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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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Constant-thrust trajectory problem with gravitational acceleration as linear function of radius vector, obtaining minimum fuel solution in integrals
Approximate solution for position and strength of shock waves about cones in steady supersonic flow
A space vehicle in an orbit around a spherical planet is considered. It is proposed to bring the vehicle, by a series of orbital maneuvers, into a final orbit. It is sought to minimize the total characteristic velocity for the maneuver. Since for a high-thrust propulsion system the characteristic velocity provides a direct measure of the fuel consumption, the optimal trajectory considered yields the minimum fuel expenditure. It is assumed that the planet is surrounded by a spherical atmosphere.
Derivation of an exact solution for the problem of line transfer by resonant scattering (assumed coherent in the fluid frame) in a differentially expanding atmosphere. The probabilistic method developed is a generalization of the method of addition of layers plus a decomposition of the radiation field into partial radiation fields due to those photons that scatter exactly n times before escaping (n = 0, 1, 2, 3,
An analysis is presented to compute the film thickness, pressure and load relations between a rigid ball and rigid groove in normal approach when lubricated by a fluid with an exponential pressure-viscosity relationship. The geometry of the ball-groove system is reduced to the equivalent system of a paraboloid approaching a flat plate. Exact and approximate solutions are presented for the load and pressure relations. There is found to be a limiting load for a given geometry and lubricant regardless of the rate of approach.
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The mathematical model considers a large particle (m sub 1), such as a space station, and a smaller particle (m sub 2), connected by an ideal, massless tether, i.e., one incapable of sustaining other than tensile loads. The problem situation described offers a practical solution which should be quite useful in certain space flight operations, especially for the transfer of cargo and personnel and for retrieval and rescue operations. The idea is simple in its application and does not appear to require sophisticated hardware. An appealing advantage is that it is infinitely reusable, i.e., it could be rewound and used over and over again.
The general solution for the optimum three-dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere is developed. A set of dimensionless variables, modified Chapman variables, is introduced. The resulting exact equations of motion, referred to as Chapman's exact equations, have the advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a completely general lift-drag relationship is used in the derivation. The results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary drag polar, and entering any planetary atmosphere. The aerodynamic controls chosen are the lift coefficient and the bank angle. General optimum control laws for these controls are developed. Several earlier particular solutions are shown to be special cases of this general result. Results are valid for both free and constrained terminal position.
This paper presents the general solution for the optimal three dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere. A set of dimensionless variables is introduced, and the resulting exact equations of motion have the distinctive advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a general lift-drag polar is used to define the aerodynamic control. Hence, the results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary polar and entering any planetary atmosphere.
A general technique for solving a system of rate equations describing the interaction of an electromagnetic field and a molecular system is presented. The method is used to obtain approximate time-dependent solutions for the upper-level population of fluorescent dyes in the presence of a pump field.
A general technique for solving a system of rate equations describing the interaction of an electromagnetic field and a molecular system is presented. The method is used to obtain approximate time-dependent solutions for the upper-level populations of fluorescent dyes in the presence of a pump field.
The two body problem was analyzed with a specific drag model. The model treats drag as a force proportional to the vector velocity and inversely proportional to the distance to the center of attraction. The solution is expressed in terms of known functions and is of a simple and compact form. The time of flight is expressed as a quadrature in the true anomaly. The results are: (1) development of a vector differential equation which allows analysis of an infinite number of gravitational and drag models; and (2) obtaining the solution of a linear differential equation using the inverse method of laplace transforms.
In connection with the normal process of control system design, the determination of the state trajectories for the controlled system is frequently required. The procedure involved in the determination is straightforward. However, extensive computations may be needed, if either time-varying control gains are used, or if small integration step sizes are required by the presence of high-frequency system dynamics. The present investigation is concerned with an approach for overcoming the computational difficulties, taking into account a change of variables for the close-loop system dynamics equation. This procedure makes it possible to obtain a closed-form expression for the state trajectories.
Various features of the solutions of Duffing's equation are described using a representation of the solutions in the Laplace-Borel transform domain. An application of this technique is illustrated for the symmetry-breaking bifurcation of a hard spring.
The diffraction problem associated with a multilayer material slab recessed in a perfectly conducting ground plane is formulated and solved via the Generalized Scattering Matrix Formulation (GSMF) in conjunction with the dual integral equation approach. The multilayer slab is replaced by a surface obeying a generalized impedance boundary condition (GIBC) to facilitate the computation of the pertinent Wiener Hopf split functions and their zeros. Both E(sub z) and H(sub z) polarizations are considered and a number of scattering patterns are presented, some of which are compared to exact results available for a homogeneous recessed slab.
A continuous fiber composite is modelled by a two-element composite cylinder in order to predict the elastoplastic response of the composite under a monotonically increasing tensile loading parallel to fibers. The fibers and matrix are assumed to be elastic-perfectly plastic materials obeying Hill's and Tresca's yield criteria, respectively. Here, the composite behavior when the fibers yield prior to the matrix is investigated.
Rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristics to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.
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