Results for “Coordinate transformations” — Page 37

NASA NTRS1992

Finite element approach for transient analysis of multibody systems

A three-dimensional, finite element based formulation for the transient dynamics of constrained multibody systems with trusslike configurations is presented. A convected coordinate system is used to define the rigid-body motion of individual elements in the system. Deformation of each element is defined relative to its convected coordinate system. The formulation is oriented toward joint-dominated structures. Through a series of sequential transformations, the joint degree of freedom is built into the equations of motion of the element to reduce geometric constraints. Based on the derivation, a general-purpose code has been developed. Two examples are presented to illustrate the application of the code.

Wu, Shih-Chin↗

NASA NTRS2004

Science Using an Electrostatic Levitation Furnace in the MUCAT Sector at the APS

The original motivation for the construction of the BESL prototype was to obtain the first proof of a 50-year-old hypothesis regarding the solidification of liquid metals. Since the 1950s it has been known that under proper conditions liquid metals can be cooled below their melting temperature (undercooled) without crystallizing to the stable solid phase. In 1952 Frank proposed that this was because the atoms in the metallic liquid were arranged with the symmetry of an icosahedron, a Platonic solid consisting of 20 tetrahedra (4-sided pyramid-shaped polyhedra) arranged around a common center. Since this local atomic order is incompatible with the long-range translational periodicity of crystal phases, a barrier is formed to the formation of small regions of the crystal phase, the nucleation barrier. A proof of Frank's hypothesis required a direct correlation between measured icosahedral order in the undercooled liquid and the nucleation barrier. The tendency of sample containers to catalyze nucleation obscured this relation, requiring containerless techniques. Combining containerless processing techniques for electrostatically levitated droplets (ESL) with x-ray synchrotron methods, a team from Washington University, St. Louis, MO, NASA Marshall Space Flight Center, and MUCAT at the APS demonstrated an increasing icosahedral order in TiZrNi liquids with decreasing temperature below the melting temperature. The increased icosahedral order caused the transformation of the liquid to a metastable icosahedral quasicrystal phase, instead of the stable tetrahedrally-coordinated crystal intermetallic, giving the first clear demonstration of the connection between the nucleation barrier and the local structure of the liquid, verifying Frank's hypothesis for this alloy.

Goldman, A.↗

NASA NTRS1977

Transformations from an oblate spheroid to a plane and vice versa: The equations used in the cartographic projection program MAP2

The relationships between the coordinates of a point on the surface on an oblate spheroid and the coordinates of the projection of that point in several common map projections are discussed. Because several of the projections are conformal, the theory of conformally mapping an oblate spheroid to the plane is summarized. For each projection considered, the equations which map the spheroid to the plane and their inverses are given.

Elliott, D. A.↗

NASA NTRS1976

Stochastic simulation of vertically nonhomogeneous gusts

The small-scale horizontal gust structure of detailed wind profiles along the vertical in the first 20 km of the atmosphere is a vertically nonhomogeneous process. A linear stochastic model is developed for the process based on the process covariance function. This model is formulated through the use of a scaling hypothesis that transforms the nonhomogeneous gust process into a nondimensional gust process which is homogeneous in a nondimensional height coordinate. The velocity scaling parameter for the gust process is the gust standard deviation, and the length scale used to nondimensionalize the altitude is the vertical space lag associated with the first zero of the gust covariance function. State space theory is used to derive a digital filter from the model, which can be readily used to simulate gusts for space vehicle design applications.

Fichtl, G. H.↗

NASA NTRSDate not supplied

Application of Agile for Systems Engineering, Project Management and Modeling and Lessons Learned

The Systems Engineering team within the Human Research Program (HRP) Exploration Medical Capability (ExMC) Element has been transforming its development processes to be more efficient, robust,and responsive to change and to its stakeholders. To these ends, the Systems Engineering team trialed the integration of agile development techniques into existing and new processes. Agile development methods are well understood within the software development community. Outside ofsoftware development, however, how non-software project management (PM) and systems engineering (SE) teams implement agile development techniques is less well understood. In its transformation efforts, the ExMC SE team focused on three main areas: Improving the project communications among subsystem teams and stakeholders by adopting a scrum-like process, Changing the status and reporting mechanisms to improve schedule coordination between the subsystem team, SE leadership, and ExMC Element leadership, and Unifying the model-based SE workflow to improve understanding of Concepts of Operations across projects.This presentation highlights several of these transformations and what the SE team learned while undergoing the transformation.

S Lumpkins↗

NASA NTRS1975

Stochastic simulation of vertically nonhomogeneous gusts

The small-scale horizontal gust structure of detailed wind profiles along the vertical in the first 20 km of the atmosphere is a vertically nonhomogeneous process. A linear stochastic model was developed based on the process covariance function. This model was formulated through the use of a scaling hypothesis which transforms the nonhomogeneous gust process into a nondimensional gust process which is homogeneous in a nondimensional gust height coordinate. The velocity scaling parameter for the gust process is the gust standard deviation, and the length scale used to nondimensionalize the altitude is the vertical space lag associated with the first zero of the gust covariance function. State space theory was used to derive a digital filter from the model, which can be readily used to simulate gusts for space vehicle design applications.

Fichtl, G. H.↗

NASA NTRS1993

Damage detection using experimentally measured mass and stiffness matrices

A method is presented for locating physical damage or change in a structure using experimentally measured mass and stiffness matrices. The approach uses a recently developed algorithm for transforming a state-space realization into a second order structural model with physical displacements as the generalized coordinates. This is accomplished by first rotating a state-space model of the identified structural dynamics into modal coordinates and approximating the mass normalized modal vectors for the output measurement set. Next, the physical mass, damping and stiffness matrices are synthesized directly from the measured modal parameters. This yields experimental mass and stiffness matrices for the structure without the use of a finite element model or a numerical search. The computed mass and stiffness are asymptotically equivalent to a static condensation of the global physical coordinate model. Techniques for solving the inverse connectivity problem are then developed whereby it is possible to assess the stiffness in a region of the structure bounded by several sensors. Applications to both simulated data and experimental data are used to discuss the effectiveness of the approach.

Peterson, L. D.↗

NASA NTRS1979

Advanced teleoperators

Advanced teleoperators are discussed, with emphasis on the remote manipulation system designed to perform such actions as grasping, orienting, moving, placing, and inserting objects. Geometrical performance dimensions are considered, indicating that a manipulator is limited to three-orders-of-magnitude ratio of workspace extension to positioning accuracy. The control system is examined, showing that a manipulative task requires coordination of several joints, with the relationship between the task definers and the joint variables given by complex trigonometrical transformations. Control modes developed in the last 30 years are noted, including program controlled industrial 'robots' which can endlessly repeat a fixed sequence of motions without operator intervention, and the sensor-referenced/computer-controlled mode manipulators. Advanced proximity sensor systems are taken into account, with emphasis on the applications of the force-torque and slip models. The proximity sensor system for the shuttle-size manipulator is described.

Bejczy, A. K.↗

NASA NTRS1986

A canonical form for nonlinear systems

The concepts of transformation and canonical form have been used in analyzing linear systems. These ideas are extended to nonlinear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form. For control design involving a nonlinear system, one approach is to put the system in its canonical form and approximate by that part having only feedback paths.

Su, R.↗

NASA NTRS1970

The far field diffraction pattern for corner reflectors with complex reflection coefficients

The far field diffraction pattern of a geometrically perfect corner reflector is examined analytically for normally incident monochromatic light. The states of polarization and the complex amplitudes of the emerging light are expressed through transformation matrices in terms of those of the original incident light for each sextant of the face in a single coordinate system. The analytic expression of the total diffraction pattern is obtained for a circular face. This expression consists of three component functions in addition to the basic Airy function. The coefficient of each function is expressed in terms of complex coefficients of reflectance of the reflecting surface. Some numerical results for different reflecting surfaces, including total internal reflection, are presented. The iso-intensity contours of the diffraction pattern evaluated from the analytical expressions for an uncoated solid corner reflector are also presented along with the photographs of the pattern.

Chang, R. F.↗

NASA NTRS1988

Application of spherical near-field measurements to microwave holographic diagnosis of antennas

Microwave diagnosis of antennas is considered as a viable tool for the determination of reflector surface distortions and location of defective radiating elements of array antennas. A hybrid technique based on the combination of the spherical near-field measurements and holographic metrology reconstruction is presented. The measured spherical near-field data are first used to construct the far-field amplitude and phase patterns of the antenna on specified regularized u-nu coordinates. These data are then utilized in the surface profile reconstruction of the holographic technique using a fast-Fourier-transform (FFT)/iterative approach. Results of an experiment using a 156-cm reflector antenna measured at 11.3 GHz are presented for both the original antenna and the antenna with four attached bumps. Several contour and gray-scaled plots are presented for the reconstructed surface profiles of the measured antennas. The recovery effectiveness of the attached bumps has been demonstrated. The hybrid procedure presented is used to assess the achieved accuracy of the holographic reconstruction technique because of its ability to determine very accurate far-field amplitude and phase data from the spherical near-field measurements.

Rahmat-Samii, Yahya↗

NASA NTRS1993

Burnett solutions along the stagnation line of a cooled cylinder in low-density hypersonic flows

The Burnett equations in the cylindrical coordinate system have been applied to the hypersonic flow over a cylinder in low density environments. Through a local similarity transformation, the Burnett equations are degenerated into nonlinear third-order ordinary differential equations which are only valid along the stagnation line. These equations are solved by the multi-staged Runge-Kutta integration technique. Steady state solutions are asymptotically reached by the time-marching procedure. A newly-developed computer code is used to solve both the Navier-Stokes and the Burnett equations within the shock layer. The computed heat transfer coefficients are consistent with wind-tunnel and STS flight data. Comparisons with the DSMC solutions and the Boltzmann solutions show that the Burnett equations are more appropriate as the governing equations than the Navier-Stokes equations in the transitional flow regime.

Liaw, G. S.↗

NASA NTRSDate not supplied

NASA Lunar Surface Innovation Initiative: Ensuring a Cohesive, Executable Strategy for Technology Development

Establishing a sustainable human presence on the Moon allows NASA to develop and test new approaches, technologies, and systems that will enable us to function in other, more challenging environments. The Lunar Surface Innovation Initiative (LSII) was established in 2019 and has evolved into a key agency asset to spur technology development and provide risk reduction for lunar surface system development and flight demonstrations. LSII coordinates activities implemented through a combination of in-house activities, competitive programs, and public-private partnerships to create transformative technologies needed for lunar surface exploration. This paper will outline the LSII model used to develop a technology pipeline that will retire the primary technology hurdles in six capability areas. In-situ resource utilization technologies for collecting, processing, storing, and using material found or manufactured on the Moon. Surface power technologies that provide the capability for sustainable, continuous power throughout the day and night for lunar missions. Dust mitigation strategies that diminish lunar dust hazards on lunar surface systems such as cameras, solar panels, space suits, habitats, and instrumentation. Extreme environments technologies that enable systems to operate throughout the full range of lunar surface conditions, including lunar noon (up to 150 at the equator), night (down to - 180 at the equator), multiple day/night cycles, and in permanently shadowed regions (down to -250). Extreme access technologies that enable humans or robotic systems to access, navigate, and explore previously inaccessible lunar surface or subsurface areas. Excavation and construction technologies that will allow affordable, autonomous manufacturing or construction. We outline key results, including milestones and achievements related to the capability areas and outcomes from partnerships with the commercial sector. A key tenet of the LSII is the Lunar Surface Innovation Consortium (LSIC), a collaboration across industry, academia, and government to successfully develop the transformative capabilities for lunar surface exploration. LSIC provides a forum for NASA to communicate technological requirements, needs, and opportunities and for the community to share existing capabilities and identify critical gaps with NASA. By working side by side with commercial enterprises and our international partners, NASA is able to combine the knowledge and expertise needed to explore the lunar surface and make technical advances that will feed technological and economic growth. Since its inception, LSII has engaged over 600 organizations across the United States and 46 countries to shape the technologies and systems needed to explore the lunar surface and stimulate a lunar surface economy.

lunar, lunar surface, technology development, ISRU↗

NASA NTRSDate not supplied

NASA Lunar Surface Innovation Initiative: Ensuring a Cohesive, Executable Strategy for Technology

Establishing a sustainable human presence on the Moon allows NASA to develop and test new approaches, technologies, and systems that will enable us to function in other, more challenging environments. The Lunar Surface Innovation Initiative (LSII) was established in 2019 and has evolved into a key agency asset to spur technology development and provide risk reduction for lunar surface system development and flight demonstrations. LSII coordinates activities implemented through a combination of in-house activities, competitive programs, and public-private partnerships to create transformative technologies needed for lunar surface exploration. This paper will outline the LSII model used to develop a technology pipeline that will retire the primary technology hurdles in six capability areas. In-situ resource utilization technologies for collecting, processing, storing, and using material found or manufactured on the Moon. Surface power technologies that provide the capability for sustainable, continuous power throughout the day and night for lunar missions. Dust mitigation strategies that diminish lunar dust hazards on lunar surface systems such as cameras, solar panels, space suits, habitats, and instrumentation. Extreme environments technologies that enable systems to operate throughout the full range of lunar surface conditions, including lunar noon (up to 150 at the equator), night (down to - 180 at the equator), multiple day/night cycles, and in permanently shadowed regions (down to -250). Extreme access technologies that enable humans or robotic systems to access, navigate, and explore previously inaccessible lunar surface or subsurface areas. Excavation and construction technologies that will allow affordable, autonomous manufacturing or construction. We outline key results, including milestones and achievements related to the capability areas and outcomes from partnerships with the commercial sector. A key tenet of the LSII is the Lunar Surface Innovation Consortium (LSIC), a collaboration across industry, academia, and government to successfully develop the transformative capabilities for lunar surface exploration. LSIC provides a forum for NASA to communicate technological requirements, needs, and opportunities and for the community to share existing capabilities and identify critical gaps with NASA. By working side by side with commercial enterprises and our international partners, NASA is able to combine the knowledge and expertise needed to explore the lunar surface and make technical advances that will feed technological and economic growth. Since its inception, LSII has engaged over 600 organizations across the United States and 46 countries to shape the technologies and systems needed to explore the lunar surface and stimulate a lunar surface economy.

Lunar↗

NASA NTRS1993

High-resolution Y-axis readout for delay-line microchannel anodes

We have devised a method to obtain a high-resolution Y-axis event position determination from microchannel plate delay-line detectors. The method is based on the double-delay-line wedge-wedge charge partition principle of Lampton et al. (1990), where the X axis is read out by a pair of side-by-side delay lines and the Y-axis coordinate is determined by comparing the charges on the two parallel delay lines. However, our new method abandons the common field return path of the two delay lines, and splits them into two adjacent but independent transformer coupled timing circuits having no common ground connection except via the charge-measurement amplifiers. Thus we eliminate the large electrostatic capacitance of the delay lines from the input of the charge-measuring system. Over its limited working field, the spatial resolution in the Y coordinate can easily equal the resolution provided in the X coordinate by the delay line. Applications to extreme and FUV photon-counting spectroscopy are envisioned.

Raffanti, R.↗

NASA NTRS1975

Evaluation of lattice sums by the Poisson sum formula

The Poisson sum formula was applied to the problem of summing pairwise interactions between an observer molecule and a semi-infinite regular array of solid state molecules. The transformed sum is often much more rapidly convergent than the original sum, and forms a Fourier series in the solid surface coordinates. The method is applicable to a variety of solid state structures and functional forms of the pairwise potential. As an illustration of the method, the electric field above the (100) face of the CsCl structure is calculated and compared to earlier results obtained by direct summation.

Ray, R. D.↗

NASA NTRS1977

Analysis of a discrete spectrum analyzer for the detection of radio frequency interference

As the radio frequency spectrum becomes increasingly overcrowded, interference with mission-critical DSN operations is rising at an alarming rate. To alleviate this problem the DSN is developing a wideband surveillance system for on-site detection and identification of potential sources of radio frequency interference (RFI), which will complement the existing frequency coordination activities. The RFI monitoring system is based on a wideband, multi-look discrete spectrum analyzer operating on fast Fourier transform principles. An extensive general statistical analysis is presented of such spectrum analyzers and derives threshold detection performance formulas for signals of interest. These results are then applied to the design of the RFI spectrum analyzer under development.

Levitt, B. K.↗

NASA NTRS1982

Development of three-dimensional spatial displays using a geographically based information system

Procedures necessary for the development of a generalized three-dimensional perspective software capability in support of graphic, topographic, and color mapping of Landsat data are reviewed. The NASA Earth Resources Laboratory developed the procedures in order to facilitate the processing and analysis of disparate, geographically oriented base maps from aircraft and satellite sensors. Perspective displays are obtained through a translation of the space-viewed object to a vantage point coordinate system, followed by a rotation through two angles for alignment along the vantage line of sight, and finally a perspective transformation to yield two-dimensional displays with no hidden lines. Matrix equations for the transformations are reviewed, including scaling, and block diagrams are provided of the data and perspective software systems. The classification data plane may be mapped onto a topographic elevation data plane.

Junkin, B. G.↗