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Angular velocity

About: Angular velocity is a(n) research topic. Over the lifetime, 13545 publication(s) have been published within this topic receiving 155253 citation(s). The topic is also known as: angular speed.

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01 Nov 1977
Abstract: A data set comprising 110 spreading rates, 78 transform fault azimuths, and 142 earthquake slip vectors has been inverted to yield a new instantaneous plate motion model, designated Relative Motion 2 (RM2). The model represents a considerable improvement over our previous estimate, RM1 [Minster et al., 1974]. The mean averaging interval for the spreading rate data has been reduced to less than 3 m.y. A detailed comparison of RM2 with angular velocity vectors which best fit the data along individual plate boundaries indicates that RM2 performs close to optimally in most regions, with several notable exceptions. The model systematically misfits data along the India-Antarctica and Pacific-India plate boundaries. We hypothesize that these discrepancies are manifestations of internal deformation within the Indian plate; the data are compatible with northwest-southeast compression across the Ninetyeast Ridge at a rate of about 1 cm/yr. RM2 also fails to satisfy the east-west trending transform fault azimuths observed in the French-American Mid-Ocean Undersea Study area, which is shown to be a consequence of closure constraints about the Azores triple junction. Slow movement between North and South America is required by the data set, although the angular velocity vector describing this motion remains poorly constrained. The existence of a Bering plate, postulated in our previous study, is not necessary if we accept the proposal of Engdahl and others that the Aleutian slip vector data are biased by slab effects. Absolute motion models are derived from several kinematical hypotheses and compared with the data from hot spot traces younger than 10 m.y. Although some of the models are inconsistent with the Wilson-Morgan hypothesis, the overall resolving power of the hot spot data is poor, and the directions of absolute motion for the several slower-moving plates are not usefully constrained.

1,999 citations

Journal ArticleDOI
Abstract: The transform fault concept is extended to a spherical surface. The earth's surface is considered to be made of a number of rigid crustal blocks. It is assumed that each block is bounded by rises (where new surface is formed), trenches or young fold mountains (where surface is being destroyed), and great faults, and that there is no stretching, folding, or distortion of any kind within a given block. On a spherical surface, the motion of one block (over the mantle) relative to another block may then be described by a rotation of one block relative to the other block. This rotation requires three parameters, two to locate the pole of relative rotation and one to specify the magnitude of the angular velocity. If two adjacent blocks have as common boundaries a number of great faults, all of these faults must lie on ‘circles of latitude’ about the pole of relative rotation. The velocity of one block relative to the other must vary along their common boundary; this velocity would have a maximum at the ‘equator’ and would vanish at a pole of relative rotation. The motion of Africa relative to South America is a case for which enough data are available to critically test this hypothesis. The many offsets on the mid-Atlantic ridge appear to be compatible with a pole of relative rotation at 62°N (±5°), 36°W (±2°). The velocity pattern predicted by this choice of pole roughly agrees with the spreading velocities determined from magnetic anomalies. The motion of the Pacific block relative to North America is also examined. The strike of faults from the Gulf of California to Alaska and the angles inferred from earthquake mechanism solutions both imply a pole of relative rotation at 53°N (±3°), 53°W (±5°). The spreading of the Pacific-Antarctic ridge shows the best agreement with this hypothesis. The Antarctic block is found to be moving relative to the Pacific block about a pole at 71°S (±2°), 118°E (±5°) with a maximum spreading rate of 5.7 (±0.2) cm/yr. An estimate of the motion of the Antarctic block relative to Africa is made by assuming closure of the Africa-America-Pacific-Antarctica-Africa circuit and summing the three angular velocity vectors for the cases above.

1,049 citations

Journal ArticleDOI
Abstract: The splitting of the frequencies of the global resonant acoustic modes of the Sun by large-scale flows and rotation permits study of the variation of angular velocity Ω with both radius and latitude within the turbulent convection zone and the deeper radiative interior. The nearly uninterrupted Doppler imaging observations, provided by the Solar Oscillations Investigation (SOI) using the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft positioned at the L1 Lagrangian point in continuous sunlight, yield oscillation power spectra with very high signal-to-noise ratios that allow frequency splittings to be determined with exceptional accuracy. This paper reports on joint helioseismic analyses of solar rotation in the convection zone and in the outer part of the radiative core. Inversions have been obtained for a medium-l mode set (involving modes of angular degree l extending to about 250) obtained from the first 144 day interval of SOI-MDI observations in 1996. Drawing inferences about the solar internal rotation from the splitting data is a subtle process. By applying more than one inversion technique to the data, we get some indication of what are the more robust and less robust features of our inversion solutions. Here we have used seven different inversion methods. To test the reliability and sensitivity of these methods, we have performed a set of controlled experiments utilizing artificial data. This gives us some confidence in the inferences we can draw from the real solar data. The inversions of SOI-MDI data have confirmed that the decrease of Ω with latitude seen at the surface extends with little radial variation through much of the convection zone, at the base of which is an adjustment layer, called the tachocline, leading to nearly uniform rotation deeper in the radiative interior. A prominent rotational shearing layer in which Ω increases just below the surface is discernible at low to mid latitudes. Using the new data, we have also been able to study the solar rotation closer to the poles than has been achieved in previous investigations. The data have revealed that the angular velocity is distinctly lower at high latitudes than the values previously extrapolated from measurements at lower latitudes based on surface Doppler observations and helioseismology. Furthermore, we have found some evidence near latitudes of 75° of a submerged polar jet which is rotating more rapidly than its immediate surroundings. Superposed on the relatively smooth latitudinal variation in Ω are alternating zonal bands of slightly faster and slower rotation, each extending some 10° to 15° in latitude. These relatively weak banded flows have been followed by inversion to a depth of about 5% of the solar radius and appear to coincide with the evolving pattern of torsional oscillations reported from earlier surface Doppler studies.

916 citations

Journal ArticleDOI
TL;DR: A new quaternion-based feedback control scheme for exponential attitude stabilization of a four-rotor vertical takeoff and landing aerial robot known as a quadrotor aircraft is proposed and the model-independent PD controller, without compensation of the Coriolis and gyroscopic torques, provides asymptotic stability for the problem.
Abstract: In this paper, we propose a new quaternion-based feedback control scheme for exponential attitude stabilization of a four-rotor vertical takeoff and landing aerial robot known as a quadrotor aircraft. The proposed controller is based upon the compensation of the Coriolis and gyroscopic torques and the use of a PD/sup 2/ feedback structure, where the proportional action is in terms of the vector quaternion and the two derivative actions are in terms of the airframe angular velocity and the vector quaternion velocity. We also show that the model-independent PD controller, where the proportional action is in terms of the vector-quaternion and the derivative action is in terms of the airframe angular velocity, without compensation of the Coriolis and gyroscopic torques, provides asymptotic stability for our problem. The proposed controller as well as some other controllers have been tested experimentally on a small-scale quadrotor aircraft.

913 citations

Journal ArticleDOI
Abstract: The evolution of rotating stars with zero-age main-sequence (ZAMS) masses in the range 8-25 M☉ is followed through all stages of stable evolution. The initial angular momentum is chosen such that the star's equatorial rotational velocity on the ZAMS ranges from zero to ~ 70% of breakup. The stars rotate rigidly on the ZAMS as a consequence of angular momentum redistribution during the pre-main-sequence evolution. Redistribution of angular momentum and chemical species are then followed as a consequence of Eddington-Sweet circulation, Solberg-Hoiland instability, the Goldreich-Schubert-Fricke instability, and secular and dynamic shear instability. The effects of the centrifugal force on the stellar structure are included. Convectively unstable zones are assumed to tend toward rigid rotation, and uncertain mixing efficiencies are gauged by observations. We find, as noted in previous work, that rotation increases the helium core masses and enriches the stellar envelopes with products of hydrogen burning. We determine, for the first time, the angular momentum distribution in typical presupernova stars along with their detailed chemical structure. Angular momentum loss due to (nonmagnetic) stellar winds and the redistribution of angular momentum during core hydrogen burning are of crucial importance for the specific angular momentum of the core. Neglecting magnetic fields, we find angular momentum transport from the core to the envelope to be unimportant after core helium burning. We obtain specific angular momenta for the iron core and overlying material of 1016-1017 cm2 s-1. These values are insensitive to the initial angular momentum and to uncertainties in the efficiencies of rotational mixing. They are small enough to avoid triaxial deformations of the iron core before it collapses, but could lead to neutron stars which rotate close to breakup. They are also in the range required for the collapsar model of gamma-ray bursts. The apparent discrepancy with the measured rotation rates of young pulsars is discussed.

891 citations

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