Structural Design Concepts for Future Space Missions
Mathematical model for subdividing and transforming polyhedron into structural sphere
Lauchner, Julian H.↗
SEARCH · Engineering Papers
Results for “POLYHEDRON”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
The two-dimensional tunnel structures of K3Sb5O14 and K2Sb4O11
The structures of K3Sb5O14 and K2Sb4O11 have been solved by the single-crystal X-ray direct method and the heavy-atom method, respectively. The structure of K3Sb5O14 is orthorhombic, with space group Pbam and cell parameters a = 24.247 (4), b = 7.157 (2), c = 7.334 (2) A, Z = 4. The structure of K2Sb4O11 is monoclinic, with space group C2/m and cell parameters a = 19.473 (4), b = 7.542 (1), c = 7.198 (1) A, beta = 94.82 (2) deg, Z = 4. A full-matrix least-squares refinement gave R = 0.072 and R = 0.067, respectively. In both structures, oxygen atoms form an octahedron around each Sb atom and an irregular polyhedron around each K atom. By sharing corners and edges, the octahedra form a skeleton network having intersecting b-axis and c-axis tunnels. The K(+) ions, which have more than ten oxygen near neighbors, are located in these tunnels. Evidence for K(+)-ion transport within and between tunnels comes from ion exchange of the alkali ions in molten salts and anisotropic temperature factors that are anomalously large in the direction of the tunnels.
Hong, H. Y.-P.↗
On Similarity Transformation and Geodetic Network Distortions Based on Doppler Satellite Observations
Models used in geodesy to transform two sets of coordinates are studied and distortions in geodetic networks are investigated. Commonly used transformation models are first reviewed and most of them are interpreted. Differences between various models are discussed. Pitfalls in partial solutions are then considered. It is shown that only as many chords and/or directional elements can be used in the computation as are needed to completely determine the size or shape of the polyhedron implied in the set of Cartesian coordinates. Each additional element causes the normal matrix to be singular provided that all correlations between the chords are used. A number of tables and maps indicating distortions in the NAD 27, Precise Traverse M-R '72, AUS, and SAD 69 geodetic datums are also included. The residuals of the coordinates are scanned for systematic patterns after transforming each geodetic system to the NWL9D Doppler system. Also, an attempt is made to show scale distortions in the NAD 27.
Leick, Alfred↗
Techniques for the correction of topographical effects in scanning Auger electron microscopy
A number of ratioing methods for correcting Auger images and linescans for topographical contrast are tested using anisotropically etched silicon substrates covered with Au or Ag. Thirteen well-defined angles of incidence are present on each polyhedron produced on the Si by this etching. If N1 electrons are counted at the energy of an Auger peak and N2 are counted in the background above the peak, then N1, N1 - N2, (N1 - N2)/(N1 + N2) are measured and compared as methods of eliminating topographical contrast. The latter method gives the best compensation but can be further improved by using a measurement of the sample absorption current. Various other improvements are discussed.
Prutton, M.↗
Crystal growth of artificial snow
Snow crystals were grown onboard the space shuttle during STS-7 and STS-8 to facilitate the investigation of crystal growth under conditions of weightlessness. The experimental design and hardware are described. Space-grown snow crystals were polyhedrons looking like spheres, which were unlike snow crystals produced in experiments on Earth.
Kimura, S.↗
The influence of scattering particles morphology on the characteristics of lidar signals
The characteristics of light scattering by a separate spherical particle are used as a priori information when interpreting the data on laser sounding of atmospheric aerosols. Analogously, it is necessary to have a priori information on the characteristics of light scattering by a single crystals in order to restitute the microstructure of crystal formation in the atmosphere. In contrast to the aerosol particles the crystals are of different shapes. On the one hand, this complicates the solution of electrodynamic problems on light scattering by such crystals. On the other hand, if obtaining such a solution is possible, one can determine the morphology of scattering particles accoring to the sounding data and this enables additonal information to be obtained on such meteorological parameters as temperature, pressure, and humidity. Using the geometric-wave approach the problem of scattering of plane electromagnetic wave on convex polyhedrons of arbitrary form was solved. As a result, the expressions were obtained for electric field components of perpendicular and parallel polarizations scattered in any given direction.
Zuev, V. E.↗
Collision detection for spacecraft proximity operations
Collision Detection for Spacecraft Proximity Operations This thesis describes the development of a new collision detection algorithm to be used when two spacecraft are operating in the same vicinity. The two spacecraft are modelled as unions of convex polyhedra, where the polyhedron resulting from the union may be either convex or nonconvex. The relative motion of the two spacecraft is assumed to be such that one vehicle is moving with constant linear and angular velocity with respect to the other. The algorithm determines if a collision is possible and, if so, predicts the time when the collision will take place. The theoretical basis for the new collision detection algorithm is the C-function formulation of the configuration space approach recently introduced by researchers in robotics. Three different types of C-functions are defined that model the contacts between the vertices, edges, and faces of the polyhedra representing the two spacecraft. These C-functions are used to formulate three "collision" conditions. The first of these conditions limits the points representing potential collisions to the zeros of the C-functions. The new algorithm is fundamentally a search for the smallest zero of any C-function that satisfies the second and third collision conditions. The C-functions are shown to be transcendental functions of time for the assumed trajectory of the moving spacecraft. The zeros of these functions cannot be expressed in dosed form. Therefore, numerical search procedures are developed to find aLl of the zeros of a C-function in specified bounded intervals of time. These bounded intervals of time are found by examining the second and third collision conditions. The capabilities of the new algorithm are demonstrated for several example cases. These include examples of collisions determined by zeros of each of the three different types of C-functions. In addition to predicting the time of first contact of the polyhedra, the algorithm identifies the features of the two polyhedra that are touching at this time. The new collision detection algorithm is the first such algorithm that is capable of solving the collision detection problem exactly for the case where the moving object has constant linear and angular velocities. This is a significant improvement on previous collision detection algorithms described in the literature. In particular, the ability to handle constant angular velocity represents a more realistic type of rotational motion than those which have been used in other algorithms.
Robin M Vaughan↗
Octree based automatic meshing from CSG models
Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is emphasized. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary respresentation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractors. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.
Perucchio, Renato↗
Geometrical and topological issues in octree based automatic meshing
Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is discussed. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary representation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractor. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.
Saxena, Mukul↗
Collision detection for spacecraft proximity operations
A new collision detection algorithm has been developed for use when two spacecraft are operating in the same vicinity. The two spacecraft are modeled as unions of convex polyhedra, where the resulting polyhedron many be either convex or nonconvex. The relative motion of the two spacecraft is assumed to be such that one vehicle is moving with constant linear and angular velocity with respect to the other. Contacts between the vertices, faces, and edges of the polyhedra representing the two spacecraft are shown to occur when the value of one or more of a set of functions is zero. The collision detection algorithm is then formulated as a search for the zeros (roots) of these functions. Special properties of the functions for the assumed relative trajectory are exploited to expedite the zero search. The new algorithm is the first algorithm that can solve the collision detection problem exactly for relative motion with constant angular velocity. This is a significant improvement over models of rotational motion used in previous collision detection algorithms.
Vaughan, Robin M.↗
Vector representation of lithium and other mica compositions
In contrast to mathematics, where a vector of one component defines a line, in chemical petrology a one-component system is a point, and two components are needed to define a line, three for a plane, and four for a space. Here, an attempt is made to show how these differences in the definition of a component can be resolved, with lithium micas used as an example. In particular, the condensed composition space theoretically accessible to Li-Fe-Al micas is shown to be an irregular three-dimensional polyhedron, rather than the triangle Al(3+)-Fe(2+)-Li(+), used by some researchers. This result is demonstrated starting with the annite composition and using exchange operators graphically as vectors that generate all of the other mica compositions.
Burt, Donald M.↗
A mixed volume grid approach for the Euler and Navier-Stokes equations
An approach for solving the compressible Euler and Navier-Stokes equations upon meshes composed of nearly arbitrary polyhedra is described. Each polyhedron is constructed from an arbitrary number of triangular and quadrilateral face elements, allowing the unified treatment of tetrahedral, prismatic, pyramidal, and hexahedral cells, as well the general cut cells produced by Cartesian mesh approaches. The basics behind the numerical approach and the resulting data structures are described. The accuracy of the mixed volume grid approach is assessed by performing a grid refinement study upon a series of hexahedral, tetrahedral, prismatic, and Cartesian meshes for an analytic inviscid problem. A series of laminar validation cases are made, comparing the results upon differing grid topologies to each other, to theory, and experimental data. A computation upon a prismatic/tetrahedral mesh is made simulating the laminar flow over a wall/cylinder combination.
Coirier, William J.↗
Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids
This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.
Liu, Yen↗
Design Study for a Global Magnetospheric Dynamics Mission
A successful design was developed, one with many advantages over the original mission. The time spent in orbit was more evenly spread over the region being investigated. The radiation close was significantly lower and the mission did not rely on gravity assist at the moon and thus did not have to make measurements that far out in the tail. A spacecraft design was developed that keeps interference from the engines to a minimum. The design however was quite specific for four spacecraft. It could not be easily scaled to five spacecraft for example. One problem was discovered that is a concern for all similar missions. Inter- spacecraft communication can determine the spacing of the vehicles easily and to the accuracy required. However, the orientation of the polyhedron with the spacecraft at its vertices is not well known for small separations. Ground station range measurements give the line of sight location well but not the angle around that vector. This is a problem any such mission needs to solve. Neither the navigation teams at Goddard nor at Lewis were willing to attempt to solve this problem. At the completion of the study a report was made to the AGU meeting in San Francisco and a paper published in the volume "Science Closure and Enabling Technologies for Constellation Class Missions". This paper is attached.
Russell, C. T.↗
An Impact Ejecta Behavior Model for Small, Irregular Bodies
In recent years, spacecraft observations of asteroids 951 Gaspra, 243 Ida, 253 Mathilde, and 433 Eros have shown the overriding dominance of impact processes with regard to the structure and surface morphology of these small, irregular bodies. In particular, impact ejecta play an important role in regolith formation, ranging from small particles to large blocks, as well as surface feature modification and obscuration. To investigate these processes, a numerical model has been developed based upon the impact ejecta scaling laws provided by Housen, Schmidt, and Holsapple, and modified to more properly simulate the late-stage ejection velocities and ejecta plume shape changes (ejection angle variations) shown in impact cratering experiments. A target strength parameter has also been added to allow the simulation of strength-dominated cratering events in addition to the more familiar gravity-dominated cratering events. The result is a dynamical simulation which models -- via tracer particles -- the ejecta plume behavior, ejecta blanket placement, and impact crater area resulting from a specified impact on an irregularly shaped target body, which is modeled in 3-dimensional polygon fashion. This target body can be placed in a simple rotation state about one of its principal axes, with the impact site and projectile/target parameters selected by the user. The gravitational force from the irregular target body (on each tracer particle) is determined using the polygonized surface (polyhedron) gravity technique developed by Werner.
Richardson, J. E.↗
A Micromechanics Finite Element Model for Studying the Mechanical Behavior of Spray-On Foam Insulation (SOFI)
A micromechanics model has been constructed to study the mechanical behavior of spray-on foam insulation (SOFI) for the external tank. The model was constructed using finite elements representing the fundamental repeating unit of the SOFI microstructure. The details of the micromechanics model were based on cell observations and measured average cell dimensions discerned from photomicrographs. The unit cell model is an elongated Kelvin model (fourteen-sided polyhedron with 8 hexagonal and six quadrilateral faces), which will pack to a 100% density. The cell faces and cell edges are modeled using three-dimensional 20-node brick elements. Only one-eighth of the cell is modeled due to symmetry. By exercising the model and correlating the results with the macro-mechanical foam behavior obtained through material characterization testing, the intrinsic stiffness and Poisson s Ratio of the polymeric cell walls and edges are determined as a function of temperature. The model is then exercised to study the unique and complex temperature-dependent mechanical behavior as well as the fracture initiation and propagation at the microscopic unit cell level.
Ghosn, Louis J.↗
Composition and method for hydrogen storage
A method for hydrogen storage includes providing water and hydrogen gas to a containment volume, reducing the temperature of the water and hydrogen gas to form a hydrogen clathrate at a first cryogenic temperature and a first pressure and maintaining the hydrogen clathrate at second cryogenic temperature within a temperature range of up to 250 K to effect hydrogen storage. The low-pressure hydrogen hydrate includes H.sub.2 O molecules, H.sub.2 molecules and a unit cell including polyhedron cages of hydrogen-bonded frameworks of the H.sub.2 O molecules built around the H.sub.2 molecules.
Mao, Wendy L.↗
Synchronized Position Hold, Engage, Reorient, Experimental Satellites
Synchronized Position Hold, Engage, Reorient, Experimental Satellites (SPHERES) are bowling-ball sized spherical satellites. They will be used inside the space station to test a set of well-defined instructions for spacecraft performing autonomous rendezvous and docking maneuvers. Three free-flying spheres will fly within the cabin of the station, performing flight formations. Each satellite is self-contained with power, propulsion, computers and navigation equipment. The results are important for satellite servicing, vehicle assembly and formation flying spacecraft configurations. SPHERES is a testbed for formation flying by satellites, the theories and calculations that coordinate the motion of multiple bodies maneuvering in microgravity. To achieve this inside the ISS cabin, bowling-ball-sized spheres perform various maneuvers (or protocols), with one to three spheres operating simultaneously . The Synchronized Position Hold, Engage, Reorient, Experimental Satellites (SPHERES) experiment will test relative attitude control and station-keeping between satellites, re-targeting and image plane filling maneuvers, collision avoidance and fuel balancing algorithms, and an array of geometry estimators used in various missions. SPHERES consists of three self-contained satellites, which are 18 sided polyhedrons that are 0.2 meter in diameter and weigh 3.5 kilograms. Each satellite contains an internal propulsion system, power, avionics, software, communications, and metrology subsystems. The propulsion system uses CO2, which is expelled through the thrusters. SPHERES satellites are powered by AA batteries. The metrology subsystem provides real-time position and attitude information. To simulate ground station-keeping, a laptop will be used to transmit navigational data and formation flying algorithms. Once these data are uploaded, the satellites will perform autonomously and hold the formation until a new command is given.
Miller, David W.↗