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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

A statistical formulation of one-dimensional electron fluid turbulence

A one-dimensional electron fluid model is investigated using the mathematical methods of modern fluid turbulence theory. Non-dissipative equilibrium canonical distributions are determined in a phase space whose co-ordinates are the real and imaginary parts of the Fourier coefficients for the field variables. Spectral densities are calculated, yielding a wavenumber electric field energy spectrum proportional to k to the negative second power for large wavenumbers. The equations of motion are numerically integrated and the resulting spectra are found to compare well with the theoretical predictions.

Fyfe, D.↗
NASA NTRS1964

Analytical Solutions for Non-Linear Differential Equations with the Help of a Digital Computer

A technique was developed with the help of a digital computer for analytic (algebraic) solutions of autonomous and nonautonomous equations. Two operational transform techniques have been programmed for the solution of these equations. Only relatively simple nonlinear differential equations have been considered. In the cases considered it has been possible to assimilate the secular terms into the solutions. For cases where f(t) is not a bounded function, a direct series solution is developed which can be shown to be an analytic function. All solutions have been checked against results obtained by numerical integration for given initial conditions and constants. It is evident that certain nonlinear differential equations can be solved with the help of a digital computer.

Cromwell, P. C.↗
NASA NTRS1977

New contributions to the problem of capture

Libration-point capture is analyzed in the framework of the restricted three-body problem in order to obtain general results capable of predicting the major features of an arbitrary postcapture orbit, with specific reference to capture as the presumed mode of origin of Jupiter's outer satellites. Some examples of libration-point capture are computed, the time a body remains captured is estimated, and a long-term numerical integration of orbits is carried out which shows that the equation used to estimate capture lifetimes is quite conservative. An extended capture criterion is proposed and used to demonstrate that direct postcapture orbits lie outside retrograde ones. Mass change involving one or both primaries is evaluated as a means of producing permanent capture, it is found that mass-change effects can produce 'pull-down capture', and consideration is given to the orbital evolution of Jupiter's outer satellites. The effect of drag in the solar nebula or in a nebula around proto-Jupiter on the capture process is briefly investigated. It is concluded that a capture origin for the outer satellites is improbable within the last 4.6 billion years but that either mass change or nebula drag could have been effective in producing capture.

Heppenheimer, T. A.↗
NASA NTRS1977

Guidance and trajectory considerations in lunar mass transportation

Flight-mechanics problems associated with large-scale transport of lunar mass to a space colony or manufacturing facility are discussed. The proposed transport method involves launch of payloads from a mass-driver on the lunar surface, onto ballistic trajectories to a passive mass-catcher located near the L2 libration point, with the caught mass subsequently being transported to the colony. Arrival velocities at L2, sensitivities in arrival dispersion due to launch errors, and effects of launch site location are treated, via numerically integrated orbits in the restricted three-body problem. From any launch site it is possible to define a target point reached with zero dispersion due to errors in a selected component of launch velocity. Effects of lunar geometrical librations and of obliquity, as well as the conditions for biasing a trajectory away from L2 so as to reduce stationkeeping costs, are dealt with along with transfer orbits from L2 to the colony. The theory of capture and the theory of resonance lead to a colony orbit, with period approximately two weeks, reached from L2 with velocity increment as low as 9.02 m/sec.

Heppenheimer, T. A.↗
NASA NTRS1977

Basic coaxial mass driver reference design

The reference design for a basic coaxial mass driver is developed to illustrate the principles and optimization procedures on the basis of numerical integration by programmable pocket calculators. The four inch caliber system uses a single-coil bucket and a single-phase propulsion track with discrete coils, separately energized by capacitors. An actual driver would use multiple-coil buckets and an oscillatory multi-phase drive system. Even the basic, table-top demonstration system should in principle be able to achieve accelerations in the 1,000 m/sq sec range. Current densities of the order of 25 ka/sq cm, continuously achievable only in superconductors, are carried by an ordinary aluminum bucket coil for a short period in order to demonstrate the calculated acceleration. Ultimately the system can be lengthened and provided with a magnetically levitated, superconducting bucket to study levitation dynamics under quasi-steady-state conditions, and to approach lunar escape velocity in an evacuated tube.

Kolm, H. H.↗
NASA NTRS1977

Electron kinematics in a plasma focus

The results of numerical integrations of the three-dimensional relativistic equations of motion of electrons subject to given electric and magnetic fields are presented. Fields due to two different models are studied: (1) a circular distribution of current filaments, and (2) a uniform current distribution; both the collapse and the current reduction phases are studied in each model. Decreasing current in the uniform current model yields 100 keV electrons accelerated toward the anode and, as for earlier ion computations, provides general agreement with experimental results.

Hohl, F.↗
NASA NTRS1977

A finite element technique for non-deterministic thermal deformation analyses including temperature dependent material properties

A technique utilizing the finite element displacement method is developed for the static analysis of structures subjected to non-deterministic thermal loading in which the material properties, assumed isotropic, are temperature dependent. Matrix equations are developed for the first two statistical moments of the displacements using a third order series expansion for the displacements in terms of the random temperatures. Sample problems are included to demonstrate the range of applicability of the third order series solutions. These solutions are compared with results from Monte Carlo analyses and also, for some problems, with solutions obtained by numerically integrating equations for the statistical properties of the displacements. In general, it is shown that the effect of temperature dependent material properties can have a significant effect on the covariances of the displacements.

Case, W. R., Jr.↗
NASA NTRS1977

An explicit solution to the exoatmospheric powered flight guidance and trajectory optimization problem for rocket propelled vehicles

A derivation of an explicit solution to the two point boundary-value problem of exoatmospheric guidance and trajectory optimization is presented. Fixed initial conditions and continuous burn, multistage thrusting are assumed. Any number of end conditions from one to six (throttling is required in the case of six) can be satisfied in an explicit and practically optimal manner. The explicit equations converge for off nominal conditions such as engine failure, abort, target switch, etc. The self starting, predictor/corrector solution involves no Newton-Rhapson iterations, numerical integration, or first guess values, and converges rapidly if physically possible. A form of this algorithm has been chosen for onboard guidance, as well as real time and preflight ground targeting and trajectory shaping for the NASA Space Shuttle Program.

Jaggers, R. F.↗
NASA NTRS1977

Third-order solution of an artificial-satellite theory

A third-order solution was developed for the motions of artificial satellites moving in the gravitational field of the earth, whose potential includes the second-, third-, and fourth-order zonal harmonics. Third-order periodic perturbations with fourth-order secular perturbations were derived by the Hori perturbation method. All quantities were expanded into power series of the eccentricity, but the solution was obtained so as to be closed with respect to the inclination. A comparison with the results of numerical integration of the equations of motion indicates that the solution can predict the position of a close-earth, small-eccentricity satellite with an accuracy of better than one cm over a period of one month.

Kinoshita, H.↗
NASA NTRS1977

Application of the TRPLT1 element to large amplitude free vibrations of plates

A finite element formulation is developed for analyzing large amplitude free flexural vibrations of thin plates in NASTRAN. Stress distributions in the plate, in addition to deflection shapes and nonlinear frequencies are determined. Linearized equations of motion governing large amplitude oscillations of plates and a linearized geometrical stiffness matrix are presented. The solution procedure and convergence characteristics are discussed. The quasi-linear geometrical stiffness matrix for an eighteen degree-of-freedom higher order triangular plate element is evaluated by using a seven-point numerical integration. Nonlinear frequencies for square, rectangular, rhombic, and isosceles triangular plates, with edges simply supported or clamped, are compared with earlier solutions. The present formulation is found to give results entirely adequate for engineering purposes.

Mei, C.↗
NASA NTRS1976

Abort Region Determinator (ARD) module feasibility report. Mission planning, mission analysis and software formulation

A detailed performance evaluation of the Abort Region Determinator (ARD) module design was provided in support of OFT-1 ascent and OFT-1 intact launch aborts. The evaluation method used compared ARD results against results obtained using the full-up Space Vehicle Dynamic Simulations program under the same conditions. Results were presented for each of the three major ARD math models: (1) the ascent numerical integrator; (2) the mass model, and (3) the second stage predictor as well as the total ARD module. These results demonstrate that the baselined ARD module meets all design objectives for mission control center orbital flight test launch/abort support.

Draeger, B. G.↗
NASA NTRS1978

GEOS-3 coherent C-band tracking data reduction and analysis

The availability of a coherent C-Band transponder on an orbiting vehicle has permitted the development of calibration techniques for C-Band radars. Prior coherent tracking was limited to test vehicles in powered flight or skin tracking of orbiting spacecraft. The pulse Doppler range rate data available concurrently and independently with normal range and angle data provides an extremely useful data set for assessing the internal consistency of the radars measurements, particularly when coupled with a trajectory well constrained by orbit dynamics. In order to further assess the precision of the range rate data, a technique was developed to numerically integrate the rate measurements into a pseudo-range data set showing extremely low noise and high sensitivity to systematic radar errors. Evaluation of integrated range data led to improvements in calibration of both the rate and conventional range data. In particular, proper evaluation of the very sensitive integrated ranges required the development of a processing correction for beacon delay variation with signal strength, a significant error in the conventional ranging data.

Krabill, W. B.↗
NASA NTRS1978

Thermal stress analysis of ceramic structures with NASTRAN isoparametric solid elements

The performance of the NASTRAN level 16.0, twenty node, isoparametric bricks (CIHEX2) at thermal loading was studied. A free ceramic plate was modelled using twenty node bricks of varying thicknesses. The thermal loading for this problem was uniform over the surface with an extremely large gradient through the thickness. No mechanical loading was considered. Temperature-dependent mechanical properties were considered in this analysis. The NASTRAN results were compared to one dimensional stress distributions calculated by direct numerical integration.

Lamberson, S. E.↗
NASA NTRS1977

An optimal Space Shuttle ascent trajectory for the first orbital flight test

An optimal solution of the ascent trajectory of the Space Shuttle for the first orbital flight test is presented; the optimization is a minimum propellant, four-control problem in yaw angle, roll angle, pitch angle and vacuum thrust of each Space Shuttle main engine. Piecewise linear segments with juncture points treated as parameters are employed to model the controls. Equations of motion for a three-dimensional flight with pitch plane moment balance about an oblate are integrated numerically with a fourth-order Runge-Kutta method; two- and one-dimensional cubic spline function curve fits of aerodynamic coefficients are used during the first and second stages, respectively. The constraint minimization problem is solved with the Davidon-Fletcher-Powell function method.

Johnson, I. L., Jr.↗
NASA NTRS1978

Diffusion of hydrogen through platinum membranes at high pressures and temperatures

The diffusion of hydrogen through platinum membranes has been measured at 450, 500, 550 and 600 C at 2000 bar pressure, using the hydrogen sensor technique. Ag + AgCl + 3M HCl was the starting solution inside the platinum tube. Hydrogen diffuses out of the platinum tube into a system containing Fe2O3 + Fe3O4 + H2O; that is, a solution with a fixed hydrogen fugacity. After quench, the drop in hydrogen fugacity inside the platinum tube was calculated from measurements of pH and chloride molality. The hydrogen fugacity is initially roughly proportional to the square root of time. Diffusion constants were calculated from these data by numerical integration.

Chou, I.-M.↗
NASA NTRS1978

Statistical formulation of one-dimensional electron fluid turbulence

A one-dimensional electron fluid model is investigated using the mathematical methods of modern fluid turbulence theory. Nondissipative equilibrium canonical distributions are determined in a phase space whose coordinates are the real and imaginary parts of the Fourier coefficients for the field variables. Spectral densities are calculated, yielding a wavenumber electric field energy spectrum proportional to 1/k squared for large wavenumbers. The equations of motion are numerically integrated and the resulting spectra are found to compare well with the theoretical predictions.

Fyfe, D.↗
NASA NTRS1978

An analytic study of impact ejecta trajectories in the atmospheres of Venus, Mars, and earth

Calculations have been made to determine the effects of atmospheric drag and gravity on impact ejecta trajectories on Venus, Mars, and earth. The equations of motion were numerically integrated for a broad range of body sizes, initial velocities, and initial elevation angles. A dimensionless parameter was found from approximate analytic solutions which correlated the ejecta range, final impact angle, and final impact velocity for all three planets.

Tauber, M. E.↗
NASA NTRS1977

Effects of solar radiation pressure on the orbit of the Solar Power Satellite

The surface area-to-weight ratio of the Solar Power Satellite (SPS) is of the order of sq m/kg. Therefore, solar radiation pressure will be an important perturbation on the orbit, causing large variations in eccentricity. An analytical solution is developed for the motion of eccentricity and the line of apsides. Included is a secular term due to the earth's orbital eccentricity. Several initial conditions are considered. For some cases, the eccentricity is nearly constant over a few years. General characteristics of the motion are discussed. Long-term (30 years) effects of gravity are investigated by using a numerical integration method. Eccentricities of approximately 0.08 can be expected for uncorrected SPS orbits.

Graf, O. F., Jr.↗