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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Geometric Interpretation of the Cluster Location Problem Part II: Application to the Pahala, Hawaii, Earthquake Sequence

In the companion “Theory” article, we presented a new framing of the seismic location problem in terms of differential geometry (Harris et al., 2025). From that viewpoint, we developed a “project and correct” approach for estimating the relative locations of earthquakes. Here, in this study, we use project and correct to estimate high-precision relative locations of events from an earthquake sequence beneath the town of Pahala, Hawaii, using high-precision correlation-derived picks. The sequence was active from 2020 through 2022 and produced many highly correlated signals at Hawaii Volcano Observatory (HVO) stations on the island of Hawaii. The data we inverted consisted of 2882 events with observations at 5 HVO stations. For comparison with the travel-time image, we also produced conventional hypocenter solutions using both the Bayesloc program (Myers et al., 2007, 2009) and a purpose-built double-difference code. There were obvious structural elements in the resulting image, the resolution of which we used to test the performance of the project and the correct algorithm. For the projection step, we first produced a 3D local basis using an singular value decomposition (SVD) of the 2882 groups of times. Projection of the travel-time vectors into this basis resulted in an image with structures similar to those produced by our conventional locators, but with distortion as predicted by theory. Removing the distortion requires an inverse operator generated from the metric tensor at the geometric centroid of the events. We compared two approaches to obtaining such an inverse operator. The first uses an estimate of the geographic centroid of the event cloud from the centroid of the travel-time data. The second approach uses the centroid of the conventionally produced locations. The first approach produces a corrected image very similar to the conventional results, but with a rotation. The corrected image produced using the conventionally derived centroid is a near-exact match to the conventional locations.

Dodge, Douglas A. [Lawrence Livermore National Lab↗
NASA NTRS1962

Post-buckling behavior of cylindrical shells. part iii. torsion

This is a continuation of two monographs bearing the same general title already published by the author under the auspices of the Publishing House of Khar'kov University. It deals with the elastic post-buckling behavior of a cylindrical shell stressed in torsion. In particular, the critical loads are determined. Generally speaking, the exposition is on an elementary level and intended for a wide circle of readers with a knowledge of the elements of shell theory and differential geometry. It will prove useful to design engineers, mechanical engineering students, and scientists interested in the theory of shells.

BUCKLING↗
NASA NTRS1973

Oscillations in nonlinear feedback systems.

It is shown how some basic ideas from system theory and differential geometry can be used to establish new results concerning the existance of oscillations for autonomous feedback systems. The conditions obtained are expressed in terms of the frequency response characteristic of the open-loop system and certain general properties of the nonlinearity.

Williamson, D.↗
NASA NTRS1975

Periodic motion in nonlinear systems

In this paper it is shown how some basic ideas from system theory and differential geometry can be used to establish some new results on the existence of periodic motion in autonomous feedback systems. The conditions are expressed in terms of the frequency response characteristic of the open-loop system and certain general properties of the nonlinearities.

Williamson, D.↗
NASA NTRS1976

Ground location of satellite scanner data

This paper presents simple and accurate mathematical formulation for determining the ground location of remote sensor data. The techniques used are based on elementary concepts of differential geometry and lead to the development of a relation that gives location as a function of surface ellipticity, satellite position, velocity, attitude, and scanner orientation. The formula lends itself to simply computer coding and will hopefully lead to a standardization of the various techniques which have been developed to solve this problem.

Puccinelli, E. F.↗
NASA NTRS1979

Possibilities and limitations of rod-beam theories

Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.

Peterson, D.↗
NASA NTRS1981

Principal normal curvature of surfaces

Certain principal normal curvatures of differential geometry were developed for use in curvature matrices associated with the asymptotic solution of electromagnetic diffraction problems. The effort is directed toward microwave antenna simulations and high speed digital computer analysis of radiometric instruments used to obtain soil moisture, sea state, salinity and temperature data. It is shown that the methods used to develop the principal normal curvatures for paraboloid, hyperboloid, ellipsoid, sphere, and cone can be applied to other radiometer geometries such as the parabolic torus, even though the surface parameterizations are different. It is concluded that deployable offset geometries, distorted by rotational forces and solar loads may be analyzed by similar means given a suitable surface description.

Schmidt, R. F.↗
NASA NTRS1982

Moving frames and prolongation algebras

Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.

Estabrook, F. B.↗
NASA NTRS1983

On families of systems and deformations

Until recently, there has not been any systematic effort towards a theory of systems with parameter variations. It is presently suggested that the concept of families of systems is basic to such an effort, and entails the techniques of Lie theory, differential geometry, and algebraic geometry. Attention is given to the geometric characterization of certain families of systems that appear in control and identification problems. The ways in which families of systems degenerate as parameter variations become large are isolated, using the topological rather than algebraic geometric case.

Krishnaprasad, P. S.↗
NASA NTRS1986

Radarclinometry for the Venus radar mapper

Already van Diggelen (1951) made use of the photometric function of a surface for the purpose of translating image variegation into slope and relief information, while the development of a method for producing a topographic map from a photometric image begins with Rindfleisch (1966). The term 'photoclinometry' was invented for the involved process. The present study is concerned with the adaptation of photoclinometry to radar imagery. The radar image as a candidate for photoclinometry offers both advantages and disadvantages when compared to ordinary optical images. The simplicity of the photometric function is the most obvious advantage. Attention is given to radiative transfer, the employment of differential geometry, and aspects of calibration.

Wildey, R. L.↗
NASA NTRS1986

A canonical expansion for nonlinear systems

The importance of differential geometry, particularly Lie brackets of vector fields, in the study of nonlinear systems is well established. Under very mild assumptions, it is shown that a real-analytic nonlinear system has an expansion in which the coefficients are computed in terms of Lie brackets. This expansion occurs in a special coordinate system. The concept of a pure feedback system is also explained. For control design involving a nonlinear system, one approach is to put the system in its canonical expansion and approximate by that part having only feedback paths.

Su, R.↗
NASA NTRS1988

Range data description based on multiple characteristics

An algorithm for describing range images based on Mean curvature (H) and Gaussian curvature (K) is presented. Range images are unique in that they directly approximate the physical surfaces of a real world 3-D scene. The curvature parameters are derived from the fundamental theorems of differential geometry and provides visible invariant pixel labels that can be used to characterize the scene. The sign of H and K can be used to classify each pixel into one of eight possible surface types. Due to the sensitivity of these parameters to noise the resulting HK-sing map does not directly identify surfaces in the range images and must be further processed. A region growing algorithm based on modeling the scene points with a Markov Random Field (MRF) of variable neighborhood size and edge models is suggested. This approach allows the integration of information from multiple characteristics in an efficient way. The performance of the proposed algorithm on a number of synthetic and real range images is discussed.

Al-Hujazi, Ezzet↗
NASA NTRS1986

Task driven feedback control of robot arms - A step toward intelligent control

The process of connecting task descriptions originating from machine intelligence planning programs to the mechanization of feedback control of robot arms is analyzed. It is shown in this paper that control theories and practices can be extended to a higher level where feedback control of robot arms directly can respond to work space task commands provided that the work space task as a command is given in the form of a closed function of time. A general mathematical procedure using tools from differential geometry is introduced for synthesizing task space motion planning so that the planned motion can be used as a direct input to the robot arm feedback control system to achieve desired robot hand motion. By definition, 'intelligent control' is being manifested through robot performance in the task space relative to task space commands. Thus, the capability of implementing feedback control of robot arms directly driven by appropriate task descriptions in the workspace as commands is a step toward intelligent control.

Bejczy, A. K.↗
NASA NTRS1987

Quadrupole source in prediction of the noise of rotating blades - A new source description

The aim of this paper is to perform a theoretical study of the quadrupole term of the Ffowcs Williams-Hawkings (FW-H) equation to obtain practical results for applications to rotating blades. The quadrupole term of the FW-H equation is algebraically manipulated into volume, surface and line sources using generalized function theory and differential geometry. The volume source is of the type in Lighthill's jet noise theory. The surface sources are on the blade and shock surfaces and the line source is at the trailing edge. It is shown that contribution of volume sources in the boundary layer and wakes can be written in the form of surface integrals. It is argued that the surface and line sources and the part of the volume sources in the boundary layer, wakes and vortices near the blades should be sufficient in calculation of the noise of high speed rotating blades. The integrals correspoding to the various sources appearing in the formula for calculation of the acoustic pressure are briefly derived.

Farassat, F.↗
NASA NTRS1989

Visual perception and grasping for the extravehicular activity robot

The development of an approach to the visual perception of object surface information using laser range data in support of robotic grasping is discussed. This is a very important problem area in that a robot such as the EVAR must be able to formulate a grasping strategy on the basis of its knowledge of the surface structure of the object. A description of the problem domain is given as well as a formulation of an algorithm which derives an object surface description adequate to support robotic grasping. The algorithm is based upon concepts of differential geometry namely, Gaussian and mean curvature.

Starks, Scott A.↗
NASA NTRS1992

Diffracted and head waves associated with waves on nonseparable surfaces

A theory is presented for computing waves radiated from waves on a smooth surface. With the assumption that attention of the surface wave is due only to radiation and not to dissipation in the surface material, the radiation coefficient is derived in terms of the attenuation factor. The excitation coefficient is determined by the reciprocity condition. Formulas for the shape and the spreading of the radiated wave are derived, and some sample calculations are presented. An investigation of resonant phase matching for nonseparable surfaces is presented with a sample calculation. A discussion of how such calculations might be related to resonant frequencies of nonseparable thin shell structures is included. A description is given of nonseparable surfaces that can be modeled in the vector that facilitates use of the appropriate formulas of differential geometry.

Barger, Raymond L.↗
NASA NTRS1992

A basis for solid modeling of gear teeth with application in design and manufacture

A new approach to modeling gear tooth surfaces is discussed. A computer graphics solid modeling procedure is used to simulate the tooth fabrication process. This procedure is based on the principles of differential geometry that pertain to envelopes of curves and surfaces. The procedure is illustrated with the modeling of spur, helical, bevel, spiral bevel, and hypoid gear teeth. Applications in design and manufacturing are discussed. Extensions to nonstandard tooth forms, to cams, and to rolling element bearings are proposed.

Huston, Ronald L.↗