Showing papers on "Angular velocity published in 1969"

Pathological oscillations of a rotating fluid

Abstract: A theoretical study is made of the free periods of oscillation of an incompressible inviscid fluid, bounded by two rigid concentric spheres of radii a, b (a > b), and rotating with angular velocity Ω about a common diameter. An attempt is made to use the Longuet-Higgins solution of the Laplace tidal equation as the first term of an expansion in powers of the parameter e = (a − b)/(a + b), of the solution to the full equations governing oscillations in a spherical shell. This leads to a singularity in the second-order terms at the two critical circles where the characteristic cones of the governing equation touch the shell boundaries.A boundary-layer type of argument is used to examine the apparent non-uniformity in the neighbourhood of these critical circles, and it is found that, in order to remove the singularity in the pressure, an integrable singularity in the velocity components must be introduced on the characteristic cone which touches the inner spherical boundary. Further integrable singularities are introduced by repeated reflexion at the shell boundaries, and so, even outside the critical region the velocity terms contain what may reasonably be described as a pathological term, generally of order e½ compared to that found by Longuet-Higgins, periodic with wavelength O(ea) in the radial and latitudinal directions.Some consequences of this result are discussed.

On the optimal angular velocity control of asymmetrical space vehicles

Abstract: The problem of reducing the angular velocities of a space vehicle to zero is considered. The required control torques are found as functions of the angular momenta. Both linear and nonlinear time-invariant feedback control systems are determined. The method of solution is based on the "inverse problem" of optimal control.

Digital Instrumentation for Angular Velocity and Acceleration

Abstract: An instrument is described for the measurement of angular velocity and angular acceleration of a rotating shaft, based upon an optical angular transducer and an associated operational digital (pulse rate) system. The angular transducer produces a pulse rate directly proportional to the instantaneous angular velocity and this quantity and its rate of change are processed by the pulse rate system and presented as parallel binary-coded decimal representations driving in-line digital displays. The operational digital system comprises essentially an electronic register controlling a variable rate pulse generator that tracks the input pulse rate in a frequency lock loop. Changes of loop frequency are brought about by changing the register contents by positive or negative correction pulses, and the rate at which these are supplied provides an accurate measure of acceleration or deceleration, respectively, provided that the loop is locked on and hence follows the changes of input pulse rate accompanying changes of angular velocity. The error correction pulse rate may be measured in a second frequency lock loop and the registers in the two loops used to control digital in-line decimal displays of angular velocity and acceleration, of ranges up to 10 000 r/min (±1 r/min) and 1000 r/min/s (±1 percent), respectively.

On the Differential Rotation with Height in the Solar Atmosphere

Abstract: Spectroscopic measurements of solar rotation having good height discrimination show no change in angular velocity through the photosphere layers but an increase of 8% for the Hα chromosphere (epoch 1968.9). Spectroscopic results in general are compared with measures made with tracers, i.e. sunspots, filaments, etc., and it is seen that the spectroscopic method always shows increased differential rotation with height, while tracers indicate none. A westward flowing wind is proposed that increases in velocity with height, but produces negligible movement to magnetic regions associated with tracers.

Magnetohydrodynamic flow between rotating coaxial disks.

Abstract: This is a study of the magnetohydrodynamic flow of an incompressible viscous fluid between coaxial disks, with a uniform axial magnetic field B. The fluid has density ρ, viseosity η and electrical conductivity σ. The flow is assumed to be steady, and to be similar in the sense that the radial and tangential components of velocity increase linearly with radial distance from the axis of rotation. Most of the work is concerned with disks which are electrical insulators, one of which rotates while the other remains stationary. The imposed conditions can then be represented by the Reynolds number R = ρΩad2/η and the Hartmann number M2 = σB2d2/η, where Ωa is the angular velocity of the rotating disk and d is the gap between the disks. Asymptotic solutions are given for R [Lt ] M2, and numerical solutions are obtained for values of R and M2 up to 512. Experimental measurements are presented which are in general agreement with the theoretical flows, and the results for small values of the Hartmann number provide the first known experimental support for the purely hydrodynamic solutions in the range 100 < R < 800.

Apparatus for indicating changes in angular velocity, and vehicle braking systems employing such apparatus

Abstract: An apparatus for indicating changes in the angular velocity of a rotating body subjected to acceleration or deceleration, e.g. an automobile, has a velocity sensor producing an output having a frequency proportional to the angular velocity, a frequency-to-DC converter, a differentiator, a comparator for comparing the differentiated signal with a reference signal and for producing an output signal whenever the signals compared differ by a predetermined magnitude, which may be indicative of the onset of wheel-locking, and an actuator for reducing the deceleration (braking force) on the body in response to the comparator output signal.

Stability in the three dimensional whirling problem

Abstract: Mathematical model for studying three dimensional whirling shaft stability as function of angular to critical velocity ratio, using Liapunov method for equations of motion

Surface speed control of spindle-related numerical control system

Abstract: In a numerical control system having apparatus for controlling feedrate as a function of spindle speed (angular velocity), a spindle encoder provides a train of basic feed pulses at a frequency fo as a function of spindle speed. Surface speed of a cutting tool over a workpiece is controlled to a value programmed in linear units where the spindle provides relative rotary motion between the tool and the workpiece by multiplying the frequency fo by the absolute command position of the tool along an axis perpendicular to the axis of rotation of the spindle, and comparing the resulting product with a train of pulses at a frequency that is a function of programmed surface speed. Any difference drives a bidirectional counter in a direction corresponding to the sign of the difference. A digital-to-analog converter couples the output of the bidirectional counter to a spindle drive mechanism to bring the actual surface speed into agreement with the desired surface speed.

The precession and nutation of deformable bodies, III

Abstract: In preceding papers of this series (Kopal, 1968; 1969) the Eulerian equations have been set up which govern the precession and nutation of self-gravitating fluid globes of arbitrary structures in inertial coordinates (space-axes) as well as with respect to the rotating body axes; with due account being taken of the effects arising from equilibrium as well as dynamical tides. In Section 1 of the present paper, the explicit form of these equations is recapitulated for subsequent solations. Section 2 contains then a detailed discussion of the coplanar case (in which the equation of the rotating configuration and the plane of its orbit coincide with the invariable plane of the system); and small fluctuations in the angular velocity of axial rotation arising from the ‘tidal breathing’ in eccentric binary systems are investigated. In Section 3, we consider the angular velocity of rotation about theZ′-axis to be constant, but allow for finite inclination of the equator to the orbital plane. The differential equations governing such a problem are set up exactly in terms of the time-dependent Eulerian angles θ and ϕ, and their coefficients averaged over a cycle. In Section 4, these equations are linearized by the assumption that the inclinations of the equator and the orbit to the invariable plane of the system are small enough for their squares to be negligible; and the equations of motion reduced to their canonical form. The solution of these equations — giving the periods of precession and nutation of rotating components of close binary systems, as well as the rate of nodal regression which is synchronised with precession — are expressed in terms of the physical properties of the respective system and of its constituent components; while the concluding Section 6 contains a discussion of the results, in which the differences between the precession and nutation of rigid and fluid bodies are pointed out.

Spin Down of Boussinesq Fluid in a Circular Cylinder

Abstract: A response of viscous heat-conducting compressible fluid to an abrupt change of angular velocity of a containing circular cylinder under the existence of stable distribution of the temperature is investigated within the frame work of Boussinesq approximation for the time duration of the order of the incompressible spin down time. The coexistence of a horizontal intermediate adjusting layer together with the Ekman layer is clarified as a characteristic feature of unsteady motion. The asymptotic amount of the total angular momentum transferred to the main bulk of the fluid is investigated in detail, and it is shown that the spin down phenomenon similar to that in the incompressible fluid does occur even for cases which are classified as compressibility dominant according to the behavior of steady motion.

Adiabatic transverse modes in a uniformly rotating fluid

Abstract: The two-dimensional adiabatic transverse normal modes of an inviscid compressible fluid, having solid body rotation about the axis of its cylindrical container, are considered. Relative to the rotating fluid there are two trains of harmonic waves, propagating in opposite directions. The first five modes of the first-order harmonic wave and the first mode of the harmonic waves of order two, five, ten, fifteen and twenty have been considered. The period and amplitude of the waves is considerably modified by the rotation. Relative to a fixed coordinate system the angular velocity of the waves initially propagating in the same direction as the rotating fluid, is larger than that of the waves propagating in the opposite direction, as might be expected. However, in the case of the first mode, relative to the rotating fluid, the waves propagating in the opposite direction are the faster.

A set of r dynamical attitude equations for an arbitrary n-body satellite having r rotational degrees of freedom

Abstract: A technique is developed for explicitly eliminating the constraint torques from a canonical system of n vector equations for the attitude dynamics of a satellite consisting of n arbitrarily interconnected rigid bodies. This elimination reduces the number of scalar second order differential equations from 3n to r, the number of degrees of rotational freedom of the satellite. At the same time, the number of dependent variables in these equations is reduced from the full set of 3n angular velocity components to just 3 such components for one body, together with r — 3 relative angular rates. This elimination and reduction saves computer time when the equations are integrated, and also avoids a possible build-up of numerical errors violating the constraints. The final equations resemble those obtained from a Lagrangian approach, but are simpler to derive and to modify to account for additional effects.

Spin-up of a contained fluid.

Abstract: : When a container filled with fluid rotates uniformly, the fluid ultimately reaches a state of rigid body rotation with the same angular velocity as the container. The process whereby the fluid changes its angular velocity from an initial value to a final one when the walls of the container are given a corresponding change is called spin-up (or spin-down if the final angular speed is less than the initial one). In a more general sense, the spin-up process is involved in the approach to steady state of all contained fluid motions in which the final state is dominated by rotation. In all spin-up phenomena, the steady state is reached not by viscous diffusion but by an internal circulation produced by the Ekman layer suction. We have shown previously that the time constant associated with the decay of motion in a contained fluid is proportional to squared root of E, where E is the Ekman number. The characteristic time for viscous diffusion, on the other hand, is proportional to E and since in most applications E is very small, a time scale of order square root of E is much shorter than one of order E. Spin-up is therefore the more effective of two mechanisms. (Author)

Theory of rotational Brownian motion

Abstract: The correlation function for the angular velocity of a Brownian particle suspended in a liquid is analyzed with an account of the viscous aftereffect. The main term in the asymptotic exression for this function is equal to the eddy correlation function for the translational velocity of a liquid found from the Navier-Stokes equations.

Simple Model for a Rotating Neutral Planetary Exosphere

Abstract: Neutral exosphere model for nonrotating planet permitting barosphere uniform rotation at certain angular velocity, determining velocity distribution and density

Electromagnetic system for scaling frequencies which are proportional to the angular velocities of selected rotating shafts

Abstract: Electromagnetic system for providing a reading proportional to the instantaneous angular velocity of any one of a plurality of rotating shafts. Each of the shafts rotates a disc which has a predetermined number of apertures distributed thereabout to consequently vary the reluctance in a magnetic flux path thereby generating an alternating voltage having a frequency proportional to both the number of apertures and the angular velocity of the shaft. The number of apertures in each disc can be selected to provide frequency scaling. Any one of the alternating voltages can be coupled to an indicating device which develops the reading.

Secondary Flow in a Rotating Straight Annular Channel

Abstract: When an incompressible liquid flows under the action of a constant pressure gradient through a channel of arbitrary cross section rotating with a uniform angular velocity about an axis perpendicular to the channel, secondary flow is set up. The secondary flow is examined, assuming the channel to be the annulus between two concentric circles. It is shown that the secondary motion may be regarded as screw motion in opposite directions about two pairs of straight lines passing through four degenerate points lying on the axis of rotation. The stream lines in the central plane are discussed and an expression for the rate of flow is obtained .The results of Barua are recovered as a particular case for a single channel of circular cross section.

Angular rate sensor

Abstract: AN APPARTUS FOR MEASURING ANGULAR VELOCITY ABOUT ONE OR MORE AXES COMPRISING AN ANGULAR ACCELEROMETER ROTATED SO THAT THE ANGLE BETWEEN ITS SENSITIVE AXIS AND MEASUREMENT AXIS VARIES WITH TIME. THIS RELATIVE MOTION CAUSES THE ANGULAR ACCELEROMETER TO EXPERIENCE A TIME-VARYING ANGULAR RATE, I.E., ACCELERATION, ABOUT ITS SENSITIVE AXIS, WITH A COMPONENT OF ITS OUTPUT INDICATIVE OF THE RATE EXISTING ABOUT THE MEASUREMENT AXIS. THE OUTPUT OF THE FUNDAMETAL DEVICE IS MODULATED BY APPROPRIATE MEANS TO SELECT THE DESIRED COMPONENT.

An actuator-disk model for azimuthally nonuniform MPD arcs.

Abstract: Recent experiments have shown that, under some conditions of operation, the current pattern in an MPD arc is azimuthally nonuniform and rotates with a constant angular velocity, which increases with current and applied magnetic field but decreases with propellant mass flow rate. A model for such a flow is proposed which is based on the physical assumption that the current flows in a single column and upon the mathematical assumption that azimuthal averages of mass, momentum, and energy fluxes are time-in variant. The model is thus analogous to the actuator disk model, which describes the flow induced by a propeller. Additional hypotheses are made concerning flow properties and arc motion which are based on a limited experimental and theoretical understanding of magnetically balanced arc columns. A dimensionless correlation of all existing experimental measurements is derived and a criterion for the existence of current spokes is suggested.

Slide drive mechanism for a press

Abstract: A SLIDE DRIVE MECHANISM FOR A PRESS IN WHICH A SLIDE ACTUATING SHAFT IS PROVIDED WITH AN ECCENTRIC SHEAVE ADAPTED TO CAUSE A CONNECTING ROD CONNECTED TO THE SLIDE OF THE PRESS TO RECIPROCATE. THE SLIDE ACTUATING SHAFT HAS IMPARTED THERETO A NON-CONSTANT ANGULAR VELOCITY MOVEMENT FROM A DRIVE SHAFT WHICH ROTATES AT A CONSTANT ANGULAR VELOCITY AND IMPARTS A NON-CONSTANT ANGULAR VELOCITY ROTATIONAL MOVEMENT TO THE SLIDE VIA AN INTERMEDIATE TRANSMISSION MEANS.

The Rotation of the Solar Atmosphere

Abstract: A model of the solar atmosphere is presented in which we discuss the conservation of angular momentum for the two basic states in which the solar gas can be: namely, either confined by closed field lines or outflowing along open magnetic field lines. It can be shown that the boundary conditions are in general different for these two cases. From this we obtain the results that in the closed configuration the gas can corotate at the solar surface with the magnetic field lines and its angular velocity will then increase with height, whereas for a gas flowing along an open field line the angular velocity will decrease. An exception to the latter case can be found where the open magnetic field lines are strongly nonradial and where the density is a slowly varying function of radius. In such regions the angular velocity may initially increase with height, reach a maximum and then decrease.

Magnitude estimations of coriolis sensations

Abstract: : This investigation was concerned with estimates of the subjective strength of the Coriolis vestibular reaction evoked by 30 deg. lateral head motions at constant angular velocity in the Slow Rotation Room. In the first experiment, a power relation was obtained between geometric mean magnitude estimates of the Coriolis reaction and angular velocity. These estimates tended to be greater when vision was present than in its absence. In both conditions of visual reference, head motions evoking a pitch-forward sensation were more disturbing than those producing a pitch-back sensation. In the second experiment, it was found that the strongest reaction was produced by the return from the left shoulder (counterclockwise rotation), and the next strongest by the return from the right shoulder. Subjective rankings did not differentiate adequately between the strengths of the right and left tilt motions. (Author)

Method and apparatus for determining angular velocity

Abstract: Apparatus is disclosed for determining angular velocity using a resolver and multiplying its stator (orthogonal vector component) signals by signals representing the functions -sin Qt and +cos Qt, combining the products arithmetically, and demodulating the sum signal. The demodulator output is proportional to the magnitude of angular velocity. For a velocity signal with proper sign, the stators are driven by the signals representing the functions -sin Qt and +cos Qt to obtain a signal across a high impedance (constant current) source which, upon compensation for phase shifts introduced by the resolver, is used as a reference in determining the proper sign for a velocity signal. When the stator signals are replaced by orthogonal vector component signals of any vector, rectangular to polar coordinate conversion is achieved. A DC signal proportional to the vector angle is obtained by a circuit which detects the phase difference between the sum signal and the signal representing the function cos Qt.

Device for obtaining a rotating motion with periodically alternating increasing and decreasing angular velocity

Abstract: A DEVICE FOR PRODUCING A ROTATING MOTION WITH PERIODICALLY ALTERNATING INCREASING AND DECREASING ANGULAR VELOCITY INCLUDES A PENDULUM PIVOTALLY MOUNTED ON A DRIVEN SHAFT OF THE DEVICE AND CARRYING A CONTROL MEMBER WHICH IS POSITIVELY COUPLED TO THE DRIVEN SHAFT AND WHICH COOPERATES WITH A FIXED POINT OF THE DEVICE TO CAUSE A PERIODIC SWINGING MOVEMENT OF THE PENDULUM DEPENDENT ON THE SPEED OF THE DRIVEN SHAFT.

Motion in a Schwarzschild Field I. Precession of a Moving Gyroscope

Abstract: A simple hypothesis is used to obtain, in lowest order, the precessional angular velocity of a slowly moving gyroscope in a Schwarzschild gravitational field. The hypothesis is that, at least to first approximation, the motion of the spin vector in a small displacement is the sum of two effects: (1) the motion the spin would have if it moved by parallel transfer in the curved 3-space, and (2) the motion of the spin as calculated directly from the principle of equivalence, treating the gravitational field in the vicinity of the gyroscope as though it were uniform. The precessional angular velocity obtained is in agreement with the general relativistic result. In another paper it will be shown that the same hypothesis also leads to the general relativistic result for the lowest order deflection of light by the central mass. These derivations are useful because they help to show how the motion of the spin vector can be understood from a 3 + 1 dimensional viewpoint.

Assessment of semicircular canal function. Part 2 - Individual differences in subjective angular displacement produced by triangular waveforms of angular velocity

Abstract: : Mean estimates (N = 26) of short arcs of passive whole-body rotation about an Earth-vertical axis were accurate when subjects used a psychophysical procedure that involved counterdisplacement of a pointer on a dial. The required retrospective displacement judgments yielded more accurate mean estimates of angular displacement than were obtained in an earlier experiment which probably involved concurrent velocity matching. The differences in response curves in the various conditions of the two experiments clearly illustrate the importance of attention to psychophysical procedures prior to attempting to develop models of the vestibular endorgans to explain results. The method used in this experiment is sufficient to detect prominent individual differences within a sample of aviation training candidates, and the results obtained thus far indicate high test-retest reliability (r12 = .94). (Author)

Method for Controlling the Operation of Antifriction Bearings and device for Carrying it into effect

Abstract: 1,158,735. Bearings. E. E. KRENTS, E. P. SURKOV, and V. I. BONDARENKO. 16 Dec., 1966 [16 Dec., 1965], No. 56504/66. Heading F2A. [Also in Division GA] A method for controlling the operation of rolling bearings comprises calculating the amount of slip of the rolling bodies in the bearing unit under control with respect to at least one rolling surface and comparing the value thus obtained with a pre-set one, the results of such comparison being the criterion for evaluating the operation of rolling bearings. The value of slip to be pre-set is determined by measuring angular velocities # 1 of the rolling bodies centres and the angular velocity # 2 of at least one rolling surface with respect to the axis of rotation of a reference rolling bearing at the mode of operation under control; by calculating the angular velocity # 3 of the rolling bodies centres with respect to the axis of rotation of the bearing, in the absence of slipping from the geometrical dimensions of the reference bearing and from the measured angular velocity # 2 of the rolling surface with respect to the axis of rotation of said reference bearing; by obtaining the relationship between the measured angular velocity # 1 of the rolling bodies centres with respect to the axis of rotation of a reference bearing operating in the same way as the one to be controlled and the calculated angular velocity # 3 of the rolling bodies centres with respect to the axis of rotation of said reference bearing; by measuring the angular velocities # 4 of the rolling bodies centres and at least one rolling surface of the bearing under control with respect to the axis of rotation of said bearing in the mode of operation under control; and by obtaining the relationship between the measured angular velocity # 4 of the rolling bodies centres of the bearing under control in the mode of operation under control and the calculated angular velocity # 3 of the rolling bodies centres with respect to the axis of rotation of the reference bearing. To determine state of working of the bearing under control a comparison is made between the values # 1 /# 3 and # 4 /# 3 . In the device for controlling the operation of rolling bearings, pick-ups 4, 5 respond to the passage respectively of balls 1 and a mark 8 on the shaft 9 to feed pulses via shapers 10, 11, on the one hand to divider 15 and gate 12, and on the other hand to gate 12 1 , coincidence circuit 19 and circuit 33. The output of the divider 15 feeds a circuit 33 1 whereby the velocities of the balls 1, suitably divided, and of the shaft are shown at 35 1 and 35. The first pulse from 11 passes through coincidence circuit 19 to set triggers 17, 18. 17 Restores coincidence circuit 19 while 18 opens gates 12, 12 1 whereby pulses from 4, 5 are now fed to counters 14, 14 1 . When counter 14 1 has counted off a specified number of rotations of the shaft switch 95 passes a signal to restore trigger 18 so closing gates 12, 12 1 and stopping the counters 14, 14 1 . An indicator 25 which divides the count in 14 by that in 14 1 shows the number of balls 1 which have passed the pick-up 4 per revolution of the shaft. For a finer measurement switches 27-29 are reversed so that several cycles of counter 14 1 take place under the control of a predetermined counter 22 and a timing relay 24.