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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 271 records · Page 15
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NASA NTRS1974

Perturbed nonlinear differential equations

For perturbed nonlinear systems, a norm, other than the supremum norm, is introduced on some spaces of continuous functions. This makes possible the study of new types of behavior. A study is presented on a perturbed nonlinear differential equation defined on a half line, and the existence of a family of solutions with special boundedness properties is established. The ideas developed are applied to the study of integral manifolds, and examples are given.

Proctor, T. G.↗
NASA NTRS1975

Station coordinates in the standard earth 3 system and radiation-pressure perturbations from ISAGEX camera data

Simultaneous and individual camera observations of GEOS 1, GEOS 2, Pageos, and Midas 4 obtained during the International Satellite Geodesy Experiment are utilized to determine station coordinates. The Smithsonian Astrophysical Observatory Standard Earth III system of coordinates is used to tie the geometrical network to a geocentric system and as a reference for calculating satellite orbits. A solution for coordinates combining geometrical and dynamical methods is obtained, and a comparison between the solutions and terrestrial data is made. The radiation-pressure and earth-albedo perturbations for Pageos are very large, and Pageos' orbits are used to evaluate the analytical treatment of these perturbations. Residual effects, which are probably of interest to aeronomists, remain in the Pageos orbits.

Gaposchkin, E. M.↗
NASA NTRS1975

Analyses of the solid earth and ocean tidal perturbations on the orbits of the GEOS-1 and GEOS-2 satellites

The luni-solar tidal perturbations in the inclination of the GEOS-I and GEOS-II satellite orbits were analyzed for the solid Earth and ocean tide conditions. Precision reduced camera and TRANET Doppler observations spanning periods of over 600 days for each satellite were used to derive mean orbital elements. Perturbations due to the earth's gravity field, solar radiation pressure, and atmospheric drag were modelled, and the resulting inclination residuals were analyzed for tidal effects. The amplitudes of the observed total tidal effects were about 1.2 arc seconds (36 meters) in the inclination of GEOS-I and 4.5 arc seconds (135 meters) for GEOS-II. The solid earth tides were then modelled using earth tide measurements, earth rotation observations, and seismic data. The resulting inclination residuals were analyzed for ocean tide parameters. The derived parameters consist of one second degree coefficient and an accompanying phase angle in a spherical harmonic expansion of the ocean tidal potential for each tidal constituent. The results are presented.

Felsentreger, T. L.↗
NASA NTRS1974

On the analytic lunar and solar perturbations of a near earth satellite

The disturbing function of the moon (sun) is expanded as a sum of products of two harmonic functions, one depending on the position of the satellite and the other on the position of the moon (sun). The harmonic functions depending on the position of the perturbing body are developed into trigonometric series with the ecliptic elements l, l prime, F, D and Gamma of the lunar theory which are nearly linear with respect to time. Perturbation of elements are in the form of trigonometric series with the ecliptic lunar elements and the equatorial elements omega and Omega of the satellite, so that analytic integration is simple and the results are accurate over a long period of time.-

Estes, R. H.↗
NASA NTRS1975

Vector potential and metric perturbations of a rotating black hole

The assumption of factorized Green's functions together with the inhomogeneous Teukolsky equations are used to derive analytic expressions for homogeneous metric (and vector potential) perturbations of a Kerr black hole. These homogeneous solutions are used to construct solutions to the perturbation equations when sources are present. What one finds are particularly simple formulas for the energy and angular momentum flux in the asymptotic regions at plus or minus infinity.-

Chrzanowski, P. L.↗
NASA NTRS1976

Investigation of environmental perturbations on passive asymmetric satellite

The effects of environmental perturbations on the attitude of a slow tumbling earth-oriented satellite are investigated. The environmental perturbations considered were aerodynamic drag, gravity-gradient, solar radiation pressure, and magnetic torques. The Euler attitude equations were solved numerically for the Skylab spacecraft. Results are presented for both torque-free motion and for cases in which aerodynamic and gravity-gradient torques are acting in a slow tumble mode. Simulations show gravity-gradient effects on satellite momentum to be cyclic and to increase the precession rate of the angular momentum vector about the radius vector. This also tends to align the minor axis along the radius vector. Aerodynamic drag initially decreases angular momentum, slowly precesses the momentum vector about the radius vector, and finally drives the satellite into an unstable mode. Combined gravity-gradient and aerodynamic torques reduce angular momentum and energy, and induce a steady precession rate of the momentum vector about the radius vector.

Tate, V.↗
NASA NTRS1976

Solution of linear systems by a singular perturbation technique

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

Ardema, M. D.↗
NASA NTRS1975

Perturbation solution of the Navier-Stokes equations and its relation to the Lighthill-Curle solution of aerodynamic sound

The aerodynamic sound described by the Lighthill-Curle solution is reexamined using a method of matched asymptotic expansions. The governing Navier-Stokes equations written in nondimensional form are expanded for a small Mach number. First- and second-order solutions for the pressure field are obtained, and the singular nature of the expansion at large distances is indicated. The nearfield pressure is governed by the Poisson equation, whereas the farfield equations describe a linear wave system in a dissipative medium. The pseudosound is related to the incompressible Reynolds stresses associated with a solenoidal velocity field, the velocity, the pressure perturbation, and their derivatives on the boundaries. A uniformly valid first-order solution for the pressure is obtained. It is shown that viscosity, thermal conductivity, and entropy in the flow do not contribute to the first-order noise generation, while the viscous stress contributes to noise only from some boundaries. The application of the proposed perturbation method to a subsonically moving surface and a hot jet is discussed.

Pan, Y. S.↗
NASA NTRS1975

A uniformly valid solution for motion about the interior libration point of the perturbed elliptic-restricted problem

Bounded motion about Lagrange collinear libration points is considered for a perturbed elliptic-restricted problem. A practical application is the motion of a satellite near a libration point collinear with the sun and the earth-moon barycenter. Such a system is treated here as an earth-sun-satellite elliptic restricted problem with lunar perturbations. The method of dual time scales is utilized to develop a uniformly valid three-dimensional analytical solution to the satellite's equations of motion. The analytical development applies somewhat generally to that class of four-body problems where the second primary mass is much greater than the first, and the third primary mass is much greater than the second.

Richardson, D. L.↗
NASA NTRS1975

Mean rates of the orbital elements of a satellite perturbed by a lens shaped mass concentration

Long arc gravity analysis of lunar orbiter tracking data in the past has been carried out with the help of averaged equations of motion, in which short period effects have been suppressed. This procedure has required that the harmonic terms in the gravity potential be averaged over an orbital period. In the present paper, this technique is extended to mass points and mass disks in the gravity field. This requires the evaluation of expressions for the mean rates of the orbit elements for a satellite perturbed by a lens shaped mass concentration. Corresponding expressions for the perturbations due to a mass point are obtained in the limit as the lens radius goes to zero. The derived equations have been programmed on the UNIVAC 1108 computer, and the results checked by numerical differencing.

Ananda, M.↗
NASA NTRS1976

Short-period and long-period perturbations of a spherical satellite due to direct solar radiation

On the basis of expressions derived by Kozai (1961) and those developed in this paper, a detailed semianalytic algorithm is presented for calculating radiation-pressure perturbations in the Keplerian elements. Through some simple modifications, the algorithm is also made to hold when e = 0, i = 0, or both. The perturbations are obtained by summing over the sunlit segment of the satellite's orbit during each revolution or part thereof. The end points of this segment are evaluated numerically once per revolution. The effect of the inherent uncertainties in the boundaries of the earth's shadow is discussed. The algorithm is tested by means of numerical integration of the equations of motion and through comparisons with observations of the balloon satellite 1963 30D during a 200-day interval.

Aksnes, K.↗
NASA NTRS1976

Perturbation theory in thermosphere dynamics

It is shown that density and pressure throughout the thermosphere can be adequately described in a logarithmic expansion that provides a sound basis for the application of perturbation theory. This expansion eliminates most of the important nonlinearities associated with density variations. On the basis of this expansion, the validity of perturbation theory can be extended to cover a large variety of atmospheric conditions in which the relative temperature amplitude is less than 0.5 and wind velocities are significantly less than the speed of sound.

Mayr, H. G.↗
NASA NTRS1976

Analyses of the solid earth and ocean tidal perturbations on the orbits of the Geos 1 and Geos 2 satellites

Perturbations in the inclination of the Geos 1 and Geos 2 satellite orbits have been analyzed for the solid earth and ocean tide contributions. Precision reduced camera and Tranet Doppler observations spanning periods of over 600 days for each satellite were used to derive mean orbital elements. Perturbations due to the earth's gravity field, solar radiation pressure, and atmospheric drag were modeled, and the resulting inclination residuals were analyzed for tidal effects. The amplitudes of the observed total tidal effects were about 1.2 arc sec (36 m) in the inclination of Geos 1 and 4.5 arc sec (135 m) for Geos 2. The solid earth tides were then modeled by using the Love number 0.30. The resulting inclination residuals were then analyzed for ocean tide spherical harmonic parameters.

Felsentreger, T. L.↗
NASA NTRS1976

Stabilizing influence of earth perturbations on polar lunar orbiters

A class of highly inclined lunar orbits is discussed for which earth perturbations have significant influence on the orbit evolution and the usefulness of the orbit for scientific exploration. The theory of the long-term motion of particles under third-body and zonal harmonic perturbations is taken as a starting point for investigations of orbits with relatively long lifetimes and evolutionary patterns that enhance the effectiveness of the satellite as a lunar farside relay. An equilibrium solution in the doubly-averaged three-body problem with oblateness is identified and the results of some numerical integrations are presented.

Uphoff, C.↗
NASA NTRS1976

Optimal perturbation models for averaged orbit generation

Averaging techniques applied to the variation of parameters (VOP) formulation of the equations of motion are being investigated as methods for long-term prediction of artificial satellite orbits. Analytically averaged equations were compared with numerically averaged equations with respect to accuracy and efficiency for computation of zonal and nonresonant third-body perturbations. Numerically averaged equations were also evaluated for computation of long-period effects from resonant third-body, tesseral harmonic, and atmospheric drag perturbations. Guidelines will be presented for application of averaged VOP equations to a broad class of orbits.

Long, A. C.↗
NASA NTRS1977

Application of MACSYMA to first order perturbation theory in celestial mechanics

The application of MACSYMA to general first order perturbation theory in celestial mechanics is explored. Methods of derivation of small variations in the Keplerian orbital elements are developed. As an example of the methods, the small general relativistic perturbations on the two-body Newtonian motion, resulting from the rotation of the central body, are developed in detail.

Anderson, J. D.↗
NASA NTRS1976

Elementary derivation of the perturbation equations of celestial mechanics

The equations of celestial mechanics that govern the temporal rates of change of orbital elements are completely derived using elementary dynamics and proceeding only from Newton's equation and its solution. Two orbital equations and the four most meaningful orbital elements - semimajor axis, eccentricity, inclination, and longitude of pericenter - are written in terms of the orbital energy (E) and angular momentum (H) per unit mass. The six resulting equations are differentiated with respect to time to see the effect on the orbital elements of small changes in E and H. The usual perturbation equations in terms of disturbing-force components are then derived by computing the manner in which perturbing forces change E and H. The results are applied in a qualitative discussion of the orbital evolution of particles in nonspherical gravitational fields, through atmospheres, and under the action of tides.

Burns, J. A.↗