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NASA NTRS1988

Nonlinear Analysis Of Rotor Dynamics

Study explores analytical consequences of nonlinear Jeffcott equations of rotor dynamics. Section 1: Summary of previous studies. Section 2: Jeffcott Equations. Section 3: Proves two theorems that provide inequalities on coefficients of differential equations and magnitude of forcing function in absence of side force. Section 4: Numerical investigation of multiple-forcing-function problem by introducing both side force and mass imbalance. Section 5: Examples of numberical solutions of complex generalized Jeffcott equation with two forcing functions of different frequencies f1 and f2. Section 6: Boundedness and stability of solutions.Section 7: Concludes report reviewing analytical results and significance.

Day, William B.↗

NASA NTRS1988

A new approach to resonance line scattering in planetary atmospheres

The invariant imbedding technique is applied to the problem of resonance line scattering with frequency redistribution. By applying the principles of invariance to the resonance line scattering problem a set of non-linear, integrodifferential equations for the scattering and transmission functions are derived. Thus, an alternate approach to the resonance line scattering problem is presented. Rather than solving for the specific intensity directly the invariant imbedding equations may be solved for the scattering and transmission functions from which the specific intensity may be calculated. The technique is very general and in principle, can accommodate scattering in inhomogeneous atmospheres with arbitrary frequency redistribution and scattering phase functions. Solutions to the invariant imbedding equations in some simple cases are presented. If the scattering is isotropic and completely noncoherent and the atmosphere may be modeled as homogeneous, the scattering and transmission functions may be expressed in terms of generalized H, X and Y functions. This technique is extended to the problems of coupled spectral lines and scattering of radiation from internal sources.

Yelle, Roger V.↗

NASA NTRS1986

Eigenfunction methods in magnetospheric radial-diffusion theory

Complete sets of orthonormal basis functions constructed according to a generalization of the quantum-mechanical WKB approximation can be used to generate a nearly-diagonal matrix representation of the radial-transport operator for ring-current ions in the presence of radial diffusion and charge exchange. The resulting eigenfunctions (constructed by weighting the basis functions in proportion to the respective components of the eigenvectors of the matrix representation) and eigenvalues provide a spatial and temporal description of the evolving phase-space density during and following a magnetospheric disturbance (e.g., a magnetic storm). A linear superposition of the basis functions can also be used to eliminate any discrepancy between the steady-state solution of the transport equation and the appropriate WKB approximation of this steady-state solution.

Schulz, Michael↗

NASA NTRS2005

Small-Scale Drop Size Variability: Impact on Estimation of Cloud Optical Properties

Most cloud radiation models and conventional data processing techniques assume that the mean number of drops of a given radius is proportional to volume. The analysis of microphysical data on liquid water drop sizes shows that, for sufficiently small volumes, this proportionality breaks down; the number of cloud drops of a given radius is instead proportional to the volume raised to a drop size-dependent nonunit power. The coefficient of proportionality, a generalized drop concentration, is a function of the drop size. For abundant small drops the power is unity as assumed in the conventional approach. However, for rarer large drops, it falls increasingly below unity. This empirical fact leads to drop clustering, with the larger drops exhibiting a greater degree of clustering. The generalized drop concentration shows the mean number of drops per cluster, while the power characterizes the occurrence frequency of clusters. With a fixed total number of drops in a cloud, a decrease in frequency of clusters is accompanied by a corresponding increase in the generalized concentration. This initiates a competing process missed in the conventional models: an increase in the number of drops per cluster enhances the impact of rarer large drops on cloud radiation while a decrease in the frequency suppresses it. Because of the nonlinear relationship between the number of clustered drops and the volume, these two opposite tendencies do not necessarily compensate each other. The data analysis suggests that clustered drops likely have a stronger radiative impact compared to their unclustered counterpart; ignoring it results in underestimation of the contribution from large drops to cloud horizontal optical path.

Knyazikhin, Y.↗

NASA NTRS1963

Digital equipment for the antenna pointing system

This paper describes the digital control and data processing portions of the antenna pointing system used to track the Telstar satellite. The description is functional in nature, giving the form of the inputs, the functions performed, and the outputs produced. A general description of the digital equipment is followed by a discussion of the functions performed by the subsystems, the operational modes provided, the equipment features, and the operating experience.

DIRECTIONAL CONTROL↗

NASA NTRS2013

Implementation of a Goal-Based Systems Engineering Process Using the Systems Modeling Language (SysML)

Building upon the purpose, theoretical approach, and use of a Goal-Function Tree (GFT) being presented by Dr. Stephen B. Johnson, described in a related Infotech 2013 ISHM abstract titled "Goal-Function Tree Modeling for Systems Engineering and Fault Management", this paper will describe the core framework used to implement the GFTbased systems engineering process using the Systems Modeling Language (SysML). These two papers are ideally accepted and presented together in the same Infotech session. Statement of problem: SysML, as a tool, is currently not capable of implementing the theoretical approach described within the "Goal-Function Tree Modeling for Systems Engineering and Fault Management" paper cited above. More generally, SysML's current capabilities to model functional decompositions in the rigorous manner required in the GFT approach are limited. The GFT is a new Model-Based Systems Engineering (MBSE) approach to the development of goals and requirements, functions, and its linkage to design. As a growing standard for systems engineering, it is important to develop methods to implement GFT in SysML. Proposed Method of Solution: Many of the central concepts of the SysML language are needed to implement a GFT for large complex systems. In the implementation of those central concepts, the following will be described in detail: changes to the nominal SysML process, model view definitions and examples, diagram definitions and examples, and detailed SysML construct and stereotype definitions.

Patterson, Jonathan D.↗

NASA NTRS2013

Implementation of a Goal-Based Systems Engineering Process Using the Systems Modeling Language (SysML)

Breckenridge, Jonathan T.↗

NASA NTRS1993

Chemical differentiation, thermal evolution, and catastrophic overturn on Venus: Predictions and geologic observations

Observations from Magellan show that: (1) the surface of Venus is generally geologically young, (2) there is no evidence for widespread recent crustal spreading or subduction, (3) the crater population permits the hypothesis that the surface is in production, and (4) relatively few impact craters appear to be embayed by volcanic deposits suggesting that the volcanic flux has drastically decreased as a function of time. These observations have led to consideration of hypotheses suggesting that the geological history of Venus may have changed dramatically as a function of time due to general thermal evolution, and/or thermal and chemical evolution of a depleted mantle layer, perhaps punctuated by catastrophic overturn of upper layers or episodic plate tectonics. We have previously examined the geological implications of some of these models, and here we review the predictions associated with two periods of Venus history. Stationary thick lithosphere and depleted mantle layer, and development of regional to global development of regional to global instabilities, and compare these predictions to the geological characteristics of Venus revealed by Magellan.

Head, James W.↗

NASA NTRS1972

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.↗

NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗

NASA NTRS1972

Advanced software techniques for data management systems. Volume 3: Programming language characteristics and comparison reference

A comparative evaluation was made of eight higher order languages of general interest in the aerospace field: PL/1; HAL; JOVIAL/J3; SPL/J6; CLASP; ALGOL 60; FORTRAN 4; and MAC360. A summary of the functional requirements for a language for general use in manned aerodynamic applications is presented. The evaluation supplies background material to be used in assessing the worth of each language for some particular application.

James, T. A.↗

NASA NTRS1977

Optimal estimation for discrete time jump processes

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Vaca, M. V.↗

NASA NTRS1988

Light scattering of large rough particles application to cometary grains

While the electromagnetic field scattered by a spherical particle is classically obtained by the Helmholtz equation, the general case of an arbitrary particle may be investigated in the general framework of the interaction of a wave with a scattering potential. A wave function then satisfies the Schroedinger equation. The general solution of the Schroedinger equation is given. The main disadvantage of this approach are its restriction to large particles and its scalar nature preventing the calculation of the polarization. However, Perrin and Lamy have shown how to avoid the second limitation and retrieve a vectorial description. They proved that in the case of large spheres when the ad hoc assumptions are satisfied, the expression of the scattering amplitude may be approximated by an expansion series in partial waves, i.e., on a discrete basis. The analogy may be generalized, and the ratio of the two components for a rough particle obtained by taking the ratio of the reflectivities for the two directions of polarization. These reflectivities involve the simple and double reflections calculated following the method developed by Wolff for rough surfaces. The theory is further detailed.

Lamy, Philippe L.↗

NASA NTRS2012

Trajectory Software With Upper Atmosphere Model

The Trajectory Software Applications 6.0 for the Dec Alpha platform has an implementation of the Jacchia-Lineberry Upper Atmosphere Density Model used in the Mission Control Center for International Space Station support. Previous trajectory software required an upper atmosphere to support atmosphere drag calculations in the Mission Control Center. The Functional operation will differ depending on the end-use of the module. In general, the calling routine will use function-calling arguments to specify input to the processor. The atmosphere model will then compute and return atmospheric density at the time of interest.

Barrett, Charles↗

NASA NTRS2018

Formation Flight System Extremum-Seeking-Control Using Blended Performance Parameters

An extremum-seeking control system for formation flight that uses blended performance parameters in a conglomerate performance function that better approximates drag reduction than performance functions formed from individual measurements. Generally, a variety of different measurements are taken and fed to a control system, the measurements are weighted, and are then subjected to a peak-seeking control algorithm. As measurements are continually taken, the aircraft will be guided to a relative position which optimizes the drag reduction of the formation. Two embodiments are discussed. Two approaches are shown for determining relative weightings: "a priori" by which they are qualitatively determined (by minimizing the error between the conglomerate function and the drag reduction function), and by periodically updating the weightings as the formation evolves.

Ryan, John J.↗

NASA NTRS1983

Electron velocity distributions near the earth's bow shock

New information is presented on the general characteristics of electron distribution functions upstream, within, and downstream of the earth's bow shock, thereby providing new insights into the instabilities in collisionless shocks. The results presented are from a survey of electron velocity distributions measured near the earth's bow shock between October 1977 and December 1978 using the Los Alamos/Garching plasma instrumentation aboard ISEE 2. A wide variety of distribution shapes is found within the different plasma regions in close proximity to the bow shock. It is found that these shapes can be classified into general types that are characteristic of three different plasma regions, namely the upstream region or electron foreshock, the shock proper where most of the heating occurs, and the downstream region or the magnetosheath. Evidence is provided that field-aligned, rather than cross-field, instabilities are the major source of electron dissipation in the earth's bow shock.

Feldman, W. C.↗

NASA NTRS1978

Coded aperture imaging - Predicted performance of uniformly redundant arrays

It is noted that uniformly redundant arrays (URAs) have autocorrelation functions with perfectly flat sidelobes. A generalized signal-to-noise equation has been developed to predict URA performance. The signal-to-noise value is formulated as a function of aperture transmission or density, the ratio of the intensity of a resolution element to the integrated source intensity, and the ratio of detector background noise to the integrated intensity. It is shown that the only two-dimensional URAs known have a transmission of one half. This is not a great limitation because a nonoptimum transmission of one half never reduces the signal-to-noise ratio more than 30%. The reconstructed URA image contains practically uniform noise, regardless of the object structure. URA's improvement over the single-pinhole camera is much larger for high-intensity points than for low-intensity points.

Fenimore, E. E.↗

NASA NTRS1987

Digital robust active control law synthesis for large order systems using constrained optimization

This paper presents a direct digital control law synthesis procedure for a large order, sampled data, linear feedback system using constrained optimization techniques to meet multiple design requirements. A linear quadratic Gaussian type cost function is minimized while satisfying a set of constraints on the design loads and responses. General expressions for gradients of the cost function and constraints, with respect to the digital control law design variables are derived analytically and computed by solving a set of discrete Liapunov equations. The designer can choose the structure of the control law and the design variables, hence a stable classical control law as well as an estimator-based full or reduced order control law can be used as an initial starting point. Selected design responses can be treated as constraints instead of lumping them into the cost function. This feature can be used to modify a control law, to meet individual root mean square response limitations as well as minimum single value restrictions. Low order, robust digital control laws were synthesized for gust load alleviation of a flexible remotely piloted drone aircraft.

Mukhopadhyay, Vivek↗