Showing papers on "Angular velocity published in 1987"

Implications of rotational kinematics for the oculomotor system in three dimensions

Abstract: 1. This paper develops three-dimensional models for the vestibuloocular reflex (VOR) and the internal feedback loop of the saccadic system. The models differ qualitatively from previous, one-dimensional versions, because the commutative algebra used in previous models does not apply to the three-dimensional rotations of the eye. 2. The hypothesis that eye position signals are generated by an eye velocity integrator in the indirect path of the VOR must be rejected because in three dimensions the integral of angular velocity does not specify angular position. Computer simulations using eye velocity integrators show large, cumulative gaze errors and post-VOR drift. We describe a simple velocity to position transformation that works in three dimensions. 3. In the feedback control of saccades, eye position error is not the vector difference between actual and desired eye positions. Subtractive feedback models must continuously adjust the axis of rotation throughout a saccade, and they generate meandering, dysmetric gaze saccades. We describe a multiplicative feedback system that solves these problems and generates fixed-axis saccades that accord with Listing's law. 4. We show that Listing's law requires that most saccades have their axes out of Listing's plane. A corollary is that if three pools of short-lead burst neurons code the eye velocity command during saccades, the three pools are not yoked, but function independently during visually triggered saccades. 5. In our three-dimensional models, we represent eye position using four-component rotational operators called quaternions. This is not the only algebraic system for describing rotations, but it is the one that best fits the needs of the oculomotor system, and it yields much simpler models than do rotation matrix or other representations. 6. Quaternion models predict that eye position is represented on four channels in the oculomotor system: three for the vector components of eye position and one inversely related to gaze eccentricity and torsion. 7. Many testable predictions made by quaternion models also turn up in models based on other mathematics. These predictions are therefore more fundamental than the specific models that generate them. Among these predictions are 1) to compute eye position in the indirect path of the VOR, eye or head velocity signals are multiplied by eye position feedback and then integrated; consequently 2) eye position signals and eye or head velocity signals converge on vestibular neurons, and their interaction is multiplicative.(ABSTRACT TRUNCATED AT 400 WORDS)

Mass property estimation for control of asymmetrical satellites

Abstract: Real-time algorithms that estimate the mass-property parameters commonly used in spacecraft control laws are developed based upon a stochastic estimation viewpoint. The elements of the inverse inertia matrix and the center-of-mass location vector are estimated from noisy measurements of the angular velocity using a secondorder filter, while estimates of the mass reciprocal are generated from noisy linear velocity measurements using a Kalman filter. Simulation results show that the rate of convergence of each estimate depends strongly upon the particular maneuver being performed, but that the mass properties can be estimated to within 1% error.

Some special cases of spin-yaw lock-in

Abstract: : A slightly asymmetric missile is a basically symmetric missile with a nonzero pitch moment at zero angle of attack. In flight this moment causes a trim angle that rotates with the missile and has a maximum when the spin is near resonance with the missile's natural pitch frequency. This report considers a roll moment that can be induced by this trim angle and can cause resonant lock- in spin. Simple expressions for this induced rolled moment are given and the existence and stability conditions for equilibrium spin are derived. The special case of the induced roll moment caused by a radial center of mass offset is considered and a number of different types of possible equilibrium spin combinations are shown. The possibility of resonant lock-in spin in the opposite sense to the expected steady-state spin is indicated. It is further shown that there are induced roll moments for which the design steady-state spin will not occur under any launch conditions. If several stable equilibrium spins are possible, the one that occurs in flight can be determined by the orientation of the initial pitch angular velocity. Finally the form of an induced pitch moment is given and its possible effect on the angular motion is discussed.

Cross-Axis Synchronous Flow-Through Coil Planet Centrifuge Free of Rotary Seals for Preparative Countercurrent Chromatography. Part I. Apparatus and Analysis of Acceleration

Abstract: A novel type of the coil planet centrifuge is introduced. The apparatus holds a coil holder in such a way that the axis of the holder is positioned perpendicular to and at a fixed distance away from the centrifuge axis. In maintaining the above orientation the holder undergoes synchronous planetary motion, i.e., revolution around the central axis-of the centrifuge and rotation about its own axis at the same angular velocity. Mathematical analysis of acceleration generated by this planetary motion revealed a unique distribution pattern of centrifugal force vectors which promises a high performance of the present scheme in counter-current chromatography.

Velocity Observations From Discrete Position Encoders

Abstract: A discrete position encoder is an inexpensive means for sensing the angular position of a rotating device. Often a system with higher performance can be achieved if the angular velocity is known in addition to the position. Typically, the output of a discrete position encoder is two square wave signals in quadrature. This paper investigates various methods for processing these signals to observe the velocity in real time. High performance observers based on Taylor series expansions, backward difference expansions, and least square curve fits are developed. The accuracy of the different observers are analyzed by simulations for systems with time measurement truncation and imperfect encoders. The least square curve fit based observers are the most tolerant observers investigated due to the inherent low pass filtering.

Apparatus and method for predicting fore/aft forces generated by tires

Abstract: An apparatus and method for predicting fore-aft translations of tires. An inflated tire is rotated at a nominally constant angular velocity against a freely rotatable rigid loadwheel under a radial load. Changes in the instantaneous effective radius of the tire as it rolls give rise to fore/aft forces which tend to translate the tire alternately forward, toward the direction of travel and aft, toward the opposite direction. The tendency of the tire to so translate is predicted by measuring variations in effective radius or a parameter correlated thereto such as changes in the motion of the tread surface of the tire or the loadwheel relative to the angular speed of the tire.

Premixed Flames in Counterflow Jets Under Rigid-Body Rotation

Abstract: The extinction characteristics of double premixed flames of methane and butane in counterflow of two cylindrical jets which undergo rigid-body rotation are investigated. Using laser Doppler velocimetry, the axial, radial and circumferential velocity profiles are measured when jets with equal angular velocity rotate in opposite directions. It is found that two symmetric lean methane flames which are merged and near extinction, will subsequently separate again upon the rotation of the jet streams. Furthermore, as the angular velocity is increased, the fuel concentration at extinction is found to first decrease to a minimum value and increase thereafter. These tendencies are described on the basis of the observed variation of the rate of stretch experienced by the flames as a function of their axial position. Also, the existence of radially inward secondary flows which produce recirculation zones on both sides of the stagnation plane are established whose thickness increase with the jet angular velo...

A Review of What Numerical Simulations Tell Us about the Internal Rotation of the Sun

Abstract: The simulated solar differential rotation from two independent numerical modeling efforts agree with each other and with present solar observations. The models solve the nonlinear, three-dimensional, time-dependent, anelastic equations of motion for thermal convection in a stratified, rotating, spherical shell. The simulated angular velocity in the convection zone is constant on cylinders coaxial with the rotation axis, maximum at the equator and decreasing with depth. The latitudinal variation of this angular velocity at the surface is in agreement with Doppler measurements of the solar surface rotation rate. The radial variation through the convection zone is consistent with the analysis of the rotational frequency splitting of solar oscillations.

On the nonlinear Born effect

Abstract: In 1920 Max Born described the coupling of the intrinsic molecular spin to the hydrodynamic vorticity. At small shear rates molecules rotate at an angular velocity ⟨ω⟩ = ½∇ × u. In this paper we report the results of NEMD simulations which show that outside the linear regime, the average angular velocity ⟨ω⟩ is less than 1/2y.

The Influence of Rotation on Premixed Flames in Stagnation-Point Flow

Abstract: Abstract-Premixed flames stabilized in a rotating stagnation-point flow is considered. A description is given for the effect of a monotonous dependence of the extinction limit on the angular velocity of rotation.

The equilibria of rotating isothermal clouds

Abstract: The effect of rotation on the equilibrium structure of an axisymmetric isothermal gas cloud embedded in a stationary external medium is investigated by means of numerical simulations. The underlying assumptions, basic equations, input parameters, and numerical approach are explained, and the results are presented in extensive tables and graphs and characterized in detail. The critical central density and rotation energy, beyond which clouds become unstable to global contraction/expansion and ring formation, respectively, are found to be 800 times the boundary-surface density (BSD) and 0.44 times the gravitational energy. Stable rotating clouds are shown to have maximum mass 31 times that of nonrotating clouds, maximum mean rotation velocity 2.7 times the sound speed, and maximum mean density 6 times BSD. An expression for the maximum height of the boundary surface above the equatorial plane is derived. 41 references.

Fitting Smooth Paths to Rotation Data

Abstract: In the study of plate tectonics in geophysics, estimates are available of the cumulative motion of continental plates relative to each other between various geological epochs. For a given pair of plates this relative movement may be summarized at each time by a 3 × 3 proper rotation matrix describing the orientation of a plate relative to its initial position. The general problem of point and interval rotation estimation at other times is addressed by using a spline method for fitting smooth paths to such sequences of cumulative rotations. The parameterization of 3 × 3 rotations as unsigned four‐dimensional directions is particularly convenient. The preferred tangent space projection also makes easy the construction of point and interval estimates of the instantaneous angular velocity vector of the relative motion.

Motion parallax and figural properties of depth control flight speed in an insect

Abstract: Male gypsy moths (Lymantria dispar L.) are able to control their forward flight speed solely by means of optical cues derived from the lateral parts of their visual field. Thereby, relative motion of the objects is required, which under free flight conditions would derive from the self-induced motion of the stationary objects within a surrounding structured in depth. Besides this "motion parallax", however, the control system for forward flight speed demands figural properties of the objects such as differences in their angular extension or contrast. In a natural surround, the images of objects closer to the moth have higher angular velocity and, in addition, are usually larger and have higher contrast than those of objects farther away. The experiments have shown that this natural pairing of angular velocity and figural properties is essential to induce a thrust response which appears suitable to counteract involuntary changes in forward flight speed, as e.g. caused by changes in wind speed under free flight conditions. Inverse pairing of the visual stimuli caused the moths to either enlarge the error signal according to positive feedback within the control circuit, or to increase thrust to a maximum as always found in experiments without motion parallax or in the absence of differences in figural properties. The open-loop experiments furthermore established that the set point of angular velocity of the closer objects lies within the range of 4.5---9°/s, and that pattern speed modulation has to cover this range in order to induce a compensatory thrust modulation. The response is largely independent of the magnitude of relative motion as long as it is present; the response amplitude, however, strongly depends on the amplitude of pattern speed modulation. The results are discussed with regard to other visual cues used for the control of forward flight speed in insects, the algorithm underlying the figure-ground discrimination in flies, and the perception of depth in man as known from psychophysical experiments.

Influence of Vorticity on Counterflow Diffusion Flames

Abstract: The extinction characteristics of diffusion flames of methane and butane in counterflow jets under opposing rigid-body rotation are investigated. It is found that the critical volumetric concentration of fuels in nitrogen corresponding to flame extinction decrease to a minimum value and increase thereafter as the jet angular velocity increases. This tendency could be described on the basis of variation of the rate of stretch and eventual breakdown of laminar flow caused by the angular velocity. An absolute mimimum fuel concentration corresponding to local extinction for diffusional burning is identified showing favorable agreement with the existing data. It is established that as the angular velocity of the jets increase, the unbalanced pressure gradients result in radially inward secondary flows. This leads to the development of recirculation zones on both sides of the stagnation plane whose thickness increase with angular velocity. Also, when oxygen enriched air is used, the jet vorticity may r...

A Diagnostic Technique for the identification of Misfiring Cylinder(s)

Abstract: This paper introduces a diagnostic technique for the detection of misfiring cylinders in internal combustion engines. The technique requires the analysis of the instantaneous angular velocity of an engine flywheel. The results show that the mean cyclic acceleration, maximum variation in angular velocity, and the cyclic period of acceleration can be used as a measure for the mean net torque and the mean net expansion pressure torque produced by each cylinder. The proposed technique has proven to be effective in identifying a faulty cylinder using efficient and simple computations.

The amplification of solar-line asymmetries by rotation

Abstract: The effect of rotation on granulation-induced line asymmetries is examined by computing composite, rotationally-broadened flux profiles from a grid of observed solar center-to-limb intensity profiles. After first demonstrating that the composite profiles are in reasonable agreement with profiles observed from the full solar disk, it is shown that rotation enhances these asymmetries. When the rotational velocity exceeds the half width of the intensity profile, the effects magnify rapidly. Using the bisector function as a measure of the asymmetries, it is found that the deviations from symmetry increase roughly as the rotational velocity squared. This study leads to the general conclusion that any curvature in the bisector function of a line having a stellar origin will be exaggerated by rotation.

Nearly two‐dimensional solutions of Euler’s equations

Abstract: Motivated by a stretched version of the Taylor–Green initial‐value problem for the Euler and Navier–Stokes equations, nearly two‐dimensional incompressible flows are considered involving a single direction of slow spatial variation. A multiple‐scale formulation of the problem leads by contour averaging to a system that determines the slow development in space and time. It is shown that the latter system is equivalent to an axisymmetric problem with nonstandard connection between circulation, cylindrical radius, and angular velocity component. Special solutions of the system in the exact axisymmetric case suggest that near‐two‐dimensionality is lost in finite time.

Scalar magnetometer with vector capabilities

Abstract: A scalar magnetometer with vector capabilities includes a cell containing 3 He gas at a pressure between 0.05 Torr and 100 Toor. The cell is energized by an oscillator which partially ionizes the 3 He gas. Metastable atoms are polarized and consequently ground state atoms are polarized with a radiation source. A pair of Helmholtz coils provides a small uniform magnetic field which initiates a precession of the polarized e He atoms by forcing their misalignment with the magnetic field to be measured. The angular velocity of the precession is proportional to the strength of the field. A voltage is induced in a plurality of coils that are mounted on the axes of the cell. The induced voltage provides vector information for identifying the angular position of the cell relative to the magnetic field being measured.

Solar rotation and the giant cells

Abstract: Departures from the mean solar differential rotation rate as a function of latitude, longitude, and epoch of the solar cycle, together with variations in the rotation rate as determined by spectroscopic and tracer measurements are reviewed. It is shown that, if giant convection cells do exist as predicted, real variations in the subsurface rotation rate should occur and that this may be responsible for the observed surface anomalies. In terms of this hypothesis, a simple account is given for the anomalous rotation rates of sunspots. Furthermore, the torsional oscillations are identified as a modulation of the differential rotation produced by a system of toroidal convective rolls generated near the poles and propagating towards the equator. It is suggested that, as these rolls progress through lower latitudes, they break up into a system of cells which are the long sought for giant cells of the convection zone. Thus the torsional oscillations are identified as direct surface evidence for the existence of these cells.

Method and device for measurement with laser beam

Abstract: A method and a device for measuring an angle required for ascertaining the coordinates of a measuring point comprise two laser beams which are rotatingly emitted from a reference point in opposite directions at the same angular velocity and, at a measuring point, time intervals for receiving the two laser beams are obtained and used for the ascertaining of the measuring point coordinates. The laser device generates two laser beams rotating in opposite angular directions at the same angular velocity. The laser beams are reflected twice in a pentaprism, a compound prism and a rectangular mirror. Errors for mounting the prisms and mirror are thus eliminated resulting in extremely small rotation irregularities. In a method and a device for measuring an angle in 3-dimensional space, laser beams in sectors and a sensor for detecting said laser beam are used; thereby, various angles required for determining coordinates in 3-dimensional space can be measured.

Electrical machine with unequal pole faces

Abstract: An electrical machine comprises a rotor (2) and a stator (5) as machine parts, means for generating an excitation flux, and active coils (W1-W5). In operation the coils link at least a portion of the excitation flux and generate a rotational e.m.f. The rotor and the stator comprise poles, the number of stator poles (N1-N6, S1-S6) differing from the number of rotor poles (T1 x -T5 x ). During operation, the flux pattern of the portion of the excitation flux linking with the active coils rotates relative to the machine part carrying the active coils with such an angular velocity that the absolute value of the difference between said angular velocity and the angular velocity of the machine part comprising the active coils is larger than the absolute value of the difference in angular velocity between the rotor and the stator. For this purpose the pole faces (RS) of the rotor poles, viewed in the circumferential direction of the rotor, have a different width than the pole faces (PS) of the stator poles. Moreover, the active coils are arranged diametrally in the form of a cylindrical winding or in the form of an annular winding.

Active compliant end-effector with force, angular position, and angular velocity sensing

Abstract: A direct-drive active compliant end-effector (10) comprises a planar linkage (28) having input links (30, 44) driven by motors (24, 26). A force sensor (52) is connected between the output link (36) and a tool mount (48) for measuring tool interaction forces, signals representative of which together with those representative of angular displacement and velocity of the input links (30, 44) are used by a controller (82) for controlling the drive motors (24, 26) to provide active electronic compliancy.