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NASA NTRS1975

Magnetic attitude control system for dual-spin satellites

A closed-loop control law is developed for a dual-spin satellite control system which utilizes the interaction of the geomagnetic field with the satellite dipole parallel to the spin axis. The control law consists of the linear combination of the pitch axis component of the rate of change of the geomagnetic field and the product of the roll angle and roll axis component of the geomagnetic field. Application of the method of multiple time scales yields approximate solutions for the feedback gains in terms of the system parameters. Approximate solutions are also obtained for the response of the system to disturbance torques. A comparison of the approximate solutions and numerical solutions obtained by numerical integration of the exact equations of motion is then given.

Alfriend, K. T.↗

NASA NTRS1976

Proton tissue dose

Program calculates dosage averaged over five major segments of blood-forming organ, treating human body geometry in detail but assuming isotropicity of incident primary particles. Approximate form of transport theory is used, incorporating nuclear star effects. Two numerical integrations are used to evaluate intermediate equation and then dosage equation.

Wilson, J. W.↗

NASA NTRS1975

Stabilization by modification of the Lagrangian

In order to reduce the error growth during a numerical integration, a method of stabilization of the differential equations of the Keplerian motion is offered. It is characterized by the use of the eccentric anomaly as an independent variable in such a way that the time transformation is given by a generalized Lagrange formalism. The control terms in the equations of motion obtained by this modified Lagrangian give immediately a completely Liapunov-stable set of differential equations. In contrast to other publications, here the equation of time integration is modified by a control term which leads to an integral which defined the time element for the perturbed Keplerian motion.

Baumgarte, J. W.↗

NASA NTRS1975

Mean colors of Cepheids

Color observations of Cepheids can be interpreted by a color effective temperature relation to give different T sub e values for each kind of mean color. Here, theoretical colors from numerical integrations of Cepheid pulsations are used to determine the proper method of taking the color mean in order to get, by the color T sub e relation, the correct nonpulsating T sub e.

Cox, A. N.↗

NASA NTRS1975

Second-order small-disturbance solutions for hypersonic flow over power-law bodies

Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.

Townsend, J. C.↗

NASA NTRS1975

STICAP: A linear circuit analysis program with stiff systems capability. Volume 1: Theory manual

STICAP (Stiff Circuit Analysis Program) is a FORTRAN 4 computer program written for the CDC-6400-6600 computer series and SCOPE 3.0 operating system. It provides the circuit analyst a tool for automatically computing the transient responses and frequency responses of large linear time invariant networks, both stiff and nonstiff (algorithms and numerical integration techniques are described). The circuit description and user's program input language is engineer-oriented, making simple the task of using the program. Engineering theories underlying STICAP are examined. A user's manual is included which explains user interaction with the program and gives results of typical circuit design applications. Also, the program structure from a systems programmer's viewpoint is depicted and flow charts and other software documentation are given.

Cooke, C. H.↗

NASA NTRS1975

A two parameter survey of periodic orbits in the restricted problem of three bodies

Within the context of the restricted problem of three bodies the effects caused by varying the mass ratio of the primaries and the eccentricity of their orbits, upon periodic orbits of the infinitesimal mass which are numerical continuations of circular orbits in the ordinary problem of two bodies are shown. A recursive power series technique is used to numerically integrate the equations of motion as well as the first variational equations in order to generate a two parameter family of perodic orbits and identify the linear stability characteristics. Seven such families are investigated with equally spaced mass ratios from 0.0 to 1.0 and eccentricities of the orbits of the primaries in a range 0.0 to 0.6. Stable orbits are associated with large distances of the infinitesimal mass from the perturbing primary, nearly circular motion of the primaries, and small mass ratios of the primaries. Unstable orbits for the infinitesimal mass are associated with small distances from the perturbing primary, highly elliptic orbits of the primaries and large mass ratios.

Shelus, P. J.↗

NASA NTRS1976

Lunar motion analysis and laser data management

Work completed in lunar motion analysis and laser data management during the period July 1, 1971 - September 30, 1975 was reported. In this context, analysis refers to theoretical or numerical studies involving real or potential applications of such observations to improvement of the physical model, and data management refers to the process by which observed photon events are turned into observations and are made available to potential users. The data analysis work included: (1) bringing to operational status of computer programs for the numerical integration of the lunar orbit motion and for the application of lunar laser time delays for the improvement of the parameters of the physical model, (2) program improvement and program integrity, (3) three-dimensional ephemeris, and (4) miscellaneous independent studies. The data management work included: (1) data identification, (2) observatory interfaces, and (3) data distribution.

Mulholland, J. D.↗

NASA NTRS1975

Earth-moon system: Dynamics and parameter estimation

A theoretical development of the equations of motion governing the earth-moon system is presented. The earth and moon were treated as finite rigid bodies and a mutual potential was utilized. The sun and remaining planets were treated as particles. Relativistic, non-rigid, and dissipative effects were not included. The translational and rotational motion of the earth and moon were derived in a fully coupled set of equations. Euler parameters were used to model the rotational motions. The mathematical model is intended for use with data analysis software to estimate physical parameters of the earth-moon system using primarily LURE type data. Two program listings are included. Program ANEAMO computes the translational/rotational motion of the earth and moon from analytical solutions. Program RIGEM numerically integrates the fully coupled motions as described above.

Breedlove, W. J., Jr.↗

NASA NTRS1976

Combustion of hydrogen injected into a supersonic airstream (a guide to the HISS computer program)

A computer program based on a finite-difference, implicit numerical integration scheme is described for the prediction of hydrogen injected into a supersonic airstream at an angle ranging from normal to parallel to the airstream main flow direction. Results of calculations for flow and thermal property distributions were compared with 'cold flow data' taken by NASA/Langley and show excellent correlation. Typical results for equilibrium combustion are presented and exhibit qualitatively plausible behavior. Computer time required for a given case is approximately one minute on a CDC 7600. A discussion of the assumption of parabolic flow in the injection region is given which demonstrates that improvement in calculation in this region could be obtained by a partially-parabolic procedure which has been developed. It is concluded that the technique described provides an efficient and reliable means for analyzing hydrogen injection into supersonic airstreams and the subsequent combustion.

Dyer, D. F.↗

NASA NTRS1976

Wide angle lenses with aspheric correcting surfaces

Refracting elements having aspheric correcting surfaces near the center of curvature are analyzed. As in the case of the Schmidt reflector, such systems can have a wide aperture and a wide field of view; in addition, they are free from obstructing surfaces. Being uncorrected for dispersion, however, the refracting systems are restricted to nearly monochromatic radiation. Typical forms of the correcting surfaces have been determined, both by third order theory and by numerical integration of exact equations.

Jones, R. T.↗

NASA NTRS1976

On the Tesseral-Harmonics Resonance Problem in Artificial-Satellite Theory, Part 2

Equations were derived for the perturbations on an artificial satellite when the motion of the satellite is commensurable with that of the earth. This was done by first selecting the tesseral harmonics that contribute the most to the perturbations and then by applying Hori's method by use of Lie series. Here, are introduced some modifications to the perturbations, which now result in better agreement with numerical integration.

Romanowicz, B. A.↗

NASA NTRS1974

Satellite-tracking and earth-dynamics research programs

Observations and research progress of the Smithsonian Astrophysical Observatory are reported. Satellite tracking networks (ground stations) are discussed and equipment (Baker-Nunn cameras) used to observe the satellites is described. The improvement of the accuracy of a laser ranging system of the ground stations is discussed. Also, research efforts in satellite geodesy (tides, gravity anomalies, plate tectonics) is discussed. The use of data processing for geophysical data is examined, and a data base for the Earth and Ocean Physics Applications Program is proposed. Analytical models of the earth's motion (computerized simulation) are described and the computation (numerical integration and algorithms) of satellite orbits affected by the earth's albedo, using computer techniques, is also considered. Research efforts in the study of the atmosphere are examined (the effect of drag on satellite motion), and models of the atmosphere based on satellite data are described.

Source record↗

NASA NTRS1976

Mathematical theory of the Goddard trajectory determination system

Basic mathematical formulations depict coordinate and time systems, perturbation models, orbital estimation techniques, observation models, and numerical integration methods.

Cappellari, J. O.↗

NASA NTRS1976

Sonic boom research

A computer program for CDC 6600 is developed for the nonlinear sonic boom analysis including the asymmetric effect of lift near the vertical plane of symmetry. The program is written in FORTRAN 4 language. This program carries out the numerical integration of the nonlinear governing equations from the input data at a finite distance from the airplane configuration at a flight altitude to yield the pressure signitude at ground. The required input data and the format for the output are described. A complete program listing and a sample calculation are given.

Zakkay, V.↗

NASA NTRS1976

LaRC design analysis report for National Transonic Facility for 9% nickel tunnel shell. Volume 1: Finite difference analysis of cone/cylinder junction

The results of extensive computer (finite element, finite difference and numerical integration), thermal, fatigue, and special analyses of critical portions of a large pressurized, cryogenic wind tunnel (National Transonic Facility) are presented. The computer models, loading and boundary conditions are described. Graphic capability was used to display model geometry, section properties, and stress results. A stress criteria is presented for evaluation of the results of the analyses. Thermal analyses were performed for major critical and typical areas. Fatigue analyses of the entire tunnel circuit are presented.

Ramsey, J. W., Jr.↗

NASA NTRS1976

LaRC design analysis report for National Transonic Facility for 304 stainless steel tunnel shell. Volume 1S: Finite difference analysis of cone/cylinder junction

Ramsey, J. W., Jr.↗

NASA NTRS1975

Lunar and solar perturbations on the orbit of a geosynchronous satellite

The luni-solar effects cause a large amplitude, long-period perturbation of the orbital plane. Canonical differential equations associated with this motion contain a singular point, and are expanded about this point to third order. A solution is given that is valid for long times and is not restricted to small inclinations. Higher order terms are investigated. Expressions are given for the inclination (I) and node as a function of time. Comparisons with a numerically integrated solution show a disagreement in inclination of only .03 deg after 11 years.

Graf, O. F., Jr.↗