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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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13 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical domain

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (i.e., the membrane eignevalue problem for the vibration equation) on the unit spherical surface are developed. Two types of spherical surface domains are considered: the interior of a spherical triangle, and the exterior of a great circle arc extending for less than pi radians (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is employed. The fundamental eigenvalue is approximated by iteration utilizing the power method and point successive overrelaxation. Some numerical results are given and compared, in certain special cases, with analytical solutions to the eigenvalue problem. The significance of the numerical eigenvalue results is discussed in terms of the singularities in the solution of three-dimensional boundary-value problems near a polyhedral corner of the domain.

Walden, H.↗
NASA NTRS1974

Solution of an eigenvalue problem for the Laplace operator on a spherical surface

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

Walden, H.↗
NASA NTRS1990

Sphere quadtrees - A new data structure to support the visualization of spherically distributed data

The concept of the sphere quadtree (SQT) is introduced to enable the structuring of spherically distributed data to be consistent with its geometry and facilitate mapping of the data onto a flat file system. The SQT is based on the recursive subdivision of the spherical triangles that result from the projection of the faces of an icosahedron onto a sphere. The SQT concept is insensitive to the distortions that occur far from the equator in spherically distributed data sets. Geographic data can be shown at several levels and at any resolution, allowing a system of referencing between data sets of different resolutions as well as data that are not geographically registered. SQTs are found to facilitate the search for particular spherically distributed data sets and improve the efficiency of surface rendering algorithms.

Fekete, Gyorgy↗
NASA NTRS1988

Three-dimensional axisymmetric ball model for the PC-TAP program

Spherical-geometry solids' thermal modeling is presently undertaken with a three-dimensional FEM method that can be used in conjunction with the IBM-PC Thermal Analyzer Program (TAP). The elements of the model's nodal network are spherical triangles having approximately equivalent volumes for transient cases, thereby decreasing computer run times. Attention is given to results for the three test cases to which the model has been applied, which are compared with results from analytical closed-form solutions. Absolute temperature errors not greater than 1 percent are indicated by the comparisons.

Pidcoke, L. H.↗
NASA NTRS1990

Determining ground trace crossovers for multiple spacecraft

Applications of the spherical-triangles method for determining ground-trace intersections of multiple spacecraft are considered. The results derived from this procedure are inconsistent with the actual ephemeris data. It is found that an alternative method based on the ground track equations provides more accurate results, is more easily implemented, and is computationally less intensive.

Chase, Robert↗
NASA NTRS1994

Space hardware designs, volume 1

The design of a solar sail space vehicle with a novel sail deployment mechanism is described. The sail is triangular in shape and is deployed and stabilized by three miniature spacecraft, one at each corner of the triangle. A concept demonstrator for a spherical microrover for the exploration of a planetary surface is described. Lastly, laboratory experiments have been conducted to study the migration of thin oil films on metal surfaces in the presence of a thermal gradient.

Meyer, Rudolf X.↗
NASA NTRS1982

Modeling of Large Latticed Surfaces

GEOMLLS program determines dimensions and coordinates of flat segmented triangular surfaces that approximate spherical and paraboloidal surfaces of revolution, where vertexes of triangles lie on true surface. GEOMLLS calculates complete geometry of segmented surface and quantities that measure surface accuracy, such as maximum deviation and root-mean-square deviation from true surface.

Anderson, M. S.↗
NASA NTRS2006

Tilt/Tip/Piston Manipulator with Base-Mounted Actuators

A proposed three-degree-of-freedom (tilt/tip/piston) manipulator, suitable for aligning an optical or mechanical component, would offer several advantages over prior such manipulators: Unlike in some other manipulators, no actuator would support the weight of another actuator: All of the actuators would be mounted on a base. Hence, there would be less manipulated weight. The basic geometry of the manipulator would afford mechanical advantage: that is, actuator motions would be larger than the motions they produce in the manipulated object. Mechanical advantage inherently increases the accuracy and resolution of manipulation. Unlike in some other manipulators, it would not be necessary to route power and/or data lines through manipulator joints. The proposed manipulator (see figure) would include three prismatic actuators (T1N1, T2N2, and T3N3) mounted on the base and operating in the same plane. Examples of suitable prismatic actuators include lead-screw mechanisms, linear hydraulic motors, piezoelectric linear drives, inchworm-movement linear stepping motors, and linear flexure drives. The actuators would control the lengths of links R1T1, R2T2, and R3T3. Three spherical joints (P1, P2, and P3) would be located at the corners of an equilateral triangle of side length q on the platform holding the object to be manipulated. Three inextensible limbs (R1P1, R2P2, and R3P3) having length r would connect the spherical joints on the platform to revolute joints (R1, R2, and R3) at the ends of the actuator-controlled links R1T1, R2T2, and R3T3. By varying the lengths of these links, one could control the tilt, tip, and piston coordinates of the platform. Closed-form equations for direct or forward kinematics of the manipulator (given the lengths of the variable links, find the tilt, tip, and piston coordinates) have been derived. The equations of inverse kinematics (find the variable link lengths needed to obtain the desired tilt, tip, and piston coordinates) have also been derived.

Tahmasebi, Farhad↗
NASA NTRS1994

Spectral signatures of polar stratospheric clouds and sulfate aerosol

Multiwavelength observations of Antarctic and midlatitude aerosol by the Cryogenic Limb Array Etalon Spectrometer (CLAES) experiment on the Upper Atmosphere Research Satellite (UARS) are used to demonstrate a technique that identifies the location of polar stratospheric clouds. The technique discussed uses the normalized area of the triangle formed by the aerosol extinctions at 925, 1257, and 1605/cm (10.8, 8.0, and 6.2 micrometers) to derive a spectral aerosol measure M of the aerosol spectrum. Mie calculations for spherical particles and T-matrix calculations for spheriodal particles are used to generate theoretical spectral extinction curves for sulfate and polar stratospheric cloud particles. The values of the spectral aerosol measure M for the sulfate and polar stratospheric cloud particles are shown to be different. Aerosol extinction data, corresponding to temperatures between 180 and 220 K at a pressure of 46 hPa (near 21-km altitude) for 18 August 1992, are used to demonstrate the technique. Thermodynamic calculations, based upon frost-point calculations and laboratory phase-equilibrium studies of nitric acid trihydrate, are used to predict the location of nitric acid trihydrate cloud particles.

Massie, S. T.↗
NASA NTRS1988

Tubular space truss structure for SKITTER 2 robot

The Skitter 2 is a three legged transport vehicle designed to demonstrate the principle of a tripod walker in a multitude of environments. The tubular truss model of Skitter 2 is a proof of principal design. The model will replicate the operational capabilities of Skitter 2 including its ability to self-right itself. The project's focus was on the use of light weight tubular members in the final structural design. A strong design for the body was required as it will undergo the most intense loading. Triangular geometry was used extensively in the body, providing the required structural integrity and eliminating the need for cumbersome shear panels. Both the basic femur and tibia designs also relied on the strong geometry of the triangle. An intense literature search aided in the development of the most suitable weld techniques, joints, linkages, and materials required for a durable design. The hinge design features the use of spherical rod end bearings. In order to obtain a greater range of mobility in the tibia, a four-bar linkage was designed which attaches both to the femur and the tibia. All component designs, specifically the body, femur, and the tibia were optimized using the software package IDEAS 3.8A Supertab. The package provided essential deformation and stress analysis information on each component's design. The final structure incurred only a 0.0544 inch deflection in a maximum (worst case) loading situation. The highest stress experienced by any AL6061-T6 tubular member was 1920 psi. The structural integrity of the final design facilitated the use of Aluminum 6061-T6 tubing. The tubular truss structure of Skitter 2 is an effective and highly durable design. All facets of the design are structurally sound and cost effective.

Beecham, Richard↗
NASA NTRS1995

Global Dynamic Modeling of Space-Geodetic Data

The proposal had outlined a year for program conversion, a year for testing and debugging, and two years for numerical experiments. We kept to that schedule. In first (partial) year, author designed a finite element for isostatic thin-shell deformation on a sphere, derived all of its algebraic and stiffness properties, and embedded it in a new finite element code which derives its basic solution strategy (and some critical subroutines) from earlier flat-Earth codes. Also designed and programmed a new fault element to represent faults along plate boundaries. Wrote a preliminary version of a spherical graphics program for the display of output. Tested this new code for accuracy on individual model plates. Made estimates of the computer-time/cost efficiency of the code for whole-earth grids, which were reasonable. Finally, converted an interactive graphical grid-designer program from Cartesian to spherical geometry to permit the beginning of serious modeling. For reasons of cost efficiency, models are isostatic, and do not consider the local effects of unsupported loads or bending stresses. The requirements are: (1) ability to represent rigid rotation on a sphere; (2) ability to represent a spatially uniform strain-rate tensor in the limit of small elements; and (3) continuity of velocity across all element boundaries. Author designed a 3-node triangle shell element which has two different sets of basis functions to represent (vector) velocity and all other (scalar) variables. Such elements can be shown to converge to the formulas for plane triangles in the limit of small size, but can also applied to cover any area smaller than a hemisphere. The difficult volume integrals involved in computing the stiffness of such elements are performed numerically using 7 Gauss integration points on the surface of the sphere, beneath each of which a vertical integral is performed using about 100 points.

Bird, Peter↗
NASA NTRS2000

Laser Interferometer Space Antenna (LISA) Far Field Phase Patterns

The Laser Interferometer Space Antenna (LISA) consists of three spacecraft in orbit about the sun. The orbits are chosen such that the three spacecraft are always at (roughly) the vertices of a equilateral triangle with 5 million kilometer leg lengths. Even though the distances between the three spacecraft are 5 million kilometers, the expected phase shifts between any two beams, due to a gravitational wave, only correspond to a distance change of about 10 pico meters, which is about 10(exp -5) waves for a laser wavelength of 1064 nm. To obtain the best signal-to-noise ratio, noise sources such as changes in the apparent distances due to pointing jitter must be controlled carefully. This is the main reason for determining the far-field phase patterns of a LISA type telescope. Because of torque on the LISA spacecraft and other disturbances, continuous adjustments to the pointing of the telescopes are required. These pointing adjustments will be a "jitter" source. If the transmitted wave is perfectly spherical then rotations (Jitter) about its geometric center will not produce any effect at the receiving spacecraft. However, if the outgoing wave is not perfectly spherical, then pointing jitter will produce a phase variation at the receiving spacecraft. The following sections describe the "brute force" computational approach used to determine the scalar wave front as a function of exit pupil (Zernike) aberrations and to show the results (mostly graphically) of the computations. This approach is straightforward and produces believable phase variations to sub-pico meter accuracy over distances on the order of 5 million kilometers. As such this analyzes the far field phase sensitivity to exit pupil aberrations.

Waluschka, Eugene↗