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At least 667 records · Page 37

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NASA NTRS1976

Four-dimensional guidance problem with control delays

This paper, assuming steady wind and zero sideslip, presents a discrete-time mathematical model to obtain a control law and three-dimensional flight path to guide an aircraft in a given time from a given initial state (position, velocity and heading) to a prescribed final state subject to the constraints on airspeed acceleration, and pitch and bank angles of the aircraft. For ease in implementing the control law, the control inputs are assumed to be delayed and are applied in a sequential fashion. The guidance problem is formulated as a discrete nonlinear optimal control problem with time delays in dynamics and a cost functional of Bolza form. With a quadratic penalty function to handle terminal constraints on velocity and heading, a solution technique to the control problem based on conjugate gradient algorithm is investigated. Numerical examples are presented to illustrate the applicability of this approach to solution of a terminal area guidance problem in an automated air traffic control environment.

Nagarajan, N.↗

NASA NTRS1976

Additional comments on 'Multistage least-squares parameter estimation'

The purpose of this correspondence is to call attention to other solutions to the problem addressed in the above paper, that of adding or deleting parameters or measurements from a given linear model. The solution algorithms proposed in the article are numerically ill-conditioned and are less efficient, in terms of both computational and storage requirements, than the methods described here. Several numerically stable, compact, flexible, and efficient algorithms for analyzing the parameter estimation problem are described and others are referenced.

Bierman, G. J.↗

NASA NTRS1979

Magnetometer bias determination and attitude determination for near-earth spacecraft

A simple linear-regression algorithm is used to determine simultaneously magnetometer biases, misalignments, and scale factor corrections, as well as the dependence of the measured magnetic field on magnetic control systems. This algorithm has been applied to data from the Seasat-1 and the Atmosphere Explorer Mission-1/Heat Capacity Mapping Mission (AEM-1/HCMM) spacecraft. Results show that complete inflight calibration as described here can improve significantly the accuracy of attitude solutions obtained from magnetometer measurements. This report discusses the difficulties involved in obtaining attitude information from three-axis magnetometers, briefly derives the calibration algorithm, and presents numerical results for the Seasat-1 and AEM-1/HCMM spacecraft.

Lerner, G. M.↗

NASA NTRS1981

Calculation of two-dimensional inlet flow fields by an implicit method including viscous effects: User's manual

Inlet flow fields for airbreathing missiles are calculated by the adaptation of a two dimensional computational method developed for the flow around airfoils. A supersonic free stream is assumed to allow the forebody calculation to be uncoupled from the inlet calculation. The inlet calculation employs an implicit, time marching finite difference procedure to solve the thin layer Navier-Stokes equations formulated in body fitted coordinates. The mathematical formulation of the problem and the solution algorithm are given. Numerical stability and accuracy as well as the initial and boundary conditions used are discussed. Instructions for program use and operation along with the overall program logic are also given.

Biringen, S.↗

NASA NTRS1981

Studies in astronomical time series analysis. I - Modeling random processes in the time domain

Several random process models in the time domain are defined and discussed. Attention is given to the moving average model, the autoregressive model, and relationships between and combinations of these models. Consideration is then given to methods for investigating pulse structure, procedures of model construction, computational methods, and numerical experiments. A FORTRAN algorithm of time series analysis has been developed which is relatively stable numerically. Results of test cases are given to study the effect of adding noise and of different distributions for the pulse amplitudes. A preliminary analysis of the light curve of the quasar 3C 272 is considered as an example.

Scargle, J. D.↗

NASA NTRS1982

Comment on 'Time-optimal orbit transfer trajectory for solar sail spacecraft'

An analytic proof is presented to show that the orbital transfer times of an earth-to-Mars solar-sail propelled spacecraft trajectory as calculated by Jayaraman (1980) are incorrect. In particular, different boundary conditions are defined, which indicate that a minimization of the Hamiltonian, which Jayaraman used, can yield the wrong stationary solution. Transfer times are calculated using a neighboring extremal algorithm based on numerical differentiation in conjunction with Krogh's variable order, variable step size integrator, resulting in a transfer time of 322 days at 2 mm/sec-sq, with endpoint restraints satisfied to within 1/1 billion. Finally, it is concluded that minimization of flight time is secondary in importance to maximization of delivered payload and minimization of overall mission cost and risk.

Wood, L. J.↗

NASA NTRS1983

On the solution of elastic-plastic static and dynamic postbuckling collapse of general structure

Many investigations have considered structural collapse from strictly the transient point of view. While such an approach is ideally correct, certain difficulties have to be overcome in its implementation. The present investigation is concerned with the development of self-adaptive algorithms which make it possible to conduct the analysis of both static elastic and elastic-plastic postbuckling, as well as static loading to the onset of buckling followed by subsequent dynamic postbuckling. The approach employed to solve the static portion of loading is to extend the constrained Incremental Newton-Raphson (INR) algorithm by incorporating elastic-plastic constitutive characterizations. Large deformation moderate strain theory is adopted to establish the overall strategy. Attention is given to governing field equations, aspects of algorithmic development, and numerical experiments conducted to illustrate the efficiency and stability of the developed schemes.

Padovan, J.↗

NASA NTRS1984

Computational problems on composite grids

Most currently used algorithms for the numerical solution of the partial differential equations encountered in fluid flow problems can be implemented on composite grid systems. Finite volume formulations are easier to derive on composite grids, and may in principle be derived for partial differential equations of all types. Except when using Alternating Difference Implicit-type schemes, the overlapping of grids is an alternative to the more common grid construction procedure where grid lines continue smoothly from one subregion to the next. In the solution of model problems, the correct choice of an interpolation formula has been found able to reduce errors by a factor of two.

Mastin, C. W.↗

NASA NTRS1985

Asteroid Collisional Evolution Studies

Understanding asteroid collisional evolution is important for characterizing the physical state of asteroids today and for learning about the processes that acted in this region of the solar system early in its history. The collisional outcome algorithm in the numerical simulation of asteroid evolution was revised to reflect pressure-strengthening. Asteroid collisions are now treated as a distribution of oblique impacts rather than as only head-on collisions. The initial and evolved size distribution of a plausible asteroid population is compared with the observed size distribution. Asteroid accretion times and reconstruction of the primordial solar nebula suggest that there was significantly more mass in this part of the solar system when the asteroids were accreting.

Davis, D. R.↗

NASA NTRS1985

Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates

The Harten (1983, 1984) total variation-diminishing (TVD) schemes, constituting a one-parameter explicit and implicit, second-order-accurate family, have the property of not generating spurious oscillations when applied to one-dimensional, nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. These methods are presently extended to the multidimensional hyperbolic conservation laws in curvilinear coordinates. Means by which to linearize the implicit operator and solution strategies, in order to improve the computation efficiency of the implicit algorithm, are discussed. Numerical experiments with steady state airfoil calculations indicate that the proposed linearized implicit TVD schemes are accurate and robust.

Yee, H. C.↗

NASA NTRS1986

Numerical simulation of diffusion-controlled droplet growth Dynamical correlation effects

Diffusion-controlled coarsening (Ostwald ripening) of precipitated solutions is studied by numerical simulation. An algorithm is devised which exploits the screening of solute concentration fields, thereby removing the restriction to small systems of previous work. Simulation of the coarsening of 5000 droplets at 10-percent volume fraction reveals long-ranged dynamical correlations which broaden the droplet size-distribution function and increase the coarsening-rate coefficient.

Beenakker, C. W. J.↗

NASA NTRS1986

Two-dimensional nonsteady viscous flow simulation on the Navier-Stokes computer miniNode

The needs of large-scale scientific computation are outpacing the growth in performance of mainframe supercomputers. In particular, problems in fluid mechanics involving complex flow simulations require far more speed and capacity than that provided by current and proposed Class VI supercomputers. To address this concern, the Navier-Stokes Computer (NSC) was developed. The NSC is a parallel-processing machine, comprised of individual Nodes, each comparable in performance to current supercomputers. The global architecture is that of a hypercube, and a 128-Node NSC has been designed. New architectural features, such as a reconfigurable many-function ALU pipeline and a multifunction memory-ALU switch, have provided the capability to efficiently implement a wide range of algorithms. Efficient algorithms typically involve numerically intensive tasks, which often include conditional operations. These operations may be efficiently implemented on the NSC without, in general, sacrificing vector-processing speed. To illustrate the architecture, programming, and several of the capabilities of the NSC, the simulation of two-dimensional, nonsteady viscous flows on a prototype Node, called the miniNode, is presented.

Nosenchuck, Daniel M.↗

NASA NTRS1987

Nonlinear transient analysis of joint dominated structures

A residual force technique is presented that can perform the transient analyses of large, flexible, and joint dominated structures. The technique permits substantial size reduction in the number of degrees of freedom describing the nonlinear structural models and can account for such nonlinear joint phenomena as free-play and hysteresis. In general, joints can have arbitrary force-state map representations but these are used in the form of residual force maps. One essential feature of the technique is to replace the arbitrary force-state maps describing the nonlinear joints with residual force maps describing the truss links. The main advantage of this replacement is that the incrementally small relative displacements and velocities across a joint are not monitored directly thereby avoiding numerical difficulties. Instead, very small and 'soft' residual forces are defined giving a numerically attractive form for the equations of motion and thereby permitting numerically stable integration algorithms. The technique was successfully applied to the transient analyses of a large 58 bay, 60 meter truss having nonlinear joints. A method to perform link testing is also presented.

Chapman, J. M.↗

NASA NTRS1987

A covariance analysis algorithm for interconnected systems

A covariance analysis algorithm for propagation of signal statistics in arbitrarily interconnected nonlinear systems is presented which is applied to six-degree-of-freedom systems. The algorithm uses statistical linearization theory to linearize the nonlinear subsystems, and the resulting linearized subsystems are considered in the original interconnection framework for propagation of the signal statistics. Some nonlinearities commonly encountered in six-degree-of-freedom space-vehicle models are referred to in order to illustrate the limitations of this method, along with problems not encountered in standard deterministic simulation analysis. Moreover, the performance of the algorithm shall be numerically exhibited by comparing results using such techniques to Monte Carlo analysis results, both applied to a simple two-dimensional space-intercept problem.

Cheng, Victor H. L.↗

NASA NTRS1987

Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. III - Impact/contact simulations

In a three-part series of papers, a generalized finite element methodology is formulated to handle traveling load problems involving large deformation fields in structure composed of viscoelastic media. The main thrust of this paper is to develop an overall finite element methodology and associated solution algorithms to handle the transient aspects of moving problems involving contact impact type loading fields. Based on the methodology and algorithms formulated, several numerical experiments are considered. These include the rolling/sliding impact of tires with road obstructions.

Nakajima, Yukio↗

NASA NTRS1989

Extensions and improvements on XTRAN3S

Improvements to the XTRAN3S computer program are summarized. Work on this code, for steady and unsteady aerodynamic and aeroelastic analysis in the transonic flow regime has concentrated on the following areas: (1) Maintenance of the XTRAN3S code, including correction of errors, enhancement of operational capability, and installation on the Cray X-MP system; (2) Extension of the vectorization concepts in XTRAN3S to include additional areas of the code for improved execution speed; (3) Modification of the XTRAN3S algorithm for improved numerical stability for swept, tapered wing cases and improved computational efficiency; and (4) Extension of the wing-only version of XTRAN3S to include pylon and nacelle or external store capability.

Borland, C. J.↗

NASA NTRS1988

Transformation techniques for minimax optimal control problems and their application to optimal flight trajectories in a windshear - Optimal abort landing trajectories

The optimal-control problem of abort-landing trajectories in the presence of low-altitude wind shear is investigated analytically. The vertical-plane Newtonian motion of a point-mass aircraft in a steady wind field is modeled, and a sequential gradient-restoration algorithm is applied. Numerical results showing the effects of wind-shear intensity, initial altitude, and power-setting rate are presented in extensive graphs and discussed in detail. Optimal trajectories for strong or severe wind shears are found to begin with a descent, followed by level flight and then an ascent after leaving the shear region.

Miele, A.↗

NASA NTRS1989

A generalized gradient algorithm for dynamic optimization

A gradient algorithm is developed that determines optimal trajectories with path equality constraints and terminal constraints. A generalized gradient is formed which improves both the performance index and the path equality constraints simultaneously. The algorithm is extended to treat terminal constraints by using Bryson's impulse response technique. The main features of this algorithm are its numerical stability and smooth convergence near the optimum.

Zhao, Yiyuan↗