Showing papers on "Angular velocity published in 1970"

Characteristics of neural transmission from the semicircular canal to the vestibular nuclei of cats

Abstract: : It has been shown that the mechanical response of a semicircular canal to rotational stimulation is such that within a limited range of stimulus conditions the angular displacement of endolymph in the canal circuit is directly related to the angular velocity of rotation. The present study examines the dynamic response of neurones in the vestibular nuclei of cats exposed to sinusoidal rotational stimulation over a range of frequencies (0.25-1.7 Hz), presumed to lie within the domain of angular velocity transduction by the end-organ hydrodynamics.

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.

A quantitative study of vestibular adaptation in humans.

Abstract: A mathematical model for short-term adaptation to vestibular stimuli is presented. A transfer function is derived relating slow phase angular velocity of resulting nystagmus to the angular velocity of head rotation. The resulting model has been tested by comparing its responses to controlled step and ramp angular velocity stimuli with those of 8 human subjects, and in all cases a close match was obtained. The mean time constant of the adaptive term was 82 sec (S.E.±6.5) and the mean cupular restoration time constant (Tc) was 21 sec (S.E.±1.5). It is suggested that previous values quoted for Tc represent underestimates of the true value owing to superposition of the adaptive term here described. The adaptive term accounts well for the phenomenon of secondary nystagmus, especially during either strong stimuli or prolonged rotations. Some implications of the findings in relation to clinical and aviation medicine are discussed.

Differential rotation caused by anisotropic turbulent viscosity

Abstract: The law of rotation as well as the corresponding meridional circulations in the hydrogen convection zone (HCZ) are investigated by solving numerically the time independent Navier-Stokes equations. The HCZ is assumed to be a spherical layer of fluid with constant density and viscosity. It is assumed further that the viscosity is caused by unisotropic turbulent motions. The results show differential rotation together with circulations. The detailed behaviour depends on a parameters characterizing the nonisotropic friction and on the kinematic viscosityv. If the friction is larger in radial direction than in lateral directions (0 ⩽s 1) the equator rotates faster and the sense of the circulation is reversed. The differential rotation observed at the solar surface is obtained for the values = 1.2. For small values ofv the angular velocity is constant on cylindrical surfaces, for large values ofv it is constant on spherical surfaces. The solar law of rotation turns out to be very close to the first case.

Velocity Profiles in Steady and Unsteady Rotating Flows for a Finite Cylindrical Geometry

Abstract: Measurements have been performed with a laser‐Doppler velocimeter of the radial dependence of azimuthal velocity components, using liquid H2O, in cylindrical containers with aspect ratios A (i.e., the ratio of height l to radius b) ranging from 0.212 to 1.64. The reciprocal Ekman number ranged from 980 to 60 000. The radius was fixed at 5.25 cm. The rotating disk was located at the top. Our data are in fair agreement with numerical results of Tomlan and Hudson. Oscillations, observed during steady flow, are inertial waves with frequencies and amplitudes depending on aspect ratio and disk angular velocity. Spin‐down parameters fit a theoretical solution given previously. Observed oscillations during spin‐down have been accounted for through a heuristic argument involving convection of boundary‐layer fluid downward along the axis near the just‐stopped disk.

Motion sickness produced by head movement as a function of rotational velocity.

Abstract: Head movement role in motion sickness as function of angular velocity, discussing prediction of human tolerance in space station

The evolution of the Jacobi ellipsoid by gravitational radiation

Abstract: The quasi-static evolution of the Jacobi ellipsoid by gravitational radiation is determined by integrating the equation that gives the rate of dissipation of the angular momentum with the constraint that the ellipsoid remains Jacobian at all times. It is found that the evolution is in the direction of increasing angular velocity toward a non-radiating state at the point of bifurcation with the Maclaurin sequence.

Angular velocity sensors

Abstract: An angular rate sensor is disclosed which includes a plurality of proof masses driven so that each has a cyclically repetitive movement and so that the motions of the proof masses balance one another to provide inertial balance, and sensor means arranged to provide an output indicative of Coriolis forces on the said masses when the sensor is subjected to angular velocity about at least one predetermined axis. The device can also be used to measure translational accelerations and rotational accelerations along two axes.

Off-vertical rotation: a convenient precise means of exposing the passive human subject to a rotating linear acceleration vector,

Abstract: Tilting rotating chair producing vestibular stimulus via linear rotating acceleration to study motion sickness

The Rotation of the Sun (Review Paper)

Abstract: The author’s 1964 article in Nature on the sun’s rotation is rediscussed in the light of new data. This article suggested that the sun might be oblate because of a gravitational quadrupole moment induced by a core rotating with a period < 2 days. Angular momentum lost from the core by molecular diffusion was assumed to be transferred to the solar wind which kept the sun’s surface rotating slowly. The estimated solar wind torque was found to be in good agreement with the torque calculated from a solution of the diffusion equation.

Rheometrical flow systems Part 1. Flow between concentric spheres rotating about different axes

Abstract: The flow of an elastico-viscous liquid contained between two concentric spheres which are rotating with the same angular velocity about axes passing through the centre of the spheres is considered. The angle between these axes is small. The solution is obtained by expanding the velocity components in terms of a small parameter α2, which is usually associated with problems involving oscillatory flows. The analysis is shown to have a direct application to the Balance Rheometer. In particular, it is shown that inertial effects in this rheometer are likely to be very small.

Method and apparatus for position location using angle encoding

Abstract: A method and apparatus for providing a position location based on transmission of substantially parallel, collimated, coherent signal beams from a reference position, the beams being rotated in fixed parallel relation to one another about the reference position. The determination of the distance of the receiving position from the reference position, or the determination of the azimuth of the receiving position from a predetermined reference direction through the reference position, or both, is determined according to incremental angular rotation of the beams independently of the angular velocity of rotation.

Numerical study of the behaviour of a system of parallel line vortices

Abstract: The dynamical behaviour of a system of parallel line vortices in an inviscid fluid is studied numerically. The initial configuration of the system is assumed to be such that the points of intersection of the line vortices with a plane normal to the vorticity form a regular polygon. The numerical experiments show that the vortex polygon is rearranged due to non-linear interactions among the line vortices in such a way as to produce a more or less uniform distribution of vortices inside the fluid with an approximately constant mean separation. The average angular velocity of the rotation of the vortex lines about the instantaneous centroid of the vortex system remains approximately constant. These results agree with the conjecture of Raja Gopal (1964). The results may prove to be of some value in a macroscopic model of liquid helium based on hydrodynamical principles.

Power transmitting system

Abstract: CYCLIC IRREGULARITIES IN THE ANGULAR VELOCITY OF THE DRIVE TO A ROTATIONAL COUPLING ARE COMPENSATED FOR BY PROVIDING ANGULAR PLAY IN THE COUPLING EQUAL TO THE PEAK TO PEAK AMPLITUDE OF THE IRREGULARITIES IN ANGULAR DISPLACEMENT OF THE DRIVE MEMBER OF THE COUPLING. THE COUPLING COMPRISES INNER AND OUTER MEMBERS HAVING COMPLEMENTARY RECESSES OR PROJECTIONS ON THEIR FACING SURFACES, FORMING HOUSING FOR COUPLING MEMBERS DIMENSIONED TO PERMIT THE DESIRED ANGULAR PLAY. THE COUPLING MEMBERS ARE PREFERABLY CYLINDRICAL AND MAY BE OF ELASTIC MATERIAL.

Differential Rotation in the Solar Interior

Abstract: One of the big problems in stellar rotation which has been the object of much debate recently concerns the magnitude of the angular velocity in the central regions of the sun. It is a good example of our general ignorance of the distribution of angular momentum in the interiors of stars. There is good reason, of course, for this ignorance. One can’t make any direct observations and from a theoretical point of view there are many real problems such as the lack of a good theory of convection and meridian circulation, and our ignorance of the structure and magnitude of magnetic fields in the deep stellar interior. These problems among others make it very difficult, for example, to specify a surface condition on the angular velocity. It was pointed out recently (Clement, 1969; this paper is referred to hereinafter as Paper I) that such a condition might enable us to estimate the magnitude of the interior stellar rotation.

The Rotation of the Main-Sequence Components of Algol-Type Semi-Detached Eclipsing Binaries

Abstract: Newly determined rotational velocities of the main-sequence components of 14 Algol-type semi-detached systems and of 2 detached systems are presented. Combination of these data with the existing data on the rotation of the components of semi-detached systems shows that (i) in systems with primaries of spectral type B8 or later and with P<5 days, deviations from synchronism between rotation and revolution are small in 14 out of 15 cases. The average rotational velocity of the primaries in such systems is 75 km/sec, viz. only 40% of the average rotational velocity of single main-sequence stars in the same spectral region: (ii) primaries of spectral type earlier than B8 in systems with short as well as long periods tend to rotate more than twice as fast as one would expect from synchronism. A tentative explanation for these results is presented.

Centrifugal-balance gravity gradiometer

Abstract: An improved gradiometer for accurately measuring gravity gradients without the need for prior calibration. Since calibration is not required, the instrument operates independent of any external standards or references, except time. Further, one instrument in one orientation can provide all the components of the gravity gradient. The gradiometer comprises a suitably configured gradient sensor mass within a case which, in turn, is mounted within a cage such that its input axis is aligned with the axis of rotation of the cage. The entire assemblage is contained within a chamber which is preferably mounted on a stabilized base. Forces are induced on the sensor due to gravity gradients, causing the mass to move relative to its case. This motion is sensed and used to rotate the cage relative to the chamber. The angular rotation of the cage, in turn, causes the sensing device (specifically, its case) to rotate about an axis perpendicular to the inertia reaction forces on the sensor which are in an opposite sense to the forces induced on the sensor by the gravity gradients. The sensor is thus dynamically balanced. The angular velocity of the cage is indicative of the magnitude and direction of the gravity gradients being measured.

Rotary mechanical translating device

Abstract: A rotary mechanical translating device may be defined as a purely mechanical device which transfers power from a prime mover to a load as a magnified function of a displacement at its input connection The device exhibits a power gain and may be employed to produce mechanical amplification A change in angular velocity of its input will result in a change in the angular velocity of its output

Storing digital data on a recording disk with the data time base proportional to disk angular velocity

Abstract: A method for inscribing a modulated spiral groove on a memory disk in which a turntable is rotated at a nominally constant rotational velocity and a digital angular encoder is fixed to the shaft of the turntable providing a stream of output pulses which varies proportionally to variations in the angular velocity. This stream of output pulses is compared in a phase comparator with a stream of pulses derived from a voltage controlled oscillator and the output from the phase comparator is applied as the control input to the voltage controlled oscillator, thereby forming a phase locked loop. The output from the voltage controlled oscillator is divided down by appropriate amounts to provide timing digital signals to control the period of the modulation waveforms applied to a cutting head, which is inscribing a spiral groove on the memory disk. The output from the voltage controlled oscillator may also be used to control the radial position of the cutting head, thereby controlling the pitch of the spiral.

Multiple rotation gyroscope with hydrodynamic suspension

Abstract: A gyroscopic device having an inertial element that is hydrodynamically suspended within a centralized cavity of a gimbal rotating simultaneously about two mutually perpendicular axes in which the moment of inertia and angular velocity about the first axis is greater than the moment of inertia and angular velocity about the second axis Synchronously applied decentralizing forces acting on the inertial element are resisted by additional bearing surfaces that combine with the component of rotation having the smaller angular velocity to increase the restoring force on the inertial element in the direction of the decentralizing forces thereby maintaining the inertial element centered within the gimbal

Variable drive apparatus

Abstract: Apparatus for imparting various rotational motions to a driven member in which a constantly rotating driving member transmits a predetermined angular velocity to the driven member by means of a frictional coupling. The angular velocity of the driven member is varied by overcoming the driving torque applied to the driven member by the frictional coupling. Means cooperating with the driving and driven members serve, respectively, to brake and to reverse the rotational motion of the driven member.

Angular velocity and acceleration measuring apparatus

Abstract: Disclosed is a combined angular velocimeter and accelerometer formed by a film of cholesteric phase liquid crystalline material retained between rotary and stationary discs. Shear-stress exerted on the liquid crystalline film by movement of the rotary disc changes the initial uniform coloration into either differently colored bands or colorless bands that are observed through the transparent stationary disc. The radii of the colored or colorless rings are proportional to the rotation rate while the radial velocity of the band of rings is proportional to the angular acceleration.

Active Damping of Free-Rotor Gyroscopes during Initial Spin-Up

Abstract: The free-rotor gyro is so named because the nearly spherical gyrorotor is not mechanically constrained to rotate about a particular axis. Therefore, it may be initially spun up about any rotor fixed axis. As seen in the rotor, the subsequent motion of the angular velocity vector after spin-up is the well-known classical polhode motion about either the maximum or the minimum principal axes of inertia. The maximum axis of inertia is the desired spin axis direction because it is the only stable free-rotor spin direction in the presence of minute energy losses during flexures of the rotor. Consequently, the rotor-fixed markings used for spin axis readout of many of these gyros are referenced to the maximum axis of inertia. The principle delays in activating typical gyros are 1) waiting for a passive d.c. field to damp the gyro spin axis into the maximum axis of inertia of the rotor after it has been spun up (this requires typically five times the spin-up time) and 2) waiting for the thermal transient (of spin-up and damping) to subside. This paper describes a method of actively controlling the spin axis in the rotor, while leaving it unchanged with respect to a case-fixed reference. A control algorithm, called "Hemispheric Torquing" is used to actively damp the spin axis to the proper rotor fixed direction. It offers the advantage of being able to reduce damping times to less than is required for initial spin-up.

Stationary-platform Maneuvers Of Gyrostat Satellites

Abstract: In this paper we present some novel results regarding the dynamics of gyrostats containing N axisymmetric rotors subject to control torques applied by the platform. The particular class of maneuvers we are interested in are termed "stationary-platform" maneuvers, because they are based on the notion of keeping the platform almost stationary throughout the maneuver. The basic idea behind this class of maneuvers is to control the rotors in such a way that the maneuver remains near a branch of equilibrium motions for which the platform angular velocity, w, is zero. Of course, u> is not actually zero, but it does remain small provided that the internal torques are small. We develop the equations of motion, and then discuss the stationary-platform conditions, which lead to the development of stationaryplatform control laws for the control torques. We give a simple proof that all stationary-platform equilibria are nonlinearly stable in the absence of energy dissipation. Numerical results are given which include the dissipative effects of a viscously damped rotor. The results confirm the effectiveness of the stationary-platform maneuver for a large-angle rotation with small angular velocity throughout the maneuver.

Spin Down of Boussinesq Fluid in the Circular Cylinder, as a Simulation of the Solar Spin-Down Procedure

Abstract: As the simplest model to simulate the solar spin down procedure from the hydrodynamical viewpoint, a spin down problem with a simple geometrical configuration within the frame work of the Boussinesq approximation is investigated. A new proposal of the origin of the solar differential rotation is made on the basis of the calculated asymptotic distribution of the angular velocity. A comment on the present day solar spin down controversy is also made.

Non-Newtonian Flow in a Rotating Straight Pipe

Abstract: A theoretical analysis is made of the flow of an incompressible non-Newtonian viscous liquid through a straight pipe of circular cross section flowing under a constant pressure gradient. The pipe is rotated about an axis perpendicular to it. Secondary motion is set up due to the interaction between the Coriolis forces and the pressure gradient. Assuming that the angular velocity about the axis of rotation is small, a solution is developed by successive approximation, the first approximation corresponding to the Newtonian flow discussed by Barua. The stream lines in the central plane and the projection of the stream lines on the cross section of the pipe are compared with those of a Newtonian liquid. An expression for the rate of outflow has been obtained.

A method for measuring angular velocities by use of the sagnac effect

Abstract: 1,210,280. Interferometry. MESSERSCHMITT-BOLKOW-BLOHM G.m.b.H. Nov. 7, 1968 [Nov. 20, 1967], No. 52834/68. Heading G2J. A method for measuring angular velocities using the Sagnac effect comprises artificially enlarging the effective area round which two light beams circulate in opposite directions relatively to a rotating support, the angular velocity of which is to be measured, by light beam deflecting devices or conducting devices or both, arranged so that light circulates round the area a predetermined number of times prior to measuring the phase difference of the two beams. The normal single circuit of a Sagnac interferometer is replaced by a pair light conducting glass-fibre helices 10 arranged on a rotating support having a speed vector w, the light from a source 20 being transmitted along one coil in the sense of rotation and along the other coil opposite to the sense of rotation. The phase difference Z due to the difference of transmission time at the outlets 14, 15 is determined interferometically, as at 30. The larger the number of coils in each helix the slower the rotational velocities of the support which can be measured.

On the Equatorial Acceleration of the Sun

Abstract: The interaction of rotation and turbulent convection gives rise to a latitude dependent turbulent energy transport. Energy conservation demands a slow meridional circulation in the solar outer convective zone. The transport of angular momentum by this circulation is balanced in a steady state by the turbulent viscous transport across an angular velocity gradient. Models are constructed which give equatorial acceleration as observed on the sun.

On the asymptotic nature of clairaut theory

Abstract: A description is given of an elementary method of justifying the perturbation theory that provides the structure of a slowly rotating, self-gravitating mass in terms of the structure of a corresponding non-rotating configuration (Clairaut Theory). The main point of the method is the adoption of the viewpoint that the density, rather than the angular velocity, be prescribed as a function of position, since this leads to a completely elementary existence theory of rotating, self-gravitating masses. The method is carried out for the case of constant angular velocity, verifying the asymptotic nature of both the classical Clairaut Theory and more general theories (including Chandrasekhar's theory of distorted polytropes) that are in use in astrophysics.