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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Assessment of advances in structural analysis for space shuttle

The latest technology for structural analysis in relation to the design tasks that lie ahead for the space shuttle is reviewed. For shell-of-revolution structures, the analysis can be formulated as a one-dimensional problem which is readily solved by using finite-difference or numerical-integration techniques. For more general asymmetric shells, a two-dimensional formulation is required. However, the governing equations are readily formulated and are amenable to solution by finite-difference techniques. For a completely general structural arrangement, such as structural frameworks, recourse is usually made to discretized formulations using finite elements. Of course, the finite-element programs could be used for shell structures, but at a loss in accuracy and increase in computer time compared with the special purpose programs.

Dixon, S. C.↗
NASA NTRS1972

Orbit improvement from satellite imaging data obtainable from the Mariner/Jupiter/Saturn 1977 missions

Equations of motion are established for a dynamic system in which a spacecraft flies close to and interacts with an outer planet and one or more of its satellites. For the computation of the state and mass partials needed in the orbit corrections, a set of variational equations is derived. These assume a notably compact form through the introduction of a matrix operator D. The above system of differential equations is integrated numerically on a computer.

Aksnes, K.↗
NASA NTRS1972

Earth zonal harmonics from rapid numerical analysis of long satellite arcs

A zonal geopotential is presented to degree 21 from evaluation of mean elements for 21 satellites including 2 of low inclination. Each satellite is represented by an arc of at least one apsidal rotation. The lengths range from 200 to 800 days. Differential correction of the initial elements in all of the arcs, together with radiation pressure and atmospheric drag coefficients, was accomplished simultaneously with the correction for the zonal harmonics. The satellite orbits and their variations are generated by numerical integration of the Lagrange equations for mean elements. Disturbances due to precession and nutation of the earth's pole, atmospheric drag, radiation pressure and luni-solar gravity are added at from 1- to 8-day intervals in the integrated orbits. The results agree well with recent solutions from other authors using different methods and different satellite sets.

Wagner, C. A.↗
NASA NTRS1972

A theoretical and experimental investigation of the hypersonic turbulent boundary layer subject to normal and longitudinal pressure gradients and cross flow along a windward plane of symmetry.

A theoretical and experimental investigation for the hypersonic turbulent boundary layer undergoing both normal and longitudinal pressure gradients and cross flow along the plane of symmetry on the windward side of a body of revolution is presented. The purpose of this investigation is to provide a method for calculating boundary layers that occur on the centerline of symmetry of an inlet. The three-dimensional compressible integral equations are written along the symmetry plane and integrated numerically, and the effect of the cross flow on the behavior of the boundary layer is also studied. The experiments were performed at Mach number 6 and Reynolds number of 44,000,000/ft for the axisymmetric case and for the case with cross flow. The velocity profiles and the boundary layer parameters agree relatively well with theoretical values with and without cross flow effects. The presence of the cross flow alters significantly the value of the profiles. Total temperature-velocity correlations deviate from the linear Crocco distribution. Heat transfer rates agree with theoretical values and values obtained by the flat plate reference enthalpy method. Cross flow influence on the heat transfer rates is of minor relevance.

Zakkay, V.↗
NASA NTRS1972

Computer study of convection of weakly ionized plasma in a nonuniform magnetic field.

A weakly ionized plasma in a strong and nonuniform magnetic field exhibits an instability analogous to the flute instability in a fully ionized plasma. The instability sets in at a critical magnetic field. To study the final state of the plasma after the onset of the instability, the plasma equations are integrated numerically assuming a certain initial spectrum of small disturbances. In the regime studied, numerical results indicate a final steadily oscillating state consisting of a single finite amplitude mode together with a time-independent modification of the original equilibrium. These results agree with the analytic results obtained by Simon in the slightly supercritical regime. As the magnetic field is increased further, the wavelength of the final oscillation becomes nonunique. There exists a subinterval in the unstable wave band. Final stable oscillation with a wavelength in this subinterval can be established if the initial disturbance has a sufficiently strong component at the particular wavelength.

Shiau, J. N.↗
NASA NTRS1972

An analytic guidance technique for planetary and lunar approach trajectories.

An explicit, analytic guidance technique is developed for the hyperbolic approach phases of interplanetary and lunar spacecraft trajectories. The guidance technique is based upon a first-order analytic solution for the perturbed planet-centered (or moon-centered) trajectory. This trajectory is represented as the sum of two components: (1) the unperturbed osculating hyperbola at pericenter, and (2) first-order position and velocity perturbations due to gravitational effects of the sun and other planets. A closed-form analytic approximation for these perturbations valid for the entire approach trajectory is derived, thereby eliminating the need for numerical integration of the equations of motion. By means of this analytic trajectory model, the approach guidance problem is reduced to an equivalent two-body problem. The guidance objectives are specified in terms of actual, attainable conditions at pericenter, and the required corrective velocity is determined explicitly for both fixed and variable times of arrival.

Carlson, N. A.↗
NASA NTRS1972

Power series evaluation of transition and covariance matrices.

Reexamination power series solutions to the matrix covariance differential equation and the transition differential equation. Truncation error bounds are derived which are computationally attractive and which extend previous results. Polynomial approximations are obtained by exploiting the functional equations satisfied by the transition and covariance matrices. The series-functional equation propagation technique represents a fast and accurate alternative to the numerical integration of the time-invariant transition and covariance equations.

Bierman, G. J.↗
NASA NTRS1972

Ionization of multielectron atoms by fast charged particles.

Using plane waves to describe the incident and scattered particles, and screened hydrogenic and Coulomb functions to describe the atomic electrons before and after ejections, we have calculated the differential and total ionization cross sections of 11 atoms and one ion by electron impact, and ionization of helium by proton impact. The effective charges of the screened hydrogenic functions are fixed by the Hartree-Fock calculations. Calculations have been carried out for the atomic s, p, and d electrons. For low atomic numbers, we find reasonable agreement with the experimental data. For intermediate atomic numbers, we expect our results to overestimate the actual cross sections, since our choice of a unit charge for the Coulomb function of the ejected electrons will overestimate the atomic dipole potential strength, and in turn the high-energy cross sections. The advantage of the method presented here is that the ionization amplitude is given in analytic form. This may allow further analysis on this amplitude, and facilitates extension of the numerical integration for the cross section to high impact energies.

Omidvar, K.↗
NASA NTRS1972

Radiation resistance of a baffled beam.

The radiation resistance of a beam is theoretically determined from the total acoustic power radiated into the farfield. The beam is supported in an infinite baffle, with both hinged and clamped supports considered. Asymptotic solutions are derived for frequencies well below the critical frequency. Curves, covering the entire frequency range between the low- and high-frequency asymptotic solutions, are obtained through numerical integration for the first ten modes of beams with various width-to-length ratios. For frequencies well below the critical frequency, the ratio of the radiation resistance of a beam clamped at each end to that of a beam hinged at each end is 0.851 for the first mode, 0.711 for the second mode, and asymptotically approaches 2 as the mode number tends to infinity. For both hinged and clamped supports, the radiation resistance of all modes increases with the beam width-to-length ratio.

Wallace, C. E.↗
NASA NTRS1972

Radiation resistance of a rectangular panel.

The radiation resistance corresponding to the natural modes of a finite rectangular panel is theoretically determined from the total energy radiated to the farfield. The panel is assumed to be simply supported in an infinite baffle. Asymptotic solutions for the low-frequency region are derived, and curves covering the entire frequency range for various mode shapes and aspect ratios are obtained through numerical integration. When the ratio of the acoustic wavenumber to the panel wavenumber is a constant much less than unity, the radiation resistance for all modes is a minimum if the intranodal area (the area between adjacent node lines) is square, and increases with the aspect ratio of the intranodal area.

Wallace, C. E.↗
NASA NTRS1972

The earth's bow shock in an oblique interplanetary field.

The pressure, magnetic field, temperature, particle density, and stream velocity throughout the magnetosheath have been calculated in the plane containing the interplanetary field and solar wind velocity vector for various orientations of the interplanetary magnetic field and various assumed ratios of specific heats of the compressed solar wind. Jump conditions at the bow shock gave initial conditions in the shocked plasma from which the appropriate hydromagnetic equations (for blunt bodies in the subsonic region near the subsolar point and for the method of characteristics in the supersonic region back in the tail) were integrated numerically back to the surface of the magnetosphere. Explicit consideration of the magnetic field shows that a net asymmetrical force on the magnetopause produces a side force, or 'lift' in addition to the well-known drag on the magnetosphere.

Shen, W.-W.↗
NASA NTRS1972

Two-dimensional vortex motion and 'negative temperatures.'

Explanation of the novel phenomenon, tentatively identified as the 'ergodic boundary' in a space of initial conditions for turbulent flow, suggested by the recent numerical integration of the two-dimensional Navier-Stokes equations at high Reynolds numbers reported by Deem and Zabusky (1971). The proposed explanation is presented in terms of negative temperatures for a point vortex model.

Montgomery, D.↗
NASA NTRS1972

Calculation of body-centered-cubic lattice sums with an application to ferromagnetism.

The lattice sums for the bcc lattice are recalculated using the method of Flax and Raich to obtain more general expressions, valid for all temperatures, in terms of a Langevin function and its derivatives. Formulas are presented which enable easy numerical evaluation. A comparison with well-known low-temperature expansions and with the results of direct numerical integration demonstrates the validity at low temperatures of the more general expressions calculated here.

Wintucky, E. G.↗
NASA NTRS1972

On the elliptic restricted three-body problem.

This article describes the most important features of the elliptic restricted three-body problem. The methods of numerical integration with recurrent power series are developed for both the equations of motion and the variational equations. The conditions for the existence of periodic orbits and families of periodic orbits are also outlined in detail, and finally illustrated with a family of symmetric periodic orbits.

Broucke, R.↗
NASA NTRS1972

Ephemeris of a highly eccentric orbit - Explorer 28.

An ephemeris has been obtained for Explorer 28 (IMP 3) which agrees well with 2 years of radio observations and with SAO observations a year later. This ephemeris is generated over the 3 year lifetime by a numerical integration method utilizing a set of initial conditions at launch and without requiring further differential correction. Because highly eccentric orbits are difficult to compute with acceptable accuracy and because a long continuous arc has been obtained which compares with actual data to a known precision, this ephemeris may be used as a standard for computing highly eccentric orbits in the earth-moon system. Orbit improvement was used to obtain the initial conditions which generated the ephemeris. This improvement was based on correcting the energy by adjusting the semimajor axis to match computed times of perigee passage with the observed. This procedure may generate errors in semimajor axis to compensate for model errors in the energy; however, this compensation error is also implicit in orbit determination itself.

Lowrey, B. E.↗
NASA NTRS1972

The optimal control of merging aircraft - Implementation of the hybrid air traffic controller.

The control of merging aircraft is formulated as a finite-time, quadratic optimal control problem of a linear system with state and control constraints. The purpose of this paper is to demonstrate that the Hybrid Air Traffic Controller (HAC), which has been previously developed as a solution to this problem, may be easily implemented. Use is made of both the properties of the algebraic solution to the matrix Riccati equation and the structure of the linear model. This approach results in a real-time synthesis procedure for the HAC which does not rely on iterative numerical integration techniques.

Schatz, J. G.↗
NASA NTRS1972

Simplified analysis and optimization of space base and space shuttle heat rejection systems

A simplified radiator system analysis was performed to predict steady state radiator system performance. The system performance was found to be describable in terms of five non-dimensional system parameters. The governing differential equations are integrated numerically to yield the enthalpy rejection for the coolant fluid. The simplified analysis was extended to produce the derivatives of the coolant exit temperature with respect to the governing system parameters. A procedure was developed to find the optimum set of system parameters which yields the lowest possible coolant exit temperature for either a given projected area or a given total mass. The process can be inverted to yield either the minimum area or the minimum mass, together with the optimum geometry, for a specified heat rejection rate.

Wulff, W.↗