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Results for “approximation theory”

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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NASA NTRS1977

Approximate theory of large-amplitude wave propagation

An orbit perturbation procedure is applied to the description of monochromatic, large-amplitude, electrostatic plasma wave propagation. In the lowest-order approximation, untrapped electrons are assumed to follow constant-velocity orbits and trapped electrons are assumed to execute simple harmonic motion. The deviations of these orbits from the actual orbits are regarded as perturbations. The nonlinear damping rate and frequency shift are then obtained in terms of simple functions. The results are in good agreement with previous less approximate analyses. A significant feature of the analysis is that it treats a single wave by techniques previously applied to turbulent spectra. The analysis can consequently be extended to the case of a large-amplitude wave interacting with a lower-amplitude spectrum of waves.

Kim, H.↗
NASA NTRS1976

Scintillations during occultations by planets. I - An approximate theory

Fluctuations are observed during occultations of both stars and spacecraft by planetary atmospheres. Existing treatments of spacecraft scintillations ignore a major effect unique to occultations: the severe flattening of the Fresnel zone or source image by defocusing. Other large effects, due to 'saturation' of the scintillation, have also been ignored. The deeper portions of atmospheric temperature and density profiles inferred from occultation data are seriously in error if other planets' atmospheres are as turbulent as our own. Thus, profiles obtained from entry probes (e.g., the Soviet Venera series) are probably more accurate than those from radio occultation (Mariner 5 and 10) data. Scintillation greatly reduces the information obtainable from occultation observations; much of the detail attributed to layering in published profiles is probably due to aliasing of turbulence. This paper gives an approximately correct theoretical treatment that is a substantial improvement over published theories, and shows how a more accurate theory could be constructed. Some methods for a more accurate determination of atmospheric structure are proposed.

Young, A. T.↗
NASA NTRS1971

An approximate theory of imperfect modeling with application to thermal modeling of spacecraft.

Proposal of a new concept of model testing which makes use of imperfect models and is based on the heuristic argument of representing the error states in a multidimensional Euclidean space when the errors in the modeling parameter are sufficiently small. By a separation of these errors into positive and negative groups, and from a consideration of the error paths in the hyperspaces, it is shown that the global effect of these errors may be evaluated with a good degree of approximation. Conditions under which the procedure would yield satisfactory results are discussed. To test the usefulness of the theory a computer experiment was conducted for the prediction of both transient and steady state thermal behavior of a hypothetical spacecraft using perfect, as well as imperfect, models.

Chao, B. T.↗
NASA NTRS1975

Scintillations during occultations by planets. 1. An approximate theory

Scintillations observed during occultations of both stars and spacecraft by planetary atmospheres are discussed theoretically. The effects of severe flattening of the Fresnel zone or source image by defocusing on occultations are presented, along with temporal power spectra. Other topics discussed include atmospheric turbulence, saturation of scintillation, effects of saturation on occultation curves, and some methods for a more accurate determination of atmospheric structure.

Young, A. T.↗
NASA NTRS1974

Analysis of laminated, composite, circular cylindrical shells with general boundary conditions

This report develops: (1) a refined approximate theory for the static and dynamic analyses of finite, laminated, composite, circular cylindrical shells with general boundary conditions; (2) an exact three-dimensional analysis of simply supported, laminated, composite, circular cylindrical shells, and (3) a thin-shell theory for laminated, composite, circular cylindrical shells. In the refined approximate theory the displacements are assumed piecewise linear across the thickness and the effects of transverse shear deformations and transverse normal stress are included. A variational approach is followed to obtain the governing differential equations and boundary conditions. A general solution of the governing differential equations is also presented. The results obtained by using the refined approximate theory and the thin-shell theory are compared with the exact results for the case of free vibrations of simply supported, laminated, composite, circular cylindrical shells. The refined approximate theory is very accurate, even for thick shells with short nodal distances, whereas thin-shell theory is reasonably accurate only for thin shells at moderate nodal distances and wave number less than 2.

Srinivas, S.↗