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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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Hopf analytical solution for values of ratio of gray absorption coefficients for insolating and escaping radiation /greenhouse parameter/ assumed constant at all depths, presenting temperature distribution graphs
Analytic solution for ignition kinetics of dry carbon monoxide-oxygen reaction obtained, assuming initiation reaction followed by chain-branching steps
Analytical solution for motion of lunar orbital satellite
This study is concerned with the analytical solutions of natural convection flows in closed-end cylindrical vessels to obtain exact solutions of temperature and velocity distribution in the laminar flow region under steady state condition. The temperature and velocity distributions, in general power series of displacements, are substituted into the three basic equations of continuity, momentum and energy. The relationships between coefficients of all powers are obtained through initial and boundary conditions and recurrence formulae. For constant wall temperature conditions the general solution of temperature and velocity may be expressed as a function of displacement, geometry ratio and Rayleigh number. Prandtl number does not enter as an independent parameter.
Analytic solution obtained for minimum impulse transfer between two neighboring low eccentricity orbits
Modern turbulence theory and applications to obtain analytical solutions to turbulent transport problems
Analytical solution for inviscid separated jet injection at oblique angle into moving stream
Boundary value problem for elliptic-parabolic partial differential equations in theory of random processes, obtaining analytical solution in terms of hypergeometric functions
Flow field pressure distribution due to plane shock wave impinging by thin wing moving in opposite direction, discussing mathematical formulation, analytic solution and applications
Optimal transfer between hyperbolic asymptotes about finite size planet, discussing twelve types of analytical solutions in terms of arrival, departure and escape velocities
General, closed-form, analytical solutions are determined for certain classes of C-minimax control problems, several alternative mathematical theories are derived, and a controller design theory is developed to give optimal control in the presence of unmeasureable external disturbances.
Approximate analytical solution for minimum impulse transfer between circular orbit and given hyperbolic velocity vector at infinity
Nonlinear system under random excitation, discussing analytic solution method and statistical properties
Comparison of finite element and analytic solutions of normal uniform beam modes under various end conditions
Compact analytic solution to distribution theory of nonsteady state model illustrated with biological data - age dependency in compartmental analysis
Integral transform methods for analytic solutions to current and potential distribution on disk in infinite plane for four limiting cases
For shallow lakes and seas such as the great lakes (especially Lake Erie) where the depth is not much greater than the Ekman depth, the usual Ekman dynamics cannot be used to predict the wind driven currents. The necessary extension to include shallow bodies of water, given by Welander, leads to a partial differential equation for the surface displacement which in turn determines all other flow quantities. A technique for obtaining exact analytical solutions to Welander's equation for bodies of water with large class of bottom topographies which may or may not contain islands is given. It involves applying conformal mapping methods to an extension of Welander's equation into the complex plane. When the wind stress is constant (which is the usual assumption for lakes) the method leads to general solutions which hold for bodies of water of arbitrary shape (the shape appears in the solutions through a set of constants which are the coefficients in the Laurent expansion of a mapping of the particular lake geometry). The method is applied to an elliptically shaped lake and a circular lake containing an eccentrically located circular island.
In the special perturbation method, Cowell and variation-of-parameters formulations of the motion equations are implemented and numerically integrated. Variations in the orbital elements due to drag are computed using the 1970 Jacchia atmospheric density model, which includes the effects of semiannual variations, diurnal bulge, solar activity, and geomagnetic activity. In the general perturbation method, two-variable asymptotic series and automated manipulation capabilities are used to obtain analytical solutions to the variation-of-parameters equations. Solutions are obtained considering the effect of oblateness only and the combined effects of oblateness and drag. These solutions are then numerically evaluated by means of a FORTRAN program in which an updating scheme is used to maintain accurate epoch values of the elements. The atmospheric density function is approximated by a Fourier series in true anomaly, and the 1970 Jacchia model is used to periodically update the Fourier coefficients. The accuracy of both methods is demonstrated by comparing computed orbital elements to actual elements over time spans of up to 8 days for the special perturbation method and up to 356 days for the general perturbation method.