: (1) propulsion, (2) power generation, and (3) environmental and life support.

Graf, P. J.↗

Kullback-Leibler information function and the sequential selection of experiments to discriminate among several linear models

A sequential adaptive experimental design procedure for a related problem is studied. It is assumed that a finite set of potential linear models relating certain controlled variables to an observed variable is postulated, and that exactly one of these models is correct. The problem is to sequentially design most informative experiments so that the correct model equation can be determined with as little experimentation as possible. Discussion includes: structure of the linear models; prerequisite distribution theory; entropy functions and the Kullback-Leibler information function; the sequential decision procedure; and computer simulation results. An example of application is given.

Sidik, S. M.↗

The tracking system analytic calibration activity for Mariner Mars 1971: Its function and scope

The functions of the Tracking System Analytic Calibration activity for Mariner Mars 1971 (MM'71), its objectives for this and future missions, and the support provided to the MM'71 Navigation Team during operations are described. Support functions encompass calibration of tracking data by estimating physical parameters whose uncertainties represent limitations to navigational accuracy, and detailed analysis of the tracking data to uncover and resolve any anomalies. Separate articles treat the activities and results of producing calibrations for the various error sources: Deep Space Station Locations, timing and polar motion, charged particles, and the troposphere. Two other articles are also included discussing the effects of the media error sources on orbit determination and the merits of the smoothing technique used for DRIVID.

Madrid, G. A.↗

Perception of the upright and susceptibility to motion sickness as functions of angle of tilt and angular velocity in off-vertical rotation

Motion sickness susceptibility of four normal subjects was measured in terms of duration of exposure necessary to evoke moderate malaise (MIIA) as a function of velocity in a chair rotated about a central axis tilted 10 deg with respect to gravitational upright. The subjects had little or no susceptibility to this type of rotation at 2.5 and 5.0 rpm, but with further increases in rate, the MIIA endpoint was always reached and with ever shorter test durations. Minimal provocative periods for all subjects were found at 15 or 20 rpm. Higher rotational rates dramatically reversed the vestibular stressor effect, and the subjects as a group tended to reach a plateau of relatively low susceptibility at 40 and 45 rpm. At these higher velocities, furthermore, the subjects essentially lost their sensation of being tilted off vertical. In the second half of the study, the effect of tilt angle was varied while the rotation rate was maintained at a constant 17.5 rpm. Two subjects were completely resistant to symptoms of motion sickness when rotated at 2.5 deg off vertical; with greater off-vertical angles, the susceptibility of all subjects increased sharply at first, then tapered off in a manner reflecting a Fechnerian function.

Earl F. Miller II↗