Minimum impulse transfers in the near vicinity of a circular orbit.
Analytic solution obtained for minimum impulse transfer between two neighboring low eccentricity orbits
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Results for “analytical solution”
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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The use of modern turbulence theory for calculating eddy diffusivities
Modern turbulence theory and applications to obtain analytical solutions to turbulent transport problems
Hill, J. C.↗
Injection of an inviscid separated jet at an oblique angle to a moving stream
Analytical solution for inviscid separated jet injection at oblique angle into moving stream
Braun, W.↗
Numerical analysis of an elliptic-parabolic partial differential equation.
Boundary value problem for elliptic-parabolic partial differential equations in theory of random processes, obtaining analytical solution in terms of hypergeometric functions
Franklin, J. N.↗
Diffraction of shock wave by moving thin wing.
Flow field pressure distribution due to plane shock wave impinging by thin wing moving in opposite direction, discussing mathematical formulation, analytic solution and applications
Gunzburger, M.↗
Optimum transfer between hyperbolic asymptotes about a planet of finite size.
Optimal transfer between hyperbolic asymptotes about finite size planet, discussing twelve types of analytical solutions in terms of arrival, departure and escape velocities
Culp, R. D.↗
Chebyshev minimax control theory
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.
Johnson, C. D.↗
Minimum impulse transfer from circular orbits Quarterly progress report
Approximate analytical solution for minimum impulse transfer between circular orbit and given hyperbolic velocity vector at infinity
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Statistical properties of nonlinear systems subject to random excitation.
Nonlinear system under random excitation, discussing analytic solution method and statistical properties
Hu, P. Y.↗
Finite element modeling studies in the normal mode method and normal mode synthesis
Comparison of finite element and analytic solutions of normal uniform beam modes under various end conditions
Courtney, R. L.↗
An example of age dependency in compartmental analysis
Compact analytic solution to distribution theory of nonsteady state model illustrated with biological data - age dependency in compartmental analysis
Matis, J. H.↗
Engineering applications of current and potential distributions in disk electrode systems
Integral transform methods for analytic solutions to current and potential distribution on disk in infinite plane for four limiting cases
Kesselman, W.↗
Wind-driven currents in a shallow lake or sea
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.
Goldstein, M. E.↗
Techniques of orbital decay and long-term ephemeris prediction for satellites in earth orbit
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.
Barry, B. F.↗
The equilibrium and stability of the gaseous component of the galaxy, 3
The stability of a self-gravitating, nonrotating, isothermal gas layer threaded by a one-dimensional equipartition magnetic field, immersed in a rigid isothermal layer of stars, is considered with respect to waves with motions in and perpendicular to the X plane, where X is the equilibrium magnetic and gravitational field vectors. When motions are perpendicular to the X plane, the magnetic field hinders gravitational instability, increasing the minimum length necessary to produce instability by the factor (1 + alpha) to the 1/2 power, where alpha is the ratio of magnetic pressure to gas pressure. When motions are in the plane, no such simple analytical solution is found. However, the resulting system of equations reduces to a single fourth order differential equation in the perturbed gas potential that defines an eigenvalue problem for the marginally unstable state when the four appropriate boundary conditions are considered.
Kellman, S. A.↗
Parameter identification using a creeping-random-search algorithm
A creeping-random-search algorithm is applied to different types of problems in the field of parameter identification. The studies are intended to demonstrate that a random-search algorithm can be applied successfully to these various problems, which often cannot be handled by conventional deterministic methods, and, also, to introduce methods that speed convergence to an extremal of the problem under investigation. Six two-parameter identification problems with analytic solutions are solved, and two application problems are discussed in some detail. Results of the study show that a modified version of the basic creeping-random-search algorithm chosen does speed convergence in comparison with the unmodified version. The results also show that the algorithm can successfully solve problems that contain limits on state or control variables, inequality constraints (both independent and dependent, and linear and nonlinear), or stochastic models.
Parrish, R. V.↗
Investigation of flaw geometry and loading effects on plane strain fracture in metallic structures
The effects on fracture and flaw growth of weld-induced residual stresses, combined bending and tension stresses, and stress fields adjacent to circular holes in 2219-T87 aluminum and 5AI-2.5Sn(ELI) titanium alloys were evaluated. Static fracture tests were conducted in liquid nitrogen; fatigue tests were performed in room air, liquid nitrogen, and liquid hydrogen. Evaluation of results was based on linear elastic fracture mechanics concepts and was directed to improving existing methods of estimating minimum fracture strength and fatigue lives for pressurized structure in spacecraft and booster systems. Effects of specimen design in plane-strain fracture toughness testing were investigated. Four different specimen types were tested in room air, liquid nitrogen and liquid hydrogen environments using the aluminum and titanium alloys. Interferometry and holograph were used to measure crack-opening displacements in surface-flawed plexiglass test specimens. Comparisons were made between stress intensities calculated using displacement measurements, and approximate analytical solutions.
Hall, L. R.↗
Polymer degradation rate control of hybrid rocket combustion
Polymer degradation to small fragments is treated as a rate controlling step in hybrid rocket combustion. Both numerical and approximate analytical solutions of the complete energy and polymer chain bond conservation equations for the condensed phase are obtained. Comparison with inert atmosphere data is very good. It is found that the intersect of curves of pyrolysis rate versus interface temperature for hybrid combustors, with the thermal degradation theory, falls at a pyrolysis rate very close to that for which a pressure dependence begins to be observable. Since simple thermal degradation cannot give sufficient depolymerization at higher pyrolysis rates, it is suggested that oxidative catalysis of the process occurs at the surface, giving a first order dependence on reactive species concentration at the wall. Estimates of the ratio of this activation energy and interface temperature are in agreement with best fit procedures for hybrid combustion data. Requisite active species concentrations and flux are shown to be compatible with turbulent transport. Pressure dependence of hybrid rocket fuel regression rate is thus shown to be describable in a consistent manner in terms of reactive species catalysis of polymer degradation.
Stickler, D. B.↗