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At least 217 records · Page 12

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NASA NTRS1977

On the logarithmic-singularity correction in the kernel function method of subsonic lifting-surface theory

A logarithmic-singularity correction factor is derived for use in kernel function methods associated with Multhopp's subsonic lifting-surface theory. Because of the form of the factor, a relation was formulated between the numbers of chordwise and spanwise control points needed for good accuracy. This formulation is developed and discussed. Numerical results are given to show the improvement of the computation with the new correction factor.

Lan, C. E.↗

NASA NTRS1978

A numerical method of detecting singularity

A numerical method is reported which determines a value C for the degree of conditioning of a matrix. This value is C = 0 for a singular matrix and has progressively larger values for matrices which are increasingly well-conditioned. This value is C sub = C max sub max (C defined by the precision of the computer) when the matrix is perfectly well conditioned.

Laporte, M.↗

NASA NTRS1979

Optimal singular control with applications to trajectory optimization

The switching conditions are expressed explicitly in terms of the derivatives of the Hamiltonians at the two ends of the switching. A new expression of the Kelley-Contensou necessary condition for the optimality of a singular arc is given. Some examples illustrating the application of the theory are presented.

Vinh, N. X.↗

NASA NTRS1979

Improvements in surface singularity analysis and design methods

The coupling of the combined source vortex distribution of Green's potential flow function with contemporary numerical techniques is shown to provide accurate, efficient, and stable solutions to subsonic inviscid analysis and design problems for multi-element airfoils. The analysis problem is solved by direct calculation of the surface singularity distribution required to satisfy the flow tangency boundary condition. The design or inverse problem is solved by an iteration process. In this process, the geometry and the associated pressure distribution are iterated until the pressure distribution most nearly corresponding to the prescribed design distribution is obtained. Typically, five iteration cycles are required for convergence. A description of the analysis and design method is presented, along with supporting examples.

Bristow, D. R.↗

NASA NTRS1979

An Analytical Singularity-Free Solution to the J2 Perturbation Problem

The development of a singularity-free solution of the J2 problem in satellite theory is presented. The procedure resembles that of Lyndane who rederives Brouwer's satellite theory using Poincare elements. A comparable procedure is used in this report in which the satellite theory of Scheifele, who used elements similar to the Delaunay elements but in the extended phase space, is rederived using Poincare elements also in the extended phase space. Only the short-period effects due to J2 are included.

Bond, V. R.↗

NASA NTRS1979

The supersonic triplet - A new aerodynamic panel singularity with directional properties

A new supersonic triplet singularity has been developed which eliminates internal waves generated by panels having supersonic edges. The triplet is a linear combination of source and vortex distributions which provides the desired directional properties in the flow field surrounding the panel. The theoretical development of the triplet is described, together with its application to the calculation of surface pressure on arbitrary body shapes. Examples are presented comparing the results of the new method with other supersonic panel methods and with experimental data.

Woodward, F. A.↗

NASA NTRS1979

Second-order estimates in singular perturbation of output regulator problems

A method of order reduction in singular perturbation problems due to Chow and Kokotovic is studied. The method is used for an output regulator problem in control theory. The quadratic term in the asymptotic expansion of Chow and Kokotovic is calculated and it is shown by some examples how this term can give evidence of the accuracy of the procedure.

Rublein, G.↗

NASA NTRS1979

Singular perturbation techniques for on-line optimal flight path control

This paper presents a partial evaluation on the use of singular perturbation methods for developing computer algorithms for on-line optimal control of aircraft. The evaluation is based on a study of the minimum time intercept problem using F-4 aerodynamic and propulsion data as a base line. The extensions over previous work on this subject are that aircraft turning dynamics (in addition to position and energy dynamics) are included in the analysis, the algorithm is developed for a moving end point and is adaptive to unpredictable target maneuvers, and short range maneuvers that do not have a cruise leg are included. Particular attention is given to identifying those quantities that can be precomputed and stored (as a function of aircraft total energy), thus greatly reducing the onboard computational load. Numerical results are given that illustrate the nature of the optimal intercept flight paths, and an estimate is given for the execution time and storage requirements of the control algorithm.

Calise, A. J.↗

NASA NTRS1979

Application of singular perturbation techniques /SPT/ and continuation methods for on-line aircraft trajectory optimization

The singular perturbation theory (SPT) approximation of optimal feedback control laws is presented and methods for on-line application of these approximations are discussed. It is demonstrated that SPT control laws break down when the current state is near the terminal target state. The use of continuation methods to improve the accuracy of the SPT approximation and to obtain global solutions of two-point boundary value problems is also discussed. As an illustration, consideration is given to the minimum-time control of a supersonic aircraft for a three-dimensional intercept problem.

Washburn, R. B.↗

NASA NTRS1980

A singular perturbation analysis of minimum time long range intercept

The application of singular perturbation theory for deriving algorithms suitable for on board real time computation of optimal aircraft trajectory control was investigated. Minimum time intercept in three dimensions was selected as a pilot problem formulation, and data for an early version F-4 aircraft was used to represent aircraft aerodynamic and propulsion characteristics. Results include the derivation of nonlinear, near optimal feedback control laws that are readily implementable in an aircraft flight computer, performance results for a variety of initial conditions (including optimal intercept at short ranges), and a point mass three dimensional simulation suitable for representing fighter aircraft under closed loop optimal control.

Calise, A.↗

NASA NTRS1978

Multi-Level Adaptive Techniques (MLAT) for singular-perturbation problems

The multilevel (multigrid) adaptive technique, a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization is described. It provides very fast general solvers, together with adaptive, nearly optimal discretization schemes. In the process, boundary layers are automatically either resolved or skipped, depending on a control function which expresses the computational goal. The global error decreases exponentially as a function of the overall computational work, in a uniform rate independent of the magnitude of the singular-perturbation terms. The key is high-order uniformly stable difference equations, and uniformly smoothing relaxation schemes.

Brandt, A.↗

NASA NTRS1979

Stability of the nakedness of Weyl singularities

The stability of the nakedness of the Weyl singularities against matter perturbations is investigated. Consideration is given to the effects of infalling test matter on the convergence of outgoing null rays. It is shown that the additional convergence induced by infalling test matter does not blow up sufficiently fast to reconverge diverging outgoing rays, at least in the equator, and that the nakedness seems to be stable in this limited sense.

Haugan, M. P.↗

NASA NTRS1979

Aircraft trajectory optimization using singular perturbation methods

Singular perturbation methods are used to derive nonlinear feedback control laws for aircraft minimum time long range interception under the assumption of complete time scale separation. The resulting algorithms are in feedback form and can be implemented on a microcomputer for on-line trajectory optimization.

Mehra, R. K.↗

NASA NTRS1981

Solution of plane cascade flow using improved surface singularity methods

A solution method was developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method's capabilities are presented.

Mcfarland, E. R.↗

NASA NTRS1980

Convergence rates for finite element problems with singularities. Part 1: Antiplane shear

The problem of a finite crack in an infinite medium under antiplane shear load is considered. It is shown that the nodal forces at the tip of the crack accurately gives the order of singularity, that n energy release methods can give the strength to better than 1 percent with element size 1/10 the crack length, and that nodal forces give a much better estimate of the stress field than do the elements themselves. The finite element formulation and the factoring of tridiagonal matrices are discussed.

Plunkett, R.↗

NASA NTRS1981

Solution of plane cascade flow using improved surface singularity methods

A solution method has been developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those found in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method's capabilities are presented.

Mcfarland, E. R.↗

NASA NTRS1980

Closed-loop stability of large space structures via singular and regular perturbation techniques - New results

Large Space Structures are treated as a special class of highly oscillatory distributed parameter systems. Practical controllers will need to be finite dimensional; however, this calls the closed-loop stability into question due to spillover interactions. Recent results, obtained using regular and singular perturbations theory, give stability bounds for closed-loop control of this type of distributed parameter system; this paper surveys these results and their implications for large space structures.

Balas, M. J.↗

NASA NTRS1982

Moving singularity creep crack growth analysis with the /Delta T/c and C/asterisk/ integrals

The physical meaning of (Delta T)c and its applicability to creep crack growth are reviewed. Numerical evaluation of (Delta T)c and C(asterisk) is discussed with results being given for compact specimen and strip geometries. A moving crack-tip singularity, creep crack growth simulation procedure is described and demonstrated. The results of several crack growth simulation analyses indicate that creep crack growth in 304 stainless steel occurs under essentially steady-state conditions. Based on this result, a simple methodology for predicting creep crack growth behavior is summarized.

Stonesifer, R. B.↗