Showing papers on "Angular velocity published in 1978"

Analysis Strapdown Navigation Using Quaternions

Abstract: A brief review of the theory of strapdown inertial navigation is presented in which the attitude of the sensor box with respect to inertial space is represented by the four-parameter quaternion vector. . A 4X4 matrix R is defined which aids in relating quaternions to direction cosines and facilitates interpretation of the equations for error propagation, which are also derived. In the interpretation, it is shown that the error in the quaternion vector causes aor-(correctable) scale factor error and an equivalent tilt vector error that propagates the same way as the platform tilt vector in a gimbaled system.

Digital method and apparatus for rotating an information storage disc

Abstract: Method and apparatus for rotating an information storage disc about its central axis at a prescribed angular velocity that varies according to the radial position of an optical transducer for recording information thereon, whereby a uniformly high density of information can be recorded over the entire disc. The apparatus includes a register for storing a digital measure of the radius of the current track being recorded by the transducer, along with velocity signal circuitry for producing a disc velocity signal having a frequency inversely proportional to the measure of radius, and a spindle motor servo, responsive to the disc velocity signal, for controlling the angular velocity of the information disc, accordingly. The velocity signal circuitry includes a crystal oscillator, a counter for counting the clock pulses produced by the oscillator, and a digital word magnitude comparator for generating a reset pulse to reset the counter to an initial zero count every time it determines that the count is equal to the digital measure of radius. The disc velocity signal is then derived by frequency dividing the successive reset pulses.

Brownian motion of coupled nonlinear oscillators: Thermalized solitons and nonlinear response to external forces

Abstract: We study the steady-state dynamical behavior of a set of torsion-coupled pendula in the presence of damping, fluctuating thermal torques, and constant applied torque For small applied torque, the average angular velocity of the pendula at low temperature is associated with the motion of thermalized sine-Gordon solitons, and, as the torque is increased, the velocity response becomes strongly nonlinear These results can be used to describe nonlinear response in Josephson transmission lines and weakly pinned one-dimensional charge-density-wave condensates

Flow between a stationary and a rotating disk with suction

Abstract: The equations for the viscous flow between two coaxial infinite disks, one stationary and the other rotating, are solved numerically. The effects of applying a uniform suction through the rotating disk are determined. Initially, the fluid and disks are at rest. The angular velocity of one disk and the amount of suction through it are gradually increased to specific values and then held constant. At large Reynolds numbers R, the equilibrium flow approaches an asymptotic state in which thin boundary layers exist near both disks and an interior core rotates with nearly constant angular velocity. We present graphs of the equilibrium flow functions for R = 104 and various values of the suction parameter a (0 ≤ a ≤ 2). When a = 0, the core rotation rate ωc is 0·3131 times that of the disk. Fluid near the rotating disk is thrown centrifugally outwards. As a increases, ωc increases and the centrifugal outflow decreases. When a > 1·3494, the core rotation rate exceeds that of the disk and the radial flow near the rotating disk is directed inwards. We also present accurate tabular results for two flows of special interest: (i) the flow between a stationary and a rotating disk with no suction (a = 0) and (ii) Bodewadt flow. The latter can be obtained by suitable scaling of the boundary-layer solution near the stationary disk for any a ≥ 0. Since several solutions to the steady-state equations of motion have been reported, the question arises as to whether other solutions to the time-dependent equations of motion with zero initial conditions can be found. We exhibit a rotational start-up scheme which leads to an equilibrium solution in which the interior fluid rotates in a direction opposite to that of the disk.

System for rotating an information storage disc at a variable angular velocity to recover information therefrom at a prescribed constant rate

Abstract: Method and apparatus for recovering information at a substantially constant rate from a rotatable information storage disc. The information is stored on the disc in a plurality of substantially circular and concentrically arranged information tracks, with a substantially uniform recording density, and it is recovered by controllably rotating the disc, relative to a transducer, at an angular velocity substantially inversely proportional to the radius of the corresponding track. The apparatus includes a coarse speed control potentiometer for producing a measure of the radius of the particular information track from which information is being recovered, and fine speed control means for comparing the relative phase angles of a periodic signal in the recovered information and a periodic reference signal and for producing a fine speed control signal proportional to the phase difference. The measure of radius and the fine speed control signal are summed together and coupled to a voltage-controlled oscillator to produce a composite speed control signal, which is coupled to a servo to rotate the disc at a corresponding angular velocity.

The rotation of the Sun

Abstract: Observations of solar rotation are reviewed. There are two basic methods of determining the rotation of the sun. One is to measure the daily or monthly positions of tracers on the surface or in the corona, and the other is to measure line-of-sight velocities with the Doppler effect in spectrum lines. The results of a number of investigations involving both methods are compared. The experimental and interpretational problems associated with observational determinations of solar rotation are reviewed and compared. The theoretical situation in this field is reviewed, including the significance of different rotation rates for surface magnetic features and the solar plasma. The rotation of the solar interior is discussed in terms of both model calculations and recent p mode oscillation rotation rates, which reflect the interior rotation.

Stability of spherical Couette flow in thick layers when the inner sphere revolves

Abstract: A natural generalization of cylindrical Couette flow is the flow of a viscous incompressible liquid between two concentric spheres rotating about the same axis with different angular velocities. As has often been noted, spherical Couette flow is, despite the apparent similarity, considerably more complex than cylindrical flow. It consists of differential rotation about the axis and one- or two-eddy circulation (depending on the ratio between the angular velocities of the two spheres ω = ω2/ω1) in the meridional plane and depends significantly on the Reynolds number Re = ω1r 1 2 and the relative thickness of the layer δ = (r2-r1)/r1 (ω1, ω2 and r1, r2 are the angular velocities and radii of the inner and outer spheres, respectively. The investigation of spherical Gouette flow and its stability has begun relatively recently (within the last 10 years) and has evidently been stimulated by applied problems associated with astro- and geophysics. Because of the great computational difficulties encountered in investigating such flow theoretically, experimental investigations have yielded more extensive and interesting results [1–8], although all the published results refer to the case of rotation of one inner sphere (ω = 0).

Three-dimensional dynamics of protostellar evolution.

Abstract: A three-dimensional finite difference numerical methodology has been developed for self-gravitating, rotating gaseous systems. The fully nonlinear equations for time-varying fluid dynamics are solved by high-speed computer in a cylindrical coordinate system rotating with an instantaneous angular velocity. The time-dependent adiabatic collapse of gravitationally bound, rotating, protostellar clouds is studied for specified uniform and nonuniform initial conditions. Uniform clouds can form axisymmetric, rotating toroidal configurations. If the thermal pressure is high, nonuniform clouds can also collapse to axisymmetric ellipsoids. For low thermal pressures, however, the collapsing cloud is unstable to perturbations. The resulting fragmentation of unstable protostellar clouds is investigated by studying the response of rotating, self-gravitating, equilibrium toroids to nonaxisymmetric perturbations. The detailed evolution of the fragmentation toroid depends upon a nondimensional function of the initial entropy, the total mass in the toroid, the angular velocity of rotation, and the number of perturbation wave-lengths around the circumference of the toroid. For low and intermediate entropies, the configuration develops into corotating components with spiral streamers. In the spiral regions retrograde vortices are observed in some examples. For high levels of entropy, barred spirals can exist as intermediate states of the fragmentation.

Processor for an inertial measurement unit

Abstract: A processor is provided for an inertial measurement unit which computes its angular velocity and translational acceleration in terms of dynamic variables chosen because they uniquely define the motion of the inertial measurement unit in terms of linear combinations of the outputs of the transducers used in the inertial measurement unit. In one embodiment, the processor includes a demodulator for obtaining d.c., in-phase and quadrature sets of signals from the outputs of the transducers, a combining circuit for deriving some of the dynamic variables from the in-phase and quadrature sets of signals, and a microprocessor for transforming the dynamic variables into angular velocity and translational acceleration vectors. The processor is used with a small rugged, precise inertial measurement unit in which vector components are measured by the use of accelerometers fixed in a spinning rotor, at least one of which is off-set from the rotor axis and has a sensitive axis parallel to that of the rotor. This off-set/parallel accelerometer permits obtaining the signs of the angular velocities in addition to their magnitudes such that complete vector components are obtained. In an alternative embodiment, two orthogonally oriented rotor systems are utilized which permits all a.c. signal processing, thereby eliminating the necessity of d.c. measurements. Error isolation and correction are easily accomplished in a specialized combining circuit which simplifies initial alignment of the instrument. Another alternative embodiment employs three rotors and provides complete redundancy.

Tidal Deceleration of the Earth’s Rotation Deduced from Astronomical Observations in the Period A. D. 1600 to the Present

Abstract: Under the action of tidal friction the Earth’s rate of rotation decreases and the Moon’s orbit expands. As the Moon’s orbit expands its orbital velocity decreases, but the orbital angular momentum (the product of the orbital radius and angular velocity) increases, such that the rotational angular momentum lost by the Earth is gained by the Moon’s orbit.

Position control system comprising a digital algebraic adder circuit

Abstract: A system for controllably driving a motor to place a movable element at a position indicated by a command signal from an external source produces, in response to a phase staggered incremental position signal pair, one and the other of two position pulse sequences at a time depending on an instantaneous angular velocity of the motor. Responsive to the command signal and the position pulses, a mode signal is produced to indicate a position control mode while a position error is within a predetermined range and otherwise a velocity control mode. Likewise, a signal is produced that represents at least one reference angular velocity and the position error during the respective modes. Responsive to the position pulses alone, gate pulses are produced either with two different pulse widths depending on the modes or with a single pulse width. During presence of each gate pulse and dependent on the sense of the instantaneous angular velocity indicated by the position pulses, a digital algebraic adder circuit calculates an algebraic sum of the reference angular velocity or the position error and a reference feedback value, which may either be memorized in the system or supplied from the source and may take two digital values depending on the modes. A digital signal representative of the sums and either the reference angular velocity or the position error during presence and absence, respectively, of the gate pulses is converted to an analog signal, which is smoothed and amplified to provide a motor drive signal.

The torque on a rotating disk in the surface of a liquid with an adsorbed film

Abstract: In this paper we consider the problem of calculating the resistive torque on a disk rotating slowly with constant angular speed in the surface of a liquid with an adsorbed surface film. Using the method of complementary representations for generalised axially symmetric potential functions, the boundary-value problem for the azimuthal velocity component is reduced to the solution of a Fredholm integral equation of the second kind. This equation is solved numerically and asymptotically for all values of the ratio of the surface shear viscosity of the film to the viscosity of the substrate fluid, and values calculated for the substrate and film torques on the disk. The results are compared with previous work of Goodrich and his co-workers.

Limited rotation moving iron motor with novel velocity sensing and feedback

Abstract: A device for providing a voltage indicating the angular velocity of rotation of the armature in a limited rotation, polarized, moving iron galvanometer. The device includes a means for providing a first voltage dependent upon the angular velocity of the armature, the self-inductance of the galvanometer drive coil, and the drive current in the drive coil. A compensation coil is magnetically coupled to the drive coil and magnetically isolated from the effects of the rotating armature to provide a second voltage which is dependent upon mutual inductance between the drive and compensation coils and upon the drive current, but is not dependent upon the effects of the rotating armature due to the magnetic isolation of the compensation coil from the armature. A combining means proportionally combines the first and second voltages to provide a voltage indicating the angular velocity of rotation of the armature. The means for providing the first voltage includes either the drive coil, with the first voltage appearing across the drive coil, or a pickoff coil wound coaxially with and adjacent to the drive coil so that the first voltage appears across the pickoff coil and is proportional to the voltage appearing across the drive coil. The velocity signal thus derived is introduced to the drive circuit to provide effective damping.

Apparatus for measuring angular speed

Abstract: Apparatus for measuring the angular velocity and speed of a rotating shaft comprises charge storage elements for storing charge. The charge storage elements are capable of being coupled to the rotating shaft so as to be rotatable about a predetermined axis at an angular speed or velocity related to the speed or velocity of the shaft. A charging brush and discharging brush are positioned relative to the charge storage elements so that the charging brush can charge the charge storage elements at a first predetermined angular position of the latter about the axis and the discharging brush can discharge the charge from the charge storage elements at a second predetermined angular position of the latter about the axis. The second position is angularly displaced and electrically isolated from the first position so that the injection of charge through said charging brush into said charge storage elements and the subsequent discharge thereof through said discharge brush following rotation of the charge storage elements through the angular displacement between said first and second angular positions will produce an electrical signal having a parameter linearly related to the angular speed of the rotating shaft to be measured. The apparatus is particularly useful in a system for measuring the instantaneous power output of the rotating shaft.

Angular accelerometer stabilized pendulum

Abstract: A gyroless vertical indicating device which tracks the local gravity vector independent of horizontal acceleration. A compound pendulum and an angular accelerometer each has a single rotational degree of freedom about a common axis. Rotational motion of the pendulum and of the angular accelerometer about the axis is coupled by a quartz fiber suspension therealong. A signal representative of the relative angular velocity between the pendulum and the angular accelerometer is fed back to a torquing system which maintains the pendulum's orientation along the local gravity vector.

Effect of rotation on a rotating hot-wire sensor

Abstract: An investigation was conducted to discern the effects of centrifugal and Coriolis forces on a rotating hot-wire. The probe was calibrated in a wind tunnel as well as in a rotating mode. The effect of rotation was found to be negligibly small. A small change in cold resistance (1.5%) was observed in the rotating wire. The rotation seems to have a negligible effect on the fluid mechanics, heat transfer and material characteristics of the wire. This is a significant conclusion in view of the potential application of the hot-wire probe in a rotating passage (such as turbomachinery).

Euler vectors and rotations about an arbitrary axis

Abstract: We consider the relationships between the rotation matrix associated with a rotation through ϑ about an arbitrary axis and the Euler vector ϑ lying along that axis with magnitude ϑ.

Electronic angular position encoder apparatus

Abstract: The encoded angular position of a rotating object is produced by an electronic digital counter that is clocked by a programmable frequency source. The source frequency is adjusted as necessary by a processor so that the number of counts registered by the counter is the same for each revolution of the rotating object. A sensor provides a signal once during each revolution of the rotating object when it passes some reference angular position. The signal strobes the current count into an output buffer register, resets the counter to zero, and then activates the processor. The processor in turn, checks if the count in the output buffer register is within a given tolerance of the desired count for one revolution, and then, if necessary, programs the source to the correct frequency. Thus, the number of counts for each revolution will remain approximately constant, independent of the angular velocity. At any point during each revolution of the rotating object, the counter can be strobed and the current count transferred to the output buffer register. This output can be used as a measure of the angular position of the rotating object at the time of the strobe signal.

Secular effects of tidal friction on the planet-satellite systems of the solar system

Abstract: We separate the tidal evolution of a planet-satellite system with zero eccentricity in two phases:phase 1—from the formation of the system to satellite's corotation (satellite's corotation means that its spin angular velocity equals the orbital angular velocity);phase 2—after satellite's corotation. We study the planet-satellite system during phase 1 with Darwin's graphical method and obtain an upper limit to satellite'sQ which discloses whether or not it is corotating. Moreover we obtain some qualitative information about the future evolution of the corotating satellites. The present work does not give any new result for the Earth-Moon case and for the Neptune-Triton case.

Vorticity Measurements Using Calibrated Vane-Vorticity Indicators and Cross-Wires

Abstract: Vane-type vorticity indicators of various sizes have been constructed, calibrated, and used for direct and rapid measurement of local mean streamwise vorticity in several swirling flows. The dependence of the calibration factor, which relates the vane rotational speed to the local angular velocity of the fluid, on the trees (ream velocity, the fluid rotational speed, and the transverse vorticity gradient was determined. When the vanes were calibrated carefully and checked and maintained regularly, good agreement was achieved with vorticity profiles obtained using cross-wire data. Otherwise, a vane could be used only to give an indication of vorticity. Nomenclature Nj- = angular velocity of the fluid, rpm Nv = angular velocity of the vane-vorticity indicator, rpm r = radial distance measured from the center of the test section Ux = freestream mean velocity W — vertical velocity in the fluid normal to the streamwise direction x - axial or streamwise distance y = lateral distance normal to streamwise direction and measured from the center of the test section z = vertical distance normal to streamwise direction and measured from the center of the test section a = half-angle setting between the airfoils rj = vane indicator ratio T = delay time in autocorrelation function Qv = vorticity in the streamwise direction

Pulse-echo ultrasonic wave-energy imaging system incorporating high-angular velocity oscillated transducer

Abstract: Transducer completely immersed in ultrasonic propagating liquid can be oscillated back and forth at a high rate, without producing significant turbulence in liquid, if oscillation velocity varies as a predetermined smooth continuous function of time.

Constraint Stabilization for Rigid Bodies: an Extension of Baumgarte’s Method

Abstract: A method of Baumgarte for the stabilization of mechanical constraints is extended to rotating bodies whose state is described by angular velocity variables and angle variables or Euler parameters. Computational results for several constraint situations are reported.