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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Adiabatic invariance

Theoretical work designed to bridge the gap between celestial mechanics and the motion of charged particles in magnetic fields is presented. Attempts are made to devise a simple uninvolved method to solve adiabatic invariant motion problems. The method is illustrated by solving a problem involving the motion of a slowly perturbed harmonic oscillator.

Stern, D.↗
NASA NTRS1972

An invariant second-order closure model of the compressible turbulent boundary layer on a flat plate

The development of an invariant model designed expressly for the computation of shear flows is discussed. The model for incompressible layers seeks a second-order closure of the equations for the mean and fluctuating fields. The development of a method for computing the behavior of shear layers in compressible forces is described. The complexity of the analysis is restrained by limiting the consideration to a flat plate boundary layer where the mean pressure can be taken to be constant.

Donaldson, C. D.↗
NASA NTRS1972

On the input-output properties of linear time-invariant systems.

Recently improved sufficient conditions for the Lp stability of multiple-input multiple-output linear time-invariant feedback systems are given. The continuous-time case is done in detail; the discrete-time case is outlined. Unstable open-loop systems with singular residue matrices are allowed.

Desoer, C. A.↗
NASA NTRS1972

A pictorial study of an invariant torus in phase space of four dimensions.

An investigation was conducted with the aid of a computer graphics device at Goddard Space Flight Center to study the behavior of the invariant manifolds of a particular fourth-order equation, as a parameter in the equation is varied over the interval from 0 to 1. The equation consists of two coupled Van der Pol equations. For a small parameter value, the manifold is an asymptotically stable torus, where the flow on the torus is simply a rotation. As the value of the parameter is increased, the only thing that changes is the nature of the flow on the torus, which itself persists throughout the parameter variation. It is shown that ultimately the four periodic cycles which appear play a more significant part in the phase profile of the system than does the torus itself.

Baxter, R.↗
NASA NTRS1972

Computation of optimal output-feedback compensators for linear time-invariant systems

The control of linear time-invariant systems with respect to a quadratic performance criterion was considered, subject to the constraint that the control vector be a constant linear transformation of the output vector. The optimal feedback matrix, f*, was selected to optimize the expected performance, given the covariance of the initial state. It is first shown that the expected performance criterion can be expressed as the ratio of two multinomials in the element of f. This expression provides the basis for a feasible method of determining f* in the case of single-input single-output systems. A number of iterative algorithms are then proposed for the calculation of f* for multiple input-output systems. For two of these, monotone convergence is proved, but they involve the solution of nonlinear matrix equations at each iteration. Another is proposed involving the solution of Lyapunov equations at each iteration, and the gradual increase of the magnitude of a penalty function. Experience with this algorithm will be needed to determine whether or not it does, indeed, possess desirable convergence properties, and whether it can be used to determine the globally optimal f*.

Platzman, L. K.↗
NASA NTRS1973

A linear shift-invariant image preprocessing technique for multispectral scanner systems

A linear shift-invariant image preprocessing technique is examined which requires no specific knowledge of any parameter of the original image and which is sufficiently general to allow the effective radius of the composite imaging system to be arbitrarily shaped and reduced, subject primarily to the noise power constraint. In addition, the size of the point-spread function of the preprocessing filter can be arbitrarily controlled, thus minimizing truncation errors.

Mcgillem, C. D.↗