RENDEZVOUS POSSIBILITIES WITH THE IMPULSE OF OPTIMUM TWOIMPULSE TRANSFER
Two-impulse orbital transfer problem for elliptical orbits, describing techniques for finding optimum transfers and optimum rendezvous trajectories
IMPULSE ORBITAL TRANSFER↗
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Periodic orbits in the elliptic restricted three-body problem Technical report, 1 Jul. 1967 - 30 Jun. 1968
Periodic orbits in restricted three body problem
Broucke, R. A.↗
A Universal Solution of Lambert's Problem
Universal solution of Lambert problem for elliptic, parbolic, and hyperbolic motion
Estes, R. H.↗
Computer discrimination procedures applicable to aerial and ERTS multispectral data
Two statistical models are compared in the classification of crops recorded on color aerial photographs. A theory of error ellipses is applied to the pattern recognition problem. An elliptical boundary condition classification model (EBC), useful for recognition of candidate patterns, evolves out of error ellipse theory. The EBC model is compared with the minimum distance to the mean (MDM) classification model in terms of pattern recognition ability. The pattern recognition results of both models are interpreted graphically using scatter diagrams to represent measurement space. Measurement space, for this report, is determined by optical density measurements collected from Kodak Ektachrome Infrared Aero Film 8443 (EIR). The EBC model is shown to be a significant improvement over the MDM model.
Richardson, A. J.↗
Computer identification of ground pattern from aerial photographs.
Two statistical models are comapared in the classification of crops recorded on color aerial photographs. A theory of error ellipses is applied to the pattern recognition problem. An elliptical boundary condition classification model (EBC), useful for recognition of candidate patterns, evolves out of error ellipse theory. The EBC model is compared with the minimum distance to the mean (MDM) classification model in terms of pattern recognition ability. The pattern recognition results of both models are interpreted graphically using scatter diagrams to represent measurement space. Measurement space, for this report, is determined by optical density measurements collected from Kodak Ektachrome Infrared Aero Film 8443 (EIR). The EBC model is shown to be a significant improvement over the MDM model.
Richardson, A. J.↗
A technique for accelerating iterative convergence in numerical integration, with application in transonic aerodynamics
A technique is described for the efficient numerical solution of nonlinear partial differential equations by rapid iteration. In particular, a special approach is described for applying the Aitken acceleration formula (a simple Pade approximant) for accelerating the iterative convergence. The method finds the most appropriate successive approximations, which are in a most nearly geometric sequence, for use in the Aitken formula. Simple examples are given to illustrate the use of the method. The method is then applied to the mixed elliptic-hyperbolic problem of steady, inviscid, transonic flow over an airfoil in a subsonic free stream.
Martin, E. D.↗
A technique for accelerating iterative convergence in numerical integration, with application in transonic aerodynamics
A technique is described for the efficient numerical solution of nonlinear partial differential equations by rapid iteration. In particular, a special approach is described for applying the Aitken acceleration formula (a simple Pade approximant) for accelerating the iterative convergence. The method finds the most appropriate successive approximations, which are in a most nearly geometric sequence, for use in the Aitken formula. Simple examples are given to illustrate the use of the method. The method is then applied to the mixed elliptic-hyperbolic problem of steady, inviscid, transonic flow over an airfoil in a subsonic free stream.
Martin, E. D.↗
Fast methods incorporating direct elliptic solvers for nonlinear applications in fluid dynamics
Semidirect methods are discussed, their present role, as well as some developments for their application in computational fluid dynamics. A semidirect method is a computational scheme that uses a fast, direct, elliptic solver as the driving algorithm for the iterative solution of finite difference equations. Specific subtopics include: (1) direct Cauchy Riemann solvers for first order elliptic equations; (2) application of the semidirect method to the mixed elliptic hyperbolic problem of steady, inviscid transonic flow; and (3) the treatment of interior conditions, such as those on an airfoil or wing, in semidirect methods.
Martin, E. D.↗
Artificial compressibility methods for numerical solutions of transonic full potential equation
New methods for transonic flow computations based on the full potential equation in conservation form are presented. The idea is to modify slightly the density (due to the artificial viscosity in the supersonic region), and solve the resulting elliptic-like problem iteratively. It is shown that standard discretization techniques (central differencing) as well as some standard iterative procedures (SOR, ADI, and explicit methods) are applicable to the modified transonic mixed-type equation. Calculations of transonic flows around cylinders and airfoils are discussed with special emphasis on the explicit methods that are suitable for vector processing on the STAR 100 computer.
Hafez, M.↗
A direct algorithm for solution of incompressible three-dimensional unsteady Navier-Stokes equations
A direct, implicit, numerical solution algorithm, with second-order accuracy in space and time, is constructed for the three-dimensional unsteady incompressible Navier-Stokes equations formulated in terms of velocity and vorticity, using generalized orthogonal coordinates to achieve the accurate solution of complex viscous flow configurations. A numerically stable, efficient, direct inversion procedure is developed for the computationally intensive divergence-curl elliptic velocity problem. This overdetermined partial differential operator is first formulated as a uniquely determined, nonsingular matrix-vector problem; this aspect of the procedure is a unique feature of the present analysis. The three-dimensional vorticity-transport equation is solved by a modified factorization technique which completely eliminates the need for any block-matrix inversions and only scalar tridiagonal matrices need to be inverted. The method is applied to the test problem of the three-dimensional flow within a shear-driven cubical box. Coherent streamwise vortex structures are observed within the steady-state flow at Re = 100.
Osswald, G. A.↗
A user guide for the EMTAC-MZ CFD code
The computer code (EMTAC-MZ) was applied to investigate the flow field over a variety of very complex three-dimensional (3-D) configurations across the Mach number range (subsonic, transonic, supersonic, and hypersonic flow). In the code, a finite volume, multizone implementation of high accuracy, total variation diminishing (TVD) formulation (based on Roe's scheme) is used to solve the unsteady Euler equations. In the supersonic regions of the flow, an infinitely large time step and a space-marching scheme is employed. A finite time step and a relaxation or 3-D approximate factorization method is used in subsonic flow regions. The multizone technique allows very complicated configurations to be modeled without geometry modifications, and can easily handle combined internal and external flow problems. An elliptic grid generation package is built into the EMTAC-MZ code. To generate the computational grid, only the surface geometry data are required. Results obtained for a variety of configurations, such as fighter-like configurations (F-14, AVSTOL), flow through inlet, multi-bodies (shuttle with external tank and SRBs), are reported and shown to be in good agreement with available experimental data.
Szema, Kuo-Yen↗
Domain decomposition: A bridge between nature and parallel computers
Domain decomposition is an intuitive organizing principle for a partial differential equation (PDE) computation, both physically and architecturally. However, its significance extends beyond the readily apparent issues of geometry and discretization, on one hand, and of modular software and distributed hardware, on the other. Engineering and computer science aspects are bridged by an old but recently enriched mathematical theory that offers the subject not only unity, but also tools for analysis and generalization. Domain decomposition induces function-space and operator decompositions with valuable properties. Function-space bases and operator splittings that are not derived from domain decompositions generally lack one or more of these properties. The evolution of domain decomposition methods for elliptically dominated problems has linked two major algorithmic developments of the last 15 years: multilevel and Krylov methods. Domain decomposition methods may be considered descendants of both classes with an inheritance from each: they are nearly optimal and at the same time efficiently parallelizable. Many computationally driven application areas are ripe for these developments. A progression is made from a mathematically informal motivation for domain decomposition methods to a specific focus on fluid dynamics applications. To be introductory rather than comprehensive, simple examples are provided while convergence proofs and algorithmic details are left to the original references; however, an attempt is made to convey their most salient features, especially where this leads to algorithmic insight.
Keyes, David E.↗
On the shear stabilization of capillary break-up of finite liquid bridges
In this paper we consider an isothermal finite liquid bridge under zero-gravity. A sinusoidal interfacial shear stress drives a nonparallel flow in the bridge. The linear stability of this flow to three-dimensional disturbances (which may deform the cylindrical gas-liquid interface) is determined numerically by solving an elliptic eigenvalue problem. Previous results on shear stabilization of capillary break-up of axially unbounded cylindrical interfaces containing a parallel flow are hereby extended to a nonparallel flow. The turning flow regions influence the stability significantly. However, for the particular cases considered, a small area in parameter space remains where the capillary instability is suppressed through interfacial shear. Second, non-axisymmetric oscillatory instabilities are found which originate from an interaction of the interface deformation and the basic flow. These instabilities may be the isothermal limit of the oscillatory instabilities observed in float-zone crystal growth.
Dijkstra, Henk A.↗
Spaceflight mechanics 1992; Proceedings of the 2nd AAS/AIAA Meeting, Colorado Springs, CO, Feb. 24-26, 1992. Pts. 1 & 2
The present conference discusses topics in orbit determination, tethered satellite systems, celestial mechanics, guidance optimization, flexible body dynamics and control, attitude dynamics and control, Mars mission analyses, earth-orbiting mission analysis/debris, space probe mission analyses, and orbital computation numerical analyses. Attention is given to electrodynamic forces for control of tethered satellite systems, orbiting debris threats to asteroid flyby missions, launch velocity requirements for interceptors of short range ballistic missiles, transfers between libration-point orbits in the elliptic restricted problem, minimum fuel spacecraft reorientation, orbital guidance for hitting a fixed point at maximum speed, efficient computation of satellite visibility periods, orbit decay and reentry prediction for space debris, and the determination of satellite close approaches.
Diehl, Roger E.↗
A preliminary analysis of the orbit of the Mars Trojan asteroid (5261) Eureka
Observations and results of orbit determination of the first known Mars Trojan asteroid (5261) Eureka are presented. We have numerically calculated the evolution of the orbital elements, and have analyzed the behavior of the motion during the next 2 Myr. Strong perturbations by planets other than Mars seem to stabilize the eccentricity of the asteroid by stirring the high order resonances present in the elliptic restricted problem. As a result, the orbit appears stable at least on megayear timescales. The difference of the mean longitudes of Mars and Eureka and the semimajor axis of the asteroid form a pair of variables that essentially behave in an adiabatic manner, while the evolution of the other orbital elements is largely determined by the pertubations due to other planets.
Mikkola, Seppo↗
A Parallel Multilevel Spectral Element Scheme
A parallel multilevel strategy is developed using spectral (p) finite elements. Hierarchic bases are particularly well suited since the element matrices and vectors are nested and the multilevel projections easiliy performed. Since the basis degree is used to specify the multigrid level, an EBE strategy is natural br the multilevel technique. Results are presented for two candidate nonlinear elliptic transport problems: the augmented drift-diffusion equations of semiconductor device modeling and the stream function-vorticity equations of incompressible fluid dynamics.
Davis, M. B.↗
Wavelet Sparse Approximate Inverse Preconditioners
There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.
Chan, Tony F.↗
Rapid Trajectory Prediction for a Fixed-Wing UAS in a Uniform Wind Field with Specified Arrival Times
This paper presents an algorithm to rapidly generate trajectories for a kinematic fixed-wing Unmanned Aircraft System (UAS) model flying at constant altitude in a uniform wind field. Arrival times are specified by operators and rapid generation is accomplished via an elliptic integral problem formulation. Simulations are provided that illustrate this approach in the context of NASA's UAS Traffic Management Project.
trajectory↗