Optimal low-thrust takeoff from an orbit about an oblate planet
Low thrust vehicle optimal takeoff calculations from orbit about oblate planet, using two variable asymptotic expansion technique
Jacobson, R. A.↗
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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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Design of a laser rangefinder for Martian terrain measurements
Three methods for using a laser for rangefinding are discussed: optical focusing, the phase difference method, and timed pulse. For application on a Mars Rover, the timed pulse method proves to be the better choice in view of the requirements set down. This is made possible by pulse expansion techniques described in detail. Initial steps taken toward building the range finder are given, followed by a conclusion.
Palumbo, D. L.↗
Quasi-linear theory via the cumulant expansion approach
The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate.
Jones, F. C.↗
Extension of Case's method to the two-region critical cylinder and its application as an analytic standard
The normal mode expansion technique is applied to the transformed monoenergetic integral transport equation to develop a solution for the rotationally invariant and axially infinite, critical, two-region cylinder with a finite outer reflector boundary. Isotropic scattering and identical neutron mean free paths in the core and reflector regions are assumed. The solution in terms of singular integral equations is obtained by applying a completeness theorem found for the singular eigenfunctions. Numerical results for a variety of core and reflector multiplying properties and reflector thickness are presented and compared with the results of other method. An example of this type of application is given in a study of approximations inherent in the neutronic design analysis of a small, fast-neutron-spectrum reactor concept proposed as a space power source.
Westfall, R. M.↗
Design of a laser rangefinder for Martian terrain measurements
Methods for using a laser for rangefinding are discussed. These are: (1) Optical Focusing, (2) the Phase Difference Method, and (3) Timed Pulse. For application on a Mars Rover, the Timed Pulse Method proves to be the better choice in view of the requirements set down. This is made possible by pulse expansion techniques described in detail. Initial steps taken toward building the range finder are given, followed by a conclusion which is actually a proposal for future steps.
Palumbo, D. L.↗
When is quasi-linear theory exact
We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.
Jones, F. C.↗
Boundary-layer theory for blast waves
It is profitable to consider the blast wave as a flow field consisting of two regions: the outer, which retains the properties of the inviscid solution, and the inner, which is governed by flow equations including terms expressing the effects of heat transfer and, concomitantly, viscosity. The latter region thus plays the role of a boundary layer. Reported here is an analytical method developed for the study of such layers, based on the matched asymptotic expansion technique combined with patched solutions.
Kim, K. B.↗
Microwave remote sensing of a two-layer random medium
A two-variable expansion technique is used to solve for the mean Green's. function from the Dyson equation under the nonlinear approximation. The Bethe-Salpeter equation then gives rise to a set of modified radiative transfer (MRT) equations which accommodate coherent effects essential to bounded media. It is found that the nonlinear approximation, instead of the more popular bilocal approximation, should be used for the case of bounded media. The two approximations yield identical results for unbounded media. The MRT equations are then solved for a two-layer random medium. The MRT equations give rise to simple and useful solutions which are applicable to both active and passive microwave remote sensing.
Tsang, L.↗
Optimal low-thrust takeoff from an orbit about an oblate planet
Future space missions to the outer planets may depend upon the use of low-thrust propulsion systems. As these planets are decidedly oblate, the question of the effect of that oblateness on a low-thrust trajectory is of some interest. In this paper the problem of optimal energy increase is attacked under the assumption that the coefficients for the second zonal harmonic, and the nondimensional thrust acceleration are the same order of magnitude. By means of a two-variable asymptotic expansion technique, a near optimal control program is generated and the first-order uniformly valid approximation for the corresponding trajectory is obtained. Tangential thrust is shown to be a good near-optimal thrust program even in the presence of oblateness effects. The optimal control program is found to be oscillatory and quite similar to the optimal control for energy increase in an inverse square gravitational field.
Jacobson, R. A.↗
The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.
Haidvogel, D. B.↗
On the efficient computation of Fraunhofer and Fresnel region fields radiated by reflector and planar-aperture antennas
Computation of fields radiated by parabolic reflectors and planar apertures is a problem of prime importance, and conventional approaches to performing these computations are often very time-consuming. The paper demonstrates the usefulness of a series expansion technique for efficient computation of radiated fields in both the Fraunhofer and Fresnel regions. The series approach is based on the use of the Jacobi polynomials. The application of the series method to determining the far-field pattern of the antenna from the near-field measurements for an arbitrary aperture antenna is also discussed.
Mittra, R.↗
Wave theory for microwave remote sensing of a half-space random medium with three-dimensional variations
The two-variable expansion technique is used to solve for the mean Green's functions from the Dyson equation under the nonlinear approximation for a half-space random medium with three-dimensional correlation functions. The Bethe-Salpeter equations are then solved under the ladder approximation. The radiative transfer equations, which have been applied extensively in the study of microwave remote sensing problems, are derived under these approximations. The limiting cases of large and small horizontal correlation lengths are discussed. It is found that there is only one propagation constant except for the case of large horizontal correlation lengths, in which there are two propagation constants. It is shown that boundary layer appears in first-order solutions and does not appear in zeroth-order solutions.
Tsang, L.↗
Development of ultraviolet rigidizable materials
A series of tests was performed to determine an optimum resin to be used as a UV rigidizable matrix in expandable rigidizable space structures. Commercially available resins including several types of polyesters, epoxies, epoxy-acrylics, an acrylic and a urethane were used as well as a polyester, produced by 3M Company's Solar Laboratory facility, which was found the best from the standpoint of physical properties and ability to be 'B' staged. Two other synthesized materials were also tested, but were not found to be superior to the Solar resin. An optimum fabric for use with the preferred resin was not found; however, the 15 ounce fabric from Solar Laboratories has the best combination of physical properties with respect to handling and processing characteristics. Expansion techniques for tubular structures, 'B' staging of the solar resin, and stowage techniques for up to 5 months were developed. A one meter high tetrahedron preprototype structure was prepared to evaluate and demonstrate stowage, deployment, and rigidization techniques.
Salisbury, D. P.↗
Boundary layer thermal stresses in angle-ply composite laminates, part 1
Thermal boundary-layer stresses (near free edges) and displacements were determined by a an eigenfunction expansion technique and the establishment of an appropriate particular solution. Current solutions in the region away from the singular domain (free edge) are found to be excellent agreement with existing approximate numerical results. As the edge is approached, the singular term controls the near field behavior of the boundary layer. Results are presented for cases of various angle-ply graphite/epoxy laminates with (theta/-theta/theta/theta) configurations. These results show high interlaminar (through-the-thickness) stresses. Thermal boundary-layer thicknesses of different composite systems are determined by examining the strain energy density distribution in composites. It is shown that the boundary-layer thickness depends on the degree of anisotropy of each individual lamina, thermomechanical properties of each ply, and the relative thickness of adjacent layers. The interlaminar thermal stresses are compressive with increasing temperature. The corresponding residual stresses are tensile and may enhance interply delaminations.
Wang, S. S.↗
Numerical Simulation of Turbulent Fluid Flows
Numerical simulation of turbulent flows is discussed. Computational requirements for the direct simulaton of turbulence, simulation of arbitrary homogeneous flows, an expansion technique for wall bounded flows with application to pipe flow, and possibilities of flow representations or modeling techniques that allow the simulation of high Reynolds number flows with a relatively small number of dependent variables are included.
Leonard, A.↗
Extinction of premixed flames by stretch and radiative loss
The extinction of laminar premixed flames by stretch and radiative loss is studied for the model problem of counterflow opposed-jet combustion by using the matched asymptotic expansion technique for the highly temperature sensitive processes of radiative heat loss and large-activation-energy reaction kinetics. Explicit expressions for the critical Damkoehler number at extinction are derived and the influence of upstream vs downstream heat losses assessed. Results show that stretch exerts a much stronger influence than radiative loss on flame extinction.
Sohrab, S. H.↗
Circularly polarized conical patterns from circular microstrip antennas
A method is presented for generating circularly polarized conical patterns from circular microstrip antennas. These antennas are excited at higher order modes and require different feed arrangements for different mode excitations. It is determined that the peak direction of the conical pattern can be varied over a wide angular range. Modal expansion technique is employed to calculate the radiation patterns of these antennas.
Huang, J.↗
The response of Helmholtz resonators to external excitation. I - Single resonators
The response of single two- and three-dimensional Helmholtz resonators subject to external excitation by a plane acoustic wave is studied. The inviscid linearized problem is solved by the matched-asymptotic-expansion technique in the low-frequency limit, i.e. when the characteristic neck dimension is small compared with the acoustic wavelength. The scale of the cavity is chosen such as to tune the system to the lowest Helmholtz mode. The results are compared with the classical lumped-element model, and refined expressions are derived for the effective mass (added length) and stiffness (effective cavity volume) of the resonator.
Monkewitz, P. A.↗