SEARCH · Engineering Papers
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.
This report is concerned with the theory of thin shallow shells. It does not employ the lines of curvature as the coordinate system, but employs "almost cartesian coordinates" or the coordinates obtained by cutting the surface into two mutually orthogonal systems of parallel planes.
A dynamical analysis is performed for a six DOF robot end-effector built to study telerobotic service and maintenance of NASA hardwares in space. The design of the end-effector is based on the concept of closed-kinematic chain mechanism capable of performing precise motion in a small workspace. After presenting a closed-form solution for the inverse kinematic problem, the Lagrangian approach is used to derive a set of equations of motion for the end-effector where the generalized coordinates are selected to be the Cartesian coordinates. A computer simulation study shows that the centrifugal and Coriolis terms can be neglected for slow motion.
Geographic data, such as seismic event locations, station locations, etc., are generally given in geographic latitude Φ ’, longitude θ , and depth below sea level, ζ , using the WGS84 ellipsoid as a reference. In software systems that use this type of geographic data, it is necessary to manipulate the data mathematically in order to perform such tasks as finding the angular distance or azimuth from one point to another, to find an array of points along a great circle, to rotate a point about a pole of rotation, to move a point some angular distance in a specified direction, to find the intersections of two great circles or to find the intersections of a great circle and a small circle. In this paper, equations are presented that convert geographic locations first to geocentric coordinates and then to Earth-centered Cartesian coordinates where many mathematical manipulations can be performed conveniently and efficiently.
Specific problems in the theory of relativity are often simplified by an appropriate choice of the coordinate system. Restricted conformal coordinates provide an especially simple analysis of motion with uniform acceleration, known as hyperbolic motion. Conformal coordinates x', t' may be obtained from Cartesian coordinates x, t by the transformation x'+ct'=F(x+ct) and x'-ct'=G(x-ct), where c is the velocity of light. A variable motion of the x' system is determined by the choice of the functions F and G.
A Polymer Molecular Analysis Display System (p-MADS) was developed for computer modeling of polymers. This method of modeling allows for the theoretical calculation of molecular properties such as equilibrium geometries, conformational energies, heats of formations, crystal packing arrangements, and other properties. Furthermore, p-MADS has the following capabilities: constructing molecules from internal coordinates (bonds length, angles, and dihedral angles), Cartesian coordinates (such as X-ray structures), or from stick drawings; manipulating molecules using graphics and making hard copy representation of the molecules on a graphics printer; and performing geometry optimization calculations on molecules using the methods of molecular mechanics or molecular orbital theory.
A methodology for improving gravity-gradient measurement data exploits the constraints imposed upon the components of the gravity-gradient tensor by the conditions of integrability needed for reconstruction of the gravitational potential. These constraints are derived from the basic equation for the gravitational potential and from mathematical identities that apply to the gravitational potential and its partial derivatives with respect to spatial coordinates. Consider the gravitational potential in a Cartesian coordinate system {x1,x2,x3}. If one measures all the components of the gravity-gradient tensor at all points of interest within a region of space in which one seeks to characterize the gravitational field, one obtains redundant information. One could utilize the constraints to select a minimum (that is, nonredundant) set of measurements from which the gravitational potential could be reconstructed. Alternatively, one could exploit the redundancy to reduce errors from noisy measurements. A convenient example is that of the selection of a minimum set of measurements to characterize the gravitational field at n3 points (where n is an integer) in a cube. Without the benefit of such a selection, it would be necessary to make 9n3 measurements because the gravitygradient tensor has 9 components at each point. The problem of utilizing the redundancy to reduce errors in noisy measurements is an optimization problem: Given a set of noisy values of the components of the gravity-gradient tensor at the measurement points, one seeks a set of corrected values - a set that is optimum in that it minimizes some measure of error (e.g., the sum of squares of the differences between the corrected and noisy measurement values) while taking account of the fact that the constraints must apply to the exact values. The problem as thus posed leads to a vector equation that can be solved to obtain the corrected values.
We report the discovery of emerged tidal tails around open cluster IC 4756 (~1 Gyr) based on 644 members identified from Gaia EDR3. Three-dimensional spatial positions and two-dimensional tangential velocities (x,y,z,κ·μ{sub α}*/ϖ,κ·μ{sub δ}/ϖ) are utilized to determine the comoving member candidates of IC 4756. Using a Bayesian method, we correct the distance for each cluster member. Two tidal tails extend up to 180 pc and display an S shape in the X'Y' space (Cartesian coordinates focused on cluster center). A clean sequence of our members in the color–absolute–magnitude diagram indicates the coeval population and matches perfectly with the PARSEC isochrone with age from Bossini et al. Mass segregation is detected in this cluster as well. Finally, we derive the tidal radius and core radius of IC 4756 about 12.13 pc and 4.33 ± 0.75 pc, respectively.
The Lightweight Surface Manipulation System, or LSMS, is a family of cable-actuated cranes, designed for surface operations on the Moon and Mars. Its structural design focuses on three fundamental traits for space environments: a high payload-to-mass ratio to reduce launch costs, compactness for space travel in reduced cargo bays, and self-erecting capabilities for operations before astronauts arrive. The resulting design confers nonlinear and switched dynamics to the LSMS, making these cranes an interesting challenge for autonomous and teleoperated applications. One of the protocols required for these applications is a Cartesian move algorithm. This algorithm is responsible for placing the end effector of the crane at a desired location, specified in Cartesian coordinates. This paper evaluates the performance of a Cartesian move algorithm developed for the LSMS at the NASA Langley Research Center. To this end, several payload manipulation tasks were performed with LSMS-L35, the smallest version within the LSMS family. The evaluated algorithm can place the end effector with accuracy, as shown in the hardware and simulation tests.
We have implemented a set of numerical simulations to numerically investigate the outcomes of non-proliferation experiments. The high explosive (HE) in the simulations is in the form of a cylinder. The two-dimensional simulations are carried out in the r-z cylindrical coordinate, and the three-dimensional simulation is in the Cartesian coordinate. From the simulation, the cavity formed after detonation stops its expansion after about 0.15 sec. At the time the cavity stops expanding, the cavity shape seems quite spherical although the initial HE is in the shape of cylinder, but the radius in the vertical direction, which is about 19.7m, is a little less than the one in the horizonal direction, which is about 21.5m. Although there is no layer of air between the HE and tuff in real experiments, in addition to the simulations without air, we add a layer of air in one simulation to assess any possible influence of the air on the shape of the cavity.
Polyatomic molecule vibrations are analyzed as harmonic vibrations along normal coordinates. The energy eigenvalues are found for linear and nonlinear symmetric triatomic molecules for valence bond models of the potential function with arbitrary coupling coefficients; such models can usually be fitted to observed energy levels with reasonably good accuracy. Approximate normal coordinates for the H2O molecule are discussed. Degenerate vibrational modes such as occur in CO2 are analyzed and expressions for Fermi resonance between close-lying states of the same symmetry are developed. The bending modes of linear triatomic molecules are expressed in terms of Laguerre polynomials in cylindrical coordinates as well as in terms of Hermite polynomials in Cartesian coordinates. The effects of large-amplitude bending such as occur in the C3 molecule are analyzed, along with anharmonic effects, which split the usually degenerate bending mode energy levels. Finally, the vibrational frequencies, degeneracies, and symmetry properties of XY3, X2Y2, and XY4 type molecules are discussed.
The objective of the paper is to examine a class of non-force-free fields analytically. Specifically, magnetic fields in magnetohydrostatic equilibrium with a plasma in a gravitational field are treated in an approximation of two independent variables but three vector components. Spherical coordinates are emphasized, although the formal results for cylindrical and Cartesian coordinates are presented in the appendices. Formal solutions for the magnetic-field components are obtained in terms of the plasma variables, and field line equations are derived. A final equation governing the plasma variables is then obtained. Procedures are developed for analyzing this equation and obtaining sets of self-consistent particular solutions to the governing equations; a number of such sets of solutions are presented. As an example, one solution set is examined, illustrating the application of the results to the analysis of solar observational data.
A neural network based system is presented which is able to generate point-to-point movements of robotic manipulators. The foundation of this approach is the use of prototypical control torque signals which are defined by a set of parameters. The parameter set is used for scaling and shaping of these prototypical torque signals to effect a desired outcome of the system. This approach is based on neurophysiological findings that the central nervous system stores generalized cognitive representations of movements called synergies, schemas, or motor programs. It has been proposed that these motor programs may be stored as torque-time functions in central pattern generators which can be scaled with appropriate time and magnitude parameters. The central pattern generators use these parameters to generate stereotypical torque-time profiles, which are then sent to the joint actuators. Hence, only a small number of parameters need to be determined for each point-to-point movement instead of the entire torque-time trajectory. This same principle is implemented for controlling the joint torques of robotic manipulators where a neural network is used to identify the relationship between the task requirements and the torque parameters. Movements are specified by the initial robot position in joint coordinates and the desired final end-effector position in Cartesian coordinates. This information is provided to the neural network which calculates six torque parameters for a two-link system. The prototypical torque profiles (one per joint) are then scaled by those parameters. After appropriate training of the network, our parametric control design allowed the reproduction of a trained set of movements with relatively high accuracy, and the production of previously untrained movements with comparable accuracy. We conclude that our approach was successful in discriminating between trained movements and in generalizing to untrained movements.
In calculating the position vector of the Moon in on-board flight software, one often begins by using a series expansion to calculate the ecliptic latitude and longitude of the Moon, referred to the mean ecliptic and equinox of date. One then performs a reduction for precession, followed by a rotation of the position vector from the ecliptic plane to the equator, and a transformation from spherical to Cartesian coordinates before finally arriving at the desired result: equatorial J2000 Cartesian components of the lunar position vector. An alternative method is developed here in which the equatorial J2000 Cartesian components of the lunar position vector are calculated directly by a series expansion, saving valuable on-board computer resources.
In calculating the position vector of the Moon in on-board flight software, one often begins by using a series expansion to calculate the ecliptic latitude and longitude of the Moon, referred to the mean ecliptic and equinox of date. One then performs a reduction for precession, followed by a rotation of the position vector from the ecliptic plane to the equator, and a transformation from spherical to Cartesian coordinates before finally arriving at the desired result: equatorial J2000 Cartesian components of the lunar position vector. An alternative method is developed here in which the equatorial J2000 Cartesian components of the lunar position vector are calculated directly by a series expansion, saving valuable onboard computer resources.
A geometrical nonlinear analysis based on an alternative definition of strain is presented. Expressions for strain are obtained by computing the change in length of the base vectors in the curvilinear element coordinate system. The isoparametric element formulation is assumed in the global Cartesian coordinate system. The approach is based on the minimization of the strain energy, and the resulting nonlinear equations are solved by the modified Newton method. Integration of the first and second variation of the strain energy is performed numerically in the case of two and three dimensional elements. Application is made to a simple long cantilever beam.
An adaptive grid algorithm has been developed in two and three dimensions that can be used dynamically with a solver or as part of a grid refinement process. The algorithm employs a transformation from the Cartesian coordinate system to a general coordinate space, which is defined as a parallelepiped in three dimensions. A weighting function, independent for each coordinate direction, is developed that will provide the desired refinement criteria in regions of high solution gradient. The adaptation is performed in the general coordinate space and the new grid locations are returned to the Cartesian space via a simple, one-step inverse mapping. The algorithm for relocation of the mesh points in the parametric space is based on the center of mass for distributed weights. Dynamic solution-adaptive results are presented for laminar flows in two and three dimensions.
A new multi-station VHF time-of-arrival (TOA) antenna network is, at the time of this writing, coming on-line in Northern Alabama. The network, called the Lightning Mapping Array (LMA), employs GPS timing and detects VHF radiation from discrete segments (effectively point emitters) that comprise the channel of lightning strokes within cloud and ground flashes. The network will support on-going ground validation activities of the low Earth orbiting Lightning Imaging Sensor (LIS) satellite developed at NASA Marshall Space Flight Center (MSFC) in Huntsville, Alabama. It will also provide for many interesting and detailed studies of the distribution and evolution of thunderstorms and lightning in the Tennessee Valley, and will offer many interesting comparisons with other meteorological/geophysical wets associated with lightning and thunderstorms. In order to take full advantage of these benefits, it is essential that the LMA channel mapping accuracy (in both space and time) be fully characterized and optimized. In this study, a new revised channel mapping retrieval algorithm is introduced. The algorithm is an extension of earlier work provided in Koshak and Solakiewicz (1996) in the analysis of the NASA Kennedy Space Center (KSC) Lightning Detection and Ranging (LDAR) system. As in the 1996 study, direct algebraic solutions are obtained by inverting a simple linear system of equations, thereby making computer searches through a multi-dimensional parameter domain of a Chi-Squared function unnecessary. However, the new algorithm is developed completely in spherical Earth-centered coordinates (longitude, latitude, altitude), rather than in the (x, y, z) cartesian coordinates employed in the 1996 study. Hence, no mathematical transformations from (x, y, z) into spherical coordinates are required (such transformations involve more numerical error propagation, more computer program coding, and slightly more CPU computing time). The new algorithm also has a more realistic definition of source altitude that accounts for Earth oblateness (this can become important for sources that are hundreds of kilometers away from the network). In addition, the new algorithm is being applied to analyze computer simulated LMA datasets in order to obtain detailed location/time retrieval error maps for sources in and around the LMA network. These maps will provide a more comprehensive analysis of retrieval errors for LMA than the 1996 study did of LDAR retrieval errors. Finally, we note that the new algorithm can be applied to LDAR, and essentially any other multi-station TWA network that depends on direct line-of-site antenna excitation.
Bolt Circle Calculation (BOLT-CALC) computer program used to reduce significant time consumed in manually computing trigonometry of rectangular Cartesian coordinates of holes in bolt circle as shown on blueprint or drawing. Eliminates risk of computational errors, particularly in cases involving many holes or in cases in which coordinates expressed to many significant digits. Program assists in many practical situations arising in machine shops. Written in BASIC. Also successfully compiled and implemented by use of Microsoft's QuickBasic v4.0.