Asymptotics for formula manipulation
Presenting proposals for implementation of subprogram for computing and manipulating asymptotic expansions
Halton, J. H.↗
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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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Adaptive stochastic control for linear systems. Part 2 - Asymptotic properties and simulation results
Asymptotic properties and simulation of adaptive stochastic control for linear systems
Athans, M.↗
Asymptotic source-function expansions for resonance lines formed in a semi-infinite medium
Abel-Tauber theorems predicting asymptotic behavior of source functions for resonance lines formed by frequency redistribution in semiinfinite atmosphere
Warming, R. F.↗
An explicit midcourse guidance technique for lunar and interplanetary trajectories based upon matched asymptotic expansions
Spacecraft midcourse guidance technique for lunar and interplanetary trajectories based on matched asymptotic expansions
Carlson, N. A.↗
Minimum delta-V, three-impulse, non-coplanar transfer from a circular parking orbit onto an asymptotic velocity vector for small declination angles - An approach to the trans-Mars launch window problem
Trans-Mars launch window problem, discussing minimum delta-V three-impulse noncoplanar transfer from circular parking orbit onto asymptotic velocity vector
Bean, W. C.↗
Asymptotic formulas for the buckling stresses of axially compressed cylinders with localized or random axisymmetric imperfections
Buckling of axially compressed circular cylindrical shells with localized or random axisymmetric imperfections, deriving asymptotic approximation formulas for stress calculation
Amazigo, J. C.↗
On the uniform asymptotic stability of functional differential equations of the neutral type
Linear neutral differential equation uniform asymptotic stability relation to perturbed differential equation containing bounded linear operators
Hale, J. K.↗
Asymptotic giant and red giant branch stars in globular clusters
Spectrophotometric observations of asymptotic giant and red giant branch stars in metal weak globular clusters
Strom, K. M.↗
Asymptotic theory of a slender rotating beam with end masses.
The method of matched asymptotic expansions is employed to solve the singular perturbation problem of the vibrations of a rotating beam of small flexural rigidity with concentrated end masses. The problem is complicated by the appearance of the eigenvalue in the boundary conditions. Eigenfunctions and eigenvalues are developed as power series in the perturbation parameter beta to the 1/2 power, and results are given for mode shapes and eigenvalues through terms of the order of beta.
Whitman, A. M.↗
The large Reynolds number - Asymptotic theory of turbulent boundary layers.
A self-consistent, asymptotic expansion of the one-point, mean turbulent equations of motion is obtained. Results such as the velocity defect law and the law of the wall evolve in a relatively rigorous manner, and a systematic ordering of the mean velocity boundary layer equations and their interaction with the main stream flow are obtained. The analysis is extended to the turbulent energy equation and to a treatment of the small scale equilibrium range of Kolmogoroff; in velocity correlation space the two-thirds power law is obtained. Thus, the two well-known 'laws' of turbulent flow are imbedded in an analysis which provides a great deal of other information.
Mellor, G. L.↗
Use of multivariable asymptotic expansions in a satellite theory
Initial conditions and perturbative force of satellite are restricted to yield motion of equatorial satellite about oblate body. In this manner, exact analytic solution exists and can be used as standard of comparison in numerical accuracy comparisons. Detailed numerical accuracy studies of uniformly valid asymptotic expansions were made.
Dallas, S. S.↗
Asymptotic expansion of an impulse for an optimal finite burn
Closed form expressions are derived for the position and velocity of a spacecraft during a finite burn using the method involving the theory of asymptotic expansion of the optimal impulsive solution. The small parameter is given by the reciprocal of the mass flow rate. The expansion is given in terms of the impulsive solution and holds up through third-order for the velocity and fourth-order for the position.
Pines, S.↗
Asymptotic solution of the problem for a thin axisymmetric cavern
The boundary value problem which describes the axisymmetric separation of the flow around a body by a stationary infinite stream is considered. It is understood that the cavitation number varies over the length of the cavern. Using the asymptotic expansions for the potential of a thin body, the orders of magnitude of terms in the equations of the problem are estimated. Neglecting small quantities, a simplified boundary value problem is obtained.
Serebriakov, V. V.↗
Asymptotic solution to the tangential low thrust energy increase trajectory
A approximate analytic solution to the low thrust constant acceleration energy increase trajectory using a tangential steering program is presented. The solution is based on a two-variable asymptotic expansion of the equations of motion formulated in regularized variables. The high accuracy of the second order solution derived is demonstrated by comparing it with numerically integrated trajectories.
Schwenzfeger, K. J.↗
On numerical methods to impose asymptotic boundary conditions of boundary-layer equations
The error minimization method proposed by Nachtsheim and Swigert (1965) to satisfy the asymptotic boundary conditions of boundary layer equations is proved to be equivalent to imposing the condition of fastest decay. As a consequence, a uniqueness problem is not arising in the solutions of boundary layer equations obtained by their method.
Liu, T. M.↗
Asymptotic solution for solar electric low thrust orbit raising with eclipse penalty
This paper describes an analytic solution for the solar electric low thrust orbit raising problem derived by application of the two-variable asymptotic expansion method. Included in the formulation are the effects of (1) high initial eccentricity, (2) large change of inclination, (3) variable mass, and (4) earth shadow penalty including the rotation of the shadow axis relative to the osculating orbit. An advantage of this mathematical strategy is that the effects of various steering policies can be evaluated readily from a physical point of view.
Flandro, G. A.↗
Asymptotic analytical methods in fluid mechanics related to drag prediction
Some recent theoretical work of a purely analytical nature is described which promises to provide engineering predictions for the important drag-related phenomena of flow in the stall regime. This analytical work deals with rigorous asymptotic studies of the complete Navier-Stokes equations that govern the viscous flow around any aerodynamic body under conditions where boundary layer separation takes place from the body surface.
Inger, G. R.↗
Time-asymptotic solutions of the Navier-Stokes equation for free shear flows using an alternating-direction implicit method
An uncoupled time asymptotic alternating direction implicit method for solving the Navier-Stokes equations was tested on two laminar parallel mixing flows. A constant total temperature was assumed in order to eliminate the need to solve the full energy equation; consequently, static temperature was evaluated by using algebraic relationship. For the mixing of two supersonic streams at a Reynolds number of 1,000, convergent solutions were obtained for a time step 5 times the maximum allowable size for an explicit method. The solution diverged for a time step 10 times the explicit limit. Improved convergence was obtained when upwind differencing was used for convective terms. Larger time steps were not possible with either upwind differencing or the diagonally dominant scheme. Artificial viscosity was added to the continuity equation in order to eliminate divergence for the mixing of a subsonic stream with a supersonic stream at a Reynolds number of 1,000.
Rudy, D. H.↗