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NASA NTRS1986

Semi-analytical theory for long-term rotational motion of uncontrolled satellites

Analytical solutions/integrals of the free rotational motion of uncontrolled satellites which contain spinning rotors are employed in conjunction with a suitable analytical/numerical averaging approach to predict long-term attitude motion. This semi-analytical method of averaging is basically similar to the one used in purely analytical 'general perturbation' theories. However, in view of the complexities involved in analytical treatment of the problem, its application is primarily numerical in character. An example is presented illustrating the use of the theory to predict the attitude motion of an axisymmetric satellite containing symmetrical constant-speed rotors under gravity-gradient torque. The use of the theory is considerably more efficient than straightforward numerical integration of the complete set of equations of motion.

Lahr, B. S.↗

NASA NTRS1986

High-accuracy computation of Delta V magnitude probability densities - Preliminary remarks

This paper describes an algorithm for the high accuracy computation of some statistical quantities of the magnitude of a random trajectory correction maneuver (TCM). The trajectory correction velocity increment Delta V is assumed to be a three-component random vector with each component being a normally distributed random scalar having a possibly nonzero mean. Knowledge of the statitiscal properties of the magnitude of a random TCM is important in the planning and execution of maneuver strategies for deep-space missions such as Galileo. The current algorithm involves the numerical integration of a set of differential equations. This approach allows the computation of density functions for specific Delta V magnitude distributions to high accuracy without first having to generate large numbers of random samples. Possible applications of the algorithm to maneuver planning, planetary quarantine evaluation, and guidance success probability calculations are described.

Chadwick, C.↗

NASA NTRS1987

Calculating Sonic-Boom Propagation

Nonlinear effects included, enabling more-realistic modeling. Modified Method of Characteristics Sonic Boom Extrapolation Program (MMOC) is computer program for sonic-boom propagation that includes shock coalescence and incorporates effects of asymmetries due to volume and lift. Numerically integrates nonlinear governing equations using data on initial data line approximately one body length from aircraft and yields sonic-boom pressure at ground as function of time or of position at given time. MMOC written in FORTRAN IV.

Darden, C. M.↗

NASA NTRS1987

Parallel Algorithm Solves Coupled Differential Equations

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Hayashi, A.↗

NASA NTRS1986

An all-purpose computer program for lidar simulations and reduction of lidar data

A general computer program was written for the dual purpose of simulating lidar returm signals and extracting H2O vapor and temperature (T) profiles from actual lidar returns. This program will be used to retrieve H2O vapor and T profiles from data obtained with the University of Maryland ground-based lidar systems. The program is designed to simulate and to analyze lidar returns from a monostatic system for two cases: when the output laser pulse is monochromatic, and when the pulse has a known wavelength spectrum. The simulation part of the program has several model H2O vapor, T, and aerosol profiles which can be combined to form different model atmospheres. The simulation program also permits the testing of different methods of numerical filtering to suppress noise, and testing the accuracy of different methods of numerical integration.

Braun, C.↗

NASA NTRS1986

The nonlinear development of Gortler vortices in growing boundary layers

The development of Gortler vortices in boundary layers over curved walls in the nonlinear regime is investigated. The growth of the boundary layer makes a parallel flow analysis impossible except in the high wavenumber regime so in general the instability equations must be integrated numerically. Here the spanwise dependence of the basic flow is described using Fourier series expansion whilst the normal and streamwise variations are taken into account using finite differences. The calculations suggest that a given disturbance imposed at some position along the wall will eventually reach a local equilibrium state essentially independent of the initial conditions. In fact, the equilibrium state reached is qualitatively similar to the large amplitude high wave-number solution described asymptotically by Hall (1982). In general, it is found that the nonlinear interactions are dominated by a mean field type of interaction between the mean flow and the fundamental. Thus, even though higher harmonics of the fundamental are necessarily generated, most of the disturbance energy is confined to the mean flow correction and the fundamental. A major result of the calculations is finding that the downstream velocity field develops a strongly inflection character as the flow moves downstream. The latter result suggests that the major effect of Gortler vortices on boundary layers of practical importance might be to make them highly receptive to rapidly growing Rayleigh modes of instability.

Hall, Philip↗

NASA NTRS1987

Transient response for interaction of two dynamic bodies

During the launch sequence of any space vehicle complicated boundary interactions occur between the vehicle and the launch stand. At the start of the sequence large forces exist between the two; contact is then broken in a short but finite time which depends on the release mechanism. The resulting vehicle response produces loads which are very high and often form the design case. It is known that the treatment of the launch pad as a second dynamic body is significant for an accurate prediction of launch response. A technique was developed for obtaining loads generated by the launch transient with the effect of pad dynamics included. The method solves uncoupled vehicle and pad equations of motion. The use of uncoupled models allows the simulation of vehicle launch in a single computer run. Modal formulation allows a closed-form solution to be written, eliminating any need for a numerical integration algorithm. When the vehicle is on the pad the uncoupled pad and vehicle equations have to be modified to account for the constraints they impose on each other. This necessitates the use of an iterative procedure to converge to a solution, using Lagrange multipliers to apply the required constraints. As the vehicle lifts off the pad the coupling between the vehicle and the pad is eliminated point by point until the vehicle flies free. Results obtained by this method were shown to be in good agreement with observed loads and other analysis methods. The resulting computer program is general, and was used without modification to solve a variety of contact problems.

Prabhakar, A.↗

NASA NTRS1987

A scaling law for accretion zone sizes

Current theories of runaway planetary accretion require small random velocities of the accreted particles. Two body gravitational accretion cross sections which ignore tidal perturbations of the Sun are not valid for the slow encounters which occur at low relative velocities. Wetherill and Cox have studied accretion cross sections for rocky protoplanets orbiting at 1 AU. Using analytic methods based on Hill's lunar theory, one can scale these results for protoplanets that occupy the same fraction of their Hill sphere as does a rocky body at 1 AU. Generalization to bodies of different sizes is achieved here by numerical integrations of the three-body problem. Starting at initial positions far from the accreting body, test particles are allowed to encounter the body once, and the cross section is computed. A power law is found relating the cross section to the radius of the accreting body (of fixed mass).

Greenzweig, Yuval↗

NASA NTRS1987

Research in computational fluid dynamics

The numerical integration of quasi-one-dimensional unsteady flow problems which involve finite rate chemistry are discussed, and are expressed in terms of conservative form Euler and species conservation equations. Hypersonic viscous calculations for delta wing geometries is also examined. The conical Navier-Stokes equations model was selected in order to investigate the effects of viscous-inviscid interations. The more complete three-dimensional model is beyond the available computing resources. The flux vector splitting method with van Leer's MUSCL differencing is being used. Preliminary results were computed for several conditions.

Murman, Earll M.↗

NASA NTRS1986

The global evolution of the primordial solar nebula

Complete radial, time-dependent calculations of the structure and evolution of the primordial solar nebula during the viscous diffusion stage are presented. The viscous stress is derived from analytic one-zone models of the vertical nebular structure based on detailed grain opacities. Comparisons with full numerical integrations indicate that the effective viscous alpha parameter is about 0.01. The evolution time of a minimum mass nebula is one-million yr or less. The flow pattern of fluid elements in the disk is examined and the implications the results have on the theory of the formation of the solar system are discussed.

Ruden, S. P.↗

NASA NTRS1985

Buckling of simply supported plate assemblies subject to shear loading

An analysis is presented of the shear buckling load of an arbitrary simply-supported prismatic plate assembly or stiffened panel configuration. The method utilizes stiffness matrices developed by Wittrick (1968). For the restraint of simple support along edges perpendicular to the longitudinal direction, various wavelengths of response are combined using an energy method that involves only a boundary integral. Numerical results for plate and panel configurations show the accuracy and convergence of the method.

Anderson, M. S.↗

NASA NTRS1986

A general theory for the Uranian satellites

A general analytical theory of the five main satellites of Uranus, including the secular and short period terms hereafter denoted by GUST, is presented. A comparison is made with an internal numerical integration with nominal masses of Veillet (1983). The precision of the theory goes from about 10 km for Miranda to 100 km for Oberon. The short period terms in the motions of Titania and Oberon are larger than 500 km. They should make possible the determination of the masses of the outer satellites through the optical data of Voyager encounter.

Laskar, J.↗

NASA NTRS1986

Formation and evolution of a circumterrestrial disk Constraints on the origin of the moon in geocentric orbit

A data base of about 25,000 numerically integrated trajectories of earth-encountering planetesimals is used to study the angular momentum problem of forming the moon out of material captured into a circumterrestrial disk from heliocentric orbits. Mass-orbital element distributions of incoming planetesimals are combined with this data base to calculate, as a function of distance from earth, the net geocentric specific angular momentum of disk-encountering material on heliocentric orbits. Results suggest that a permanent disk population is not possible.

Herbert, Floyd↗

NASA NTRS1987

Dynamic analysis of satellites with deployable hinged appendages

The nonlinear equations of motion determining the planar dynamical behavior of an orbiting satellite deploying both one and two rigid appendages have been formulated using Lagrange's equations. The analysis accounts for large angle rotations, Coriolis effects, and the gravitational gradient, and the resulting coupled governing equations are integrated numerically. The analysis is applied to the Space Shuttle based deployment of rigid truss-like members, and results show that spacecraft inertia parameters, appendage mass and length, deployment velocity, and initial conditions all influence the system response. It is found that the resulting librational movement is related to the size of the deployment payload, and that gravitational forces lead to vehicle stabilization.

Oakes, Kevin F.↗

NASA NTRS1987

Three-dimensional computations of transverse hydrogen jet combustion in a supersonic airstream

A computational fluid dynamics (CFD) code is being developed to compute the mixing and combustion of hydrogen fuel in the turbulent flow fields of supersonic combustion ramjets (scramjet). The code solves the three-dimensional Reynolds time-averaged complete Navier-Stokes equations including transport equations for a four species, two reaction, global finite rate chemistry model. The code was applied to the case of transverse injection of hydrogen from a sonic circular orifice into a supersonic airstream. The equations were numerically integrated using MacCormack's explicit method, and the algebraic eddy viscosity model of Baldwin-Lomax was used to model the turbulence. In the species transport and energy equations, diffusion coefficients based on Fick's Law and an assumption of unit Lewis number were applied. Computed features of the three-dimensional flow field are depicted by static pressure, static temperature, mass fraction of species, and velocity vectors. For engineering interest, mixing and combustion parameters were examined to assess the effect of injector diameter, injected fuel pressure, fuel-air ratio, and spacing of fuel injectors. The objective of the present paper is to demonstrate the capability of the present three-dimensional spatially elliptic, CFD code for turbulent, reacting flow. Application of the code to specific supersonic combustion configurations is planned.

Uenishi, K.↗

NASA NTRS1986

Numerical planetary and lunar ephemerides - Present status, precision and accuracies

Features of the emphemeris creation process are described with attention given to the equations of motion, the numerical integration, and the least-squares fitting process. Observational data are presented and ephemeride accuracies are estimated. It is believed that radio measurements, VLBI, occultations, and the Space Telescope and Hipparcos will improve ephemerides in the near future. Limitations to accuracy are considered as well as relativity features. The export procedure, by which an outside user may obtain and use the JPL ephemerides, is discussed.

Standish, E. Myles, Jr.↗

NASA NTRS1987

Stability analysis of two coupled Lorenz lasers and the coupling-induced periodic to chaotic transition

A linear stability analysis of two Lorenz lasers coupled by their electric fields has been performed, and it is shown that the bad cavity condition becomes a function of coupling and that a good cavity instability may occur if the injected fields are inverted before injection. In addition, it is shown that the symmetrically coupled Lorenz system is isomorphic to the original Lorenz system with new parameters. The stability analysis also predicts a lowering of the second laser threshold with coupling for both the chaotic and self-pulsing regimes. Numerical integration of the equations is in agreement with these predictions and has revealed a coupling induced transition from self-pulsing to chaotic behavior. The classification of the behavior of the coupled system in the parameter space of the coupling constants has been investigated and shows that the results of symmetric coupling allow enough of a margin for an experimental test of the theory. This would allow experimentalists to observe the actual Lorenz instability at excitations as low as 4-5 times above threshold.

Lawandy, N. M.↗

NASA NTRS1987

An approximate semi-analytical method for prediction of interlaminar shear stresses in an arbitrarily laminated thick plate

An approximate semianalytical method for determination of interlaminar shear stress distribution through the thickness of an arbitrarily laminated thick plate has been presented. The method is based on the assumptions of transverse inextensibility and layerwise constant shear angle theory (LCST) and utilizes an assumed quadratic displacement potential energy based finite element method (FEM). Centroid of the triangular surface has been proved from a rigorous mathematical point of view (Aubin-Nitsche theory), to be the point of exceptional accuracy for the interlaminar shear stresses. Numerical results indicate close agreement with the available three-dimensional elasticity theory solutions. A comparison between the present theory and that due to an assumed stress hybrid FEM suggest that the (normal) traction-free-edge condition is not satisfied in the latter approach. Furthermore, the present paper is the first to present the results for interlaminar shear stresses in a two-layer thick square plate of balanced unsymmetric angle-ply construction. A comparison with the recently proposed Equilibrium Method (EM) indicates the superiority of the present method, because the latter assures faster convergence as well as simultaneous vanishing of the transverse shear stresses on both of the exposed surfaces of the laminate. Superiority of the present method over the EM, in the case of a symmetric laminate, is limited to faster convergence alone. It has also been demonstrated that the combination of the present method and the reduced (quadratic order) numerical integration scheme yields convergence of the interlaminar shear stresses almost as rapidly as that of the nodal displacements, in the case of a thin plate.

Chaudhuri, Reaz A.↗