Nonlinear, time-domain models of human controllers
Applicability of nonlinear time domain analysis to problem of modeling human operator /pilot/
Taylor, L. W., Jr.↗
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Comparison of several numerical optimization methods.
Numerical optimization methods compared for nonlinear two point boundary value problem associated with optimum spacecraft trajectory
Lewallen, J. M.↗
Iteration procedures for indirect trajectory optimization methods.
Numerical method solution of nonlinear two point boundary value problem associated with optimum transfer of spacecraft
Lewallen, J. M.↗
Application of the method of particular solutions to boundary-layer analyses.
Particular solutions and quasi-linearization combined to solve nonlinear two point boundary value problems, illustrating method with Falkner- Skan equation
Heideman, J. C.↗
On second order necessary conditions of optimality
Second order necessary conditions of optimality with straightforward application to nonlinear programming of optimal control problems
Messerli, E. J.↗
Model for color conversion
Color conversion model of equivalences under various illuminants, reducing problem to chromatic adaptation with nonlinear von Kries formulation
Parks, E. A.↗
Digital image processing for the rectification of television camera distortions.
All television systems introduce distortions into the imagery they record which influence the results of quantitative photometric and geometric measurements. Digital computer techniques provide a powerful approach to the calibration and rectification of these systematic effects. Nonlinear as well as linear problems can be attacked with flexibility and precision. Methods which have been developed and applied for the removal of structured system noises and the correction of photometric, geometric, and resolution distortions in vidicon systems are briefly described. Examples are given of results derived primarily from the Mariner Mars 1969 television experiment.
Rindfleisch, T. C.↗
Research on combustion instability and application to solid propellant rocket motors. II.
Review of the current state of analyses of combustion instability in solid-propellant rocket motors, citing appropriate measurements and observations. The work discussed has become increasingly important, both for the interpretation of laboratory data and for predicting the transient behavior of disturbances in full-scale motors. Two central questions are considered - namely, linear stability and nonlinear behavior. Several classes of problems are discussed as special cases of a general approach to the analysis of combustion instability. Application to motors, and particularly the limitations presently understood, are stressed.
Culick, F. E. C.↗
Transient ion neutralization by electrons.
The nonlinear initial-boundary-value problems describing the lateral neutralization of ion beams for the cases that (1) an auxiliary electric field accelerates the electrons into the ion space, and (2) the electrons are injected into the ion space at a prescribed current density are treated. Analytical solutions are derived which give the position and speed of the neutralization front as a function of time, and the temporal development of the electron density, velocity, and electric fields during the neutralization process.
Wilhelm, H. E.↗
Low thrust space vehicle trajectory optimization using regularized variables
Optimizing the trajectory of a low thrust space vehicle usually means solving a nonlinear two point boundary value problem. In general, accuracy requirements necessitate extensive computation times. In celestial mechanics, regularizing transformations of the equations of motion are used to eliminate computational and analytical problems that occur during close approaches to gravitational force centers. It was shown in previous investigations that regularization in the formulation of the trajectory optimization problem may reduce the computation time. In this study, a set of regularized equations describing the optimal trajectory of a continuously thrusting space vehicle is derived. The computational characteristics of the set are investigated and compared to the classical Newtonian unregularized set of equations. The comparison is made for low thrust, minimum time, escape trajectories and numerical calculations of Keplerian orbits. The comparison indicates that in the cases investigated for bad initial guesses of the known boundary values a remarkable reduction in the computation time was achieved. Furthermore, the investigated set of regularized equations shows high numerical stability even for long duration flights and is less sensitive to errors in the guesses of the unknown boundary values.
Schwenzfeger, K. J.↗
Application of variational and Galerkin equations to linear and nonlinear finite element analysis
The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.
Yu, Y.-Y.↗
Inversion of passive microwave remote sensing data from satellites
Global passive microwave observations from earth-orbiting satellites have mapped humidity and liquid water over ocean, temperature profiles, ice and snow, and other geophysical parameters. In most applications, the inversion problem is adequately approximated as linear with jointly Gaussian statistics, and, thus, a linear retrieval performs well. In some cases, the problem is typically factored into a decision process followed by appropriate linear or quasilinear processes. Certain problems, however, require more powerful nonlinear or nonstationary procedures, such as Kalman filtering.
Staelin, D. H.↗
Optimal large angle maneuvers with simultaneous shape control/vibration arrest
A relaxation method is demonstrated which reliably solves the nonlinear two point boundary value problem which arises when optimal control theory is applied to determination of large angle maneuvers of flexible spacecraft. The basic ideas are summarized and several idealized maneuvers are determined. The emphasis is upon demonstrating the basic ideas and practical aspects of the methodology.
Turner, J. D.↗
Feedback invariants for nonlinear systems
The effect of nonlinear feedback on nonlinear systems is discussed for problems where the controls are entered linearly. The invariance of certain quantities under feedback are established, and it is shown that these quantities contain enough information to determine if the system can be linearized using feedback and change of coordinates. Attention is given to scalar input systems emphasizing a new F-invariant property.
Brockett, R. W.↗
Stochastic control system parameter identifiability
The parameter identification problem of general discrete time, nonlinear, multiple input/multiple output dynamic systems with Gaussian white distributed measurement errors is considered. The knowledge of the system parameterization was assumed to be known. Concepts of local parameter identifiability and local constrained maximum likelihood parameter identifiability were established. A set of sufficient conditions for the existence of a region of parameter identifiability was derived. A computation procedure employing interval arithmetic was provided for finding the regions of parameter identifiability. If the vector of the true parameters is locally constrained maximum likelihood (CML) identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the constrained maximum likelihood estimation sequence will converge to the vector of true parameters.
Lee, C. H.↗
Applications of adaptive state estimation theory
Two main areas of application of adaptive state estimation theory are presented. Following a review of the basic estimation approach, its application to both the control of nonlinear plants and to the problem of tracking maneuvering targets is presented. Results are brought together from these two areas of investigation to provide insight into the wide range of possible applications of the general estimation method.
Moose, R. L.↗
Recent advances in electromagnetic synthesis and analysis of dual-shaped reflector antennas
Dual-shaped reflectors have been used for many years. Thus, these reflectors have been used as high gain antennas on Voyagers 1 and 2. The objectives of the geometrical optics (GO) dual shaped synthesis are considered. Concerning the synthesis of dual shaped reflectors, it has been shown for circular symmetric reflectors that an exact GO solution can be found to the problem of transforming, by two reflections, any feed pattern into any aperture distribution. This problem involves solving two simultaneous nonlinear ordinary differential equations. The same approach for offset geometry leads to two simultaneous nonlinear partial differential equations. It is shown that these equations could also be integrated numerically, except that in general these equations are not total and therefore, in general, they do not have a 'smooth' solution. It is further shown that the offset partial differentials often very nearly form a total differential in many cases of practical importance.
Galindo-Israel, V.↗
Computational technique for three-dimensional compressible flow past wings at high angles of attack
A computational technique, based on the integral solution of the full potential equation, has been developed for the solution of three-dimensional high-subsonic flows past wings at high angles of attack. The problem includes two sources of nonlinearities: a boundary oriented nonlinearity (separated flow roll up) and a region oriented nonlinearity (flow compressibility). The former is represented by a nonlinear vortex lattice while the latter is represented by a source distribution inside a finite volume. The solution is obtained by using double iteration cycles; a separated flow (wake) iteration cycle and a compressibility iteration cycle. The computational technique is applied to a delta wing. The results show that the technique is very promising and efficient.
Kandil, O. A.↗