Showing papers on "Angular velocity published in 1977"

Present-day plate motions

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.

Spatial Information Capacity of Compound Eyes

Abstract: The capacity of the compound eye to perceive its spatial environment is quantified by determining the number of different pictures that can be reconstructed by its array of retinula cells. We can then decide on the best compromise between an animal's capacity for fine detail and contrast sensitivity. The theory accounts for imperfect optics, photon noise, and angular motion limitations to acuity. 1. There is an optimum parameterp = D Δ φ, whereD is the facet diameter andΔ φ is the interommatidial angle, for each mean luminance, angular velocity and mean object contrast. We find that this value ofp is approximately that found by Snyder (1977) for threshold resolution of a sinusoidal grating at the ommatidial sampling frequency. 2. A diffraction limited eye (D Δ φ ≅λ/√¯3) is the optimum design only for those animals that are active in the brightest sunlight, and have a region of their eye that normally experiences low angular velocity, otherwise it is better to have a largerD Δ φ. λ is the wavelength of light in vacuum. 3. The design of the flyMusca is consistent with that of an animal with high angular velocity.

On the angular momentum loss of late-type stars

Abstract: The observed surface angular velocity of main-sequence stars shows a sharp decrease at about spectral type F6. It is suggested that stars more massive than F6 cannot experience an appreciable angular-momentum loss because their convection zones cannot sustain a magnetic dynamo: without a magnetic field the angular-momentum loss is very small. The influence of rotation on the convective motions is essential for the existence of a solar-type dynamo. Rotation can influence these convective motions only if the typical convective time is larger than the rotation time. For main-sequence stars of different masses and chemical compositions the dimensionless parameter (convective velocity/sum's angular velocity times mixing length in the lower part of the convection zone) is evaluated. It is shown that this parameter increases very sharply for stars whose mass exceeds that defined by the relation log(star mass/solar mass) is of the order of 0.1. Thus even for large angular velocities, magnetic dynamos are not feasible if log(star mass/solar mass) appreciably exceeds 0.1.

The balance of energy in earthquake faulting

Abstract: Summary An earthquake is modelled kinematically by specifying the tangential slip history on a fault surface which expands within a uniformly rotating, self-gravitating, slightly anelastic earth model. The total amount of energy released by such an idealized earthquake is the sum of three distinct quantities: kinetic energy of rotation, gravitational potential energy and thermodynamic elastic internal energy. The first two of these quantities may also be interpreted as the work done throughout the earth model against the action of the apparent centrifugal and real gravitational body forces respectively. The total energy released by an earthquake fault is in general considerably smaller than any of its three individual constituents, since the work performed against body forces is very nearly balanced by the work performed against the initial hydrostatic pressure in the earth model. The smallest individual constituent is the change in the kinetic energy of rotation of the earth model, which may be as much as two orders of magnitude larger than the total energy released, even though the corresponding change in the angular velocity of rotation due to the redistribution of mass is extremely small. The total energy released by an earthquake fault may also be expressed in terms only of the final static displacement and the initial and final static traction on the fault surface itself. This alternative representation of the energy change is explicitly independent of both the rotation and the self-gravitation of the earth model. All of the energy released by an earthquake fault must be dissipated somewhere within the earth model. Energy may be dissipated during faulting either in heating on the walls of the fault surface, where work must generally be done against the action of the frictional traction acting to resist slip, or at the instantaneously expanding boundary of the fault surface, where some energy may be required to overcome cohesion and where there may be additional heating. The remainder of the energy released, which is generally referred to as the seismic energy, is dissipated both during and subsequent to faulting by the slight bodily friction which must be assumed to exist throughout the entire volume of any physically realizable earth model. The seismic energy may also be expressed in terms only of the displacement and incremental traction histories on the instantaneous fault surface during the course of faulting. This alternative representation of the seismic energy is explicitly independent of both the rotation and the self-gravitation of the earth model, and so therefore is the seismic efficiency, which is defined to be the ratio of the seismic energy to the total energy released. Classical formulae for the total energy released by an earthquake fault, the seismic energy and the seismic efficiency are based not only upon the neglect of rotation and self-gravitation, but also upon the assumption that the initial hydrostatic pressure and deviatoric stress are infinitesimal quantities; those classical formulae, upon which many seismological applications depend, are justified if the initial deviatoric stress at the hypocentre is small compared to the hypocentral rigidity.

The effect of dissipation on the gas response to oval distortions of disk galaxies.

Abstract: The time-dependent response of a ensemble of noninteracting test particles to a rotating oval distortion of a realistic axisymmetric galactic disk is numerically calculated for several assumed values of the distortion angular velocity. The test-particle response is found to be barlike and to strongly reinforce the imposed perturbation if the angular velocity of the distortion permits only one inner Lindblad resonance. The calculations are then repeated, with the mass of each particle distributed over some sufficiently large volume. In such a representation, the test particles become fluid elements in a Lagrangian sense, and an artificial viscosity may be defined in the usual manner. If this bulk viscosity is the only gas dynamical effect considered, the ''gas'' responds to the rotating oval distortion by forming a material bar inside the inner resonance and trailing spiral density waves beyond the resonance. It is only the dissipation provided by the artificial viscosity which distinguishes the bar response of the stars from the bar-plus-spiral-density waves of the gas response.

Relativistically rotating dust cylinders

Abstract: A previously derived method for obtaining the general differentially rotating dust metric is applied to the cylindrically symmetric case. The dust metric, the exterior vacuum metric, the matching conditions at the boundary, and the asymptotic behavior at infinity are worked out explicitly. As a special case, the solutions include van Stockum’s rigidly rotating models. Inertial dragging effects are found to be enhanced when the angular velocity decreases outward so that the angular momentum is concentrated near the axis. In the extreme relativistic case, the null cones emanating from points on the axis develop a caustic surface at which they turn around and eventually refocus at the axis. However, this is associated with acausal behavior rather than horizons.

First-Order Torques and Solid-Body Spinning Velocities in Intense Sound Fields.

Abstract: The letter reports an observation of first-order nonzero time-averaged torques and solid-body spinning velocities in intense acoustic fields. The experimental apparatus consisted of a vertical cylindrical rod supported on an air bearing and passing through a box with two loudspeakers centered on adjoining vertical sides. The rim velocity of the cylinder and the torque on the cylinder are measured as functions of air-particle velocity and the phase difference between the x and y components of the particle velocity. It is found that both rim velocity and torque are linear functions of particle velocity. Difficulties in constructing a proper theoretical description of the observed effects are discussed.

Internal waves in the earth's core

Abstract: Summary. This paper investigates possible long-period oscillations of the earth’s fluid outer core. Equations describing free oscillations in a stratified, self-gravitating, rotating fluid sphere are developed using a regular perturbation on the equations of hydrodynamics. The resulting system is reduced to a finite set of ordinary differential equations by ignoring the local horizontal component of the earth’s angular velocity vector, S2, and retaining only the vertical component. The angular dependence of the eigensolutions is described by Hough functions, which are solutions to Laplace’s tidal equation. The model considered here consists of a uniform solid elastic mantle and inner core surrounding a stratified, rotating, inviscid fluid outer core. The quantity which describes the core’s stratification is the Brunt-Vaigla frequency N, and for particular distributions of this parameter, analytical solutions are presented. The interaction of buoyancy, and rotation results in two types of wave motion, the amplitudes of which are confined predominantly to the outer core: (1) internal gravity waves which exist when N2 > 0, and (2) inertial oscillations which exist when N2 < 4Q2. For a model with a stable density stratification similar to that proposed by Higgins & Kennedy (1971), the resulting internal gravity wave eigenperiods are all at least 8 hr, and the fundamental modes have periods of at least 13 hr. A model with an unstable density stratification admits no internal gravity waves but does admit inertial oscillations whose eigenperiods have a lower bound of 12 hr.

Electronic balancer for vehicle wheels

Abstract: This invention is directed to an off-the-vehicle type of wheel-tire balancer for vehicular wheels. A wheel and tire assembly which is to be balanced is disposed on a rotating shaft under the control of a signal responsive electronic control apparatus utilizing rotational velocity signals, rotational, directional, and positional signals and velocity of displacement of the mounting apparatus for the shaft to provide a suitably calibrated indicators, the amount of weight to be added at certain angular positions on the inner and outer planes of the wheel rim to provide a dynamic balance of the wheel-tire system. Further indicators are provided for relating the indicated weight to be added to an angular position of the wheel and tire system. The entire apparatus is automatic in operation in that once the system is started, a motor is energized to rapidly rotate the wheel-tire system up to a predetermined rotational velocity. Once this is attained, the magnitude and angular disposition of the weights to be disposed on the rims of the wheel-tire system is rapidly detected over but a few revolutions of the shaft and following this, the motor is energized in a reverse direction to provide a dynamic breaking force to rapdily bring the wheel-tire system to a rest position, the energization of the motor in the reversed direction being maintained until the shaft is actually reversed its direction of rotation for a predetermined angular displacement.

The use of angles and angular rates

Abstract: MIT's Lincoln Laboratory has developed a computer driven, rapidly slewing (≃4° s−1), electro-optical (≃3″ resolution) telescope. This enables the rapid measurement of angles and instantaneous angular rates for artificial satellites. The simultaneous acquisition of angles and angular rates constitutes a new initial orbit problem which has been solved. Three different methods of solution are presented including an exact, analytical one. Numerical tests on six widely different satellite orbits indicate that the topocentric distance can be determined to better than 1% (and usually as well as 0.1%) for most satellites after a 5–10 min observation interval.

Convection in a rotating deep compressible spherical shell: application to the sun

Abstract: In this paper we study the interaction of rotation with convection in a deep compressible spherical shell as the Sun's convection zone. We examine how the energy transport and the large scale motions can be affected by rotation. In particular we study how a large scale meridional circulation can give rise to variations of angular velocity with latitude and depth.

Combined effects of free and forced convection on magnetohydrodynamic flow in a rotating channel

Abstract: The steady flow in a channel rotating with an angular velocity\(\vec \Omega \) and subjected to a constant transverse magnetic field is analysed. An exact solution of the governing equations is obtained. The solution in the dimensionless form contains three parameters: the Grash of number,G, the Hartmann number,M 2 and the rotation parameter,K 2. The effects of these parameters on the velocity and magnetic field distributions are studied. For large values ofK 2 andM 2, there arise thin boundary layers on the walls of the channel which may be identified as the Ekman-Hartmann layers.

Slow steady rotation of an axially symmetric body in a micropolar fluid

Abstract: This paper examines the Stokes' flow due to an axially symmetric body rotating about its axis of symmetry in a micropolar fluid which sustains anti-symmetric stress and couple stress. General solutions are obtained to the coupled differential equations governing such a flow and the special case of a sphere is deduced. Then, with the aid of a concentrated couple, a simple formula for the couple experienced by a body is derived in terms of the angular velocity of the flow field.

Device for tilting the body of a high-speed vehicle relative to an underframe thereof

Abstract: A tilting arrangement for a vehicle with the aid of which a body of the vehicle is adjustable in a roll direction relative to an underframe of the vehicle to compensate for centrifugal force exerted in curves on subjects resting on the body is controlled by a control signal which is produced with the aid of a device comprising a speedometer and a gyro arrangement for producing signals which are representative of the travelling velocity and the yaw angular velocity of the vehicle as well as the roll angular velocity and the roll angle of either one of said parts of the vehicle. The signals are combined to produce a control signal the magnitude of which is representative of the expression |m.V.θ gir |-|k.g.θ roll |, and has a sign, plus or minus, determined by the sign of the signal representative of θ roll , in which expression V is the travelling velocity of the vehicle, θ gir is the yaw angular velocity of the vehicle, θ roll is the roll angle of either of said parts of the vehicle, and m and k are each coefficients normally equalling 1 for full compensation of the centrifugal force exerted on subjects resting on the vehicle body.

Rotational correlations in rough sphere fluids

Abstract: The coupling of the angular velocity of a test rough sphere to the collective modes of the surrounding bath of rough spheres is studied as a function of the mass and diameter of the test sphere using renormalized kinetic theory. As the diameter of the tagged particle increases, the collective contribution to the relaxation changes from a situation where coupling to the fluid transverse angular velocity field dominates to one in which coupling to the transverse linear velocity field dominates. As the mass of the test particle increases, the collective contribution becomes increasingly sensitive to the nonhydrodynamic states which appear in the kinetic theory. The long time behavior of the angular velocity correlation function and the associated memory kernels are found to have interesting dependence on the test sphere diameter. The results are used to elucidate some features of the hydrodynamic character of microscopic relaxation processes.

Parametric excitation of equilibrium surface ripples on magnetically confined nonneutral plasma columns

Abstract: The parametric excitation of equilibrium surface ripples on a drifting, magnetically confined nonneutral plasma column is investigated by passing it through a spatially periodic magnetic field. Measurements of the relationship between the ripple amplitude and the pump frequency, the number of pump periods, and the pump amplitude verify most of the features predicted theoretically. Measurements also verify the predicted relationship between the rigid rotor angular velocity of the plasma column and the amplitude of these equlibrium ripples. Rotation of the column opposite to the direction that an isolated electron would gyrate in the same magnetic field and rotation at an angular velocity greater than the cyclotron frequency are observed. The relation between the ripple amplitude and the propagation characteristics of space‐charge waves is discussed.

Solar tracking device

Abstract: A solar tracking device constructed in accordance with the present invention includes an azimuthal drive mechanism which utilizes the variable angular velocity of the driven member of a universal joint as the source of power for driving a carriage about a fixed axis at a variable angular velocity corresponding to the variable angular velocity of the sun about the fixed axis. The driving element of the universal joint is mounted on a driving shaft which extends parallel to the axis of rotation of the earth. The altitude control mechanism includes a driving element mounted on the driving shaft which rotates about an axis parallel to the axis of rotation of the earth. The driving element rotates in an equitorial plane whereby its angle of inclination varies in accordance with the variation in altitude of the sun as it rotates in azimuth. A transmission system is provided for connecting the driving element to a tracking head to rotate the tracking head about an axis to track the sun in altitude as the tracking head is driven about the fixed axis in azimuth.

Two-dimensional stochastic motions and the problem of differential rotation

Abstract: This paper deals with the spatial dependence of the angular velocity in a rotating turbulent fluid sphere. The original turbulence unaffected by the global rotation is assumed to be two-dimensional where the stochastic force field producing the turbulence does not possess a radial component. By using results of earlier papers we proceed to the treatment of a rotational rate, Ω, no longer small compared to Ω c (frequency of turbulent mode). It is shown that for Ω≪Ω c the angular velocity increases with increasing radius but no latitudinal dependence exists. Contrary to this, for 2Ω∼Ω c an equatorial acceleration is possible and related to negativity of the two-dimensional eddy viscosity. Furthermore, the outer layers rotate faster than the inner ones. These findings coincide with Gilman's numerical results. Ward's observations, as well as the characteristic scales of supergranulation and giant cells, suggest the presence of negative two-dimensional eddy viscosity on the Sun.

Speed control device for a heavy duty shaft

Abstract: A speed control device characterized by a reference speed shaft spatially related to a heavy duty shaft, a drive train for driving the reference speed shaft at a constant angular velocity, a drive train for driving the heavy duty shaft at a variable angular velocity and a speed control assembly for continuously comparing the angular velocity of the heavy duty shaft with the angular velocity of the reference speed shaft, and a brake assembly connected to the heavy duty shaft adapted to respond to errors in the angular velocity of the heavy duty shaft for reducing the angular velocity of the heavy duty shaft to that of the reference speed shaft.

Acceleration of pulsars by asymmetric radiation. III. Observational evidence

Abstract: The theory of pulsar acceleration by asymmetric radiation predicts that the pulsar velocities ought to be aligned parallel to their spin axes. Assuming that the orientation of the pulsar spin axis in the plane of the sky is determined by the position angle of polarization, this prediction is tested by a comparison of polarization position angles and velocity position angles determined by proper motion measurements for 10 pulsars. Allowing for an ambiguity of 90degree in the angle between the polarization position angle and the projection of the spin axis in the sky which is suggested by single-pulse observations, the data are in excellent agreement with a parallel alignment of velocity and spin axis. The data are not generally in agreement with the angle differences between velocity and spin axis in space having a random distribution or being preferentially near 90degree unless the spin axes are also preferentially in the plane of the sky.

Relation of dipole and angular velocity autocorrelation functions

Abstract: A truncated Mori expansion for the angular velocity autocorrelation function is used as a starting-point to calculate the orientational auto-correlation function for a disk and a sphere using the newly developed methods of Lewis et al. [9]. Assuming the angular velocity to be a gaussian process, one obtains for a spherical top the first few terms of a development in powers of time. In the free rotor and Debye limits this series can be rearranged to agree with the corresponding terms of the expansion in powers of time of the known limiting expressions. A closed form is obtained for the disk which does the same. It becomes clear that this three-variable Kivelson/Keyes formalism [3] when used for the angular velocity is equivalent to the inertia-corrected itinerant oscillator in two dimensions [24]. Thus it is possible now to relate analytically a realistic, oscillatory angular velocity autocorrelation function to a realistic orientational autocorrelation function for the same molecular symmetry.

High-Resolution Shaft Speed Measurements Using a Microcomputer

Abstract: A Motorola 6800 microcomputer has been applied to the measurement of instantaneous angular velocity at one degree intervals on a pair of coupled shafts. Velocity is determined by accurately measuring the time intervals between pulses produced by shaft encoders. Variations in relative velocity can be detected when precision timing is available. Using an essentially software approach time can be measured in 30-?s increments. The number of instructions in the timing loop can be reduced by adding a small amount of hardware to permit parallel data acquisition. Time increments of 12?s were obtained using inputs from two shafts. The results of measurements on a pair of shafts coupled by noncircular gears is included as an example.