Showing papers on "Angular velocity published in 1973"

Hydromagnetic wavelike instabilities in a rapidly rotating stratified fluid

Abstract: We examine the hydromagnetic stability of a radially stratified fluid rotating between two coaxial cylinders, with particular emphasis on the case when the angular velocity greatly exceeds both buoyant and Alfven frequencies. If the magnetic field is predominantly azimuthal instabilities then have an essentially non-axisymmetric and wavelike character. Various bounds on their phase speeds and growth rates are derived, including a ‘quadrant’ theorem analogous to Howard's semicircle theorem for Kelvin–Helmholtz instability. Their strong tendency to propagate against the basic rotation (i.e. ‘westward’), previously noted by the author in the study of a more simplified (homogeneous) model, seems relatively insensitive to the generation mechanism (e.g. unstable gradient of magnetic field, angular velocity or density), but a number of counterexamples show that this constraint need not apply if the magnetic field displays significant spatial variations of direction as well as magnitude and that eastward-propagating amplifying modes are then possible.

On nonlinear Ekman and Stewartson layers in a rotating fluid

Abstract: Boundary and shear layers parallel to the axis of rotation in a rapidly rotating fluid are modified by inertial effects when the Rossby number R is not small enough to be neglected. If E is the Ekman number, inertial modifications to Stewartson E ¼ layers become important when the Rossby number is comparable with, or larger than, E ¼ and changes in the thickness and the structure of the layer then occur. The nature of the change depends on whether the total component of vorticity parallel to the axis of rotation is increased or diminished by the contribution from the layer. When inertial effects are important in these layers, the Ekman layers are also modified by inertia and a nonlinear Ekman condition must be used. Such a condition is obtained and it is used to discuss the flow between rotating disks when there is a discontinuity in their angular velocity and source-sink flow in an annulus.

Methods for experimentally determining the angular velocity relaxation in liquids

Abstract: It is shown that the angular velocity autocorrelation function for symmetric top molecules can in principle be determined from infrared and Raman band shapes, and from thermal neutron scattering when the molecular tumbling rate is slow compared with the relaxation of angular momentum. The theory is compared with molecular dynamics studies on a liquid crystal and an isotropic liquid.

Method of measuring torque

Abstract: The method for measuring torque described is based upon the fact that angular velocity omega and angular acceleration Alpha are independent dynamical variables at any given time. Thus, for any given omega , a simultaneous determination of Alpha and omega can be utilized for a determination of power. The method of measurement requires a negligible perturbation of the rotating system. It is easily susceptible to modification over a wide range of variations. Particular reference is made to the determination of the contribution to the torque of a rotating system by a part or subsystem.

Method and apparatus for accurate die-cutting

Abstract: Inaccurate cuts often occur in paperboard blanks passing between a pair of cooperating die and anvil cylinders because of anvil cylinder wear, irregular blank velocity, and other factors. Such inaccuracies are reduced by the method of driving the die cylinder at a preselected angular velocity and driving the anvil cylinder at an angular velocity proportional to the angular velocity of the die cylinder with the preselected proportion being maintained during changes in angular velocity of the die cylinder. The apparatus generally preferred for performing the method includes a mechanical variable speed transmission having an input driven by the die cylinder and an output for driving the anvil cylinder at an angular velocity corresponding to the angular velocity of the input and with the output velocity being selectively variable with respect to the input to provide an output velocity selectively proportional to the input velocity. However, the apparatus primarily preferred for performing the method includes a sensor means for sensing the velocity of the die cylinder, a variable speed motor means for driving the anvil cylinder, and a motor controller means responsive to the sensor means for controlling the output speed of the motor means to proportionally correspond to the velocity of the die cylinder, the controller means also including variable speed control means for changing the proportion of the anvil cylinder velocity to the die cylinder velocity for changing the output speed of the motor means. Another embodiment utilizes a mechanical variable speed transmission means in lieu of the motor means and a ratio control motor means responsive to the sensor through a similar motor controller means for varying the output of the transmission means to achieve a preselected proportion which is maintained during changes in velocity of the die cylinder.

Convection in Rotating Stars

Abstract: The influence of rotation on convection in stellar interiors is discussed. It is shown that the character of convective motions can be affected in relatively slowly rotating stars. Although the transport of energy by convection is anisotropic, the requirement that the divergence of total energy flux vanishes means that meridional circulation currents will be set up. These will mix the material of a convective core in a time which is not much different from the time taken by convection in the absence of rotation. Although rotation does not seriously impede mixing processes in a convective core, the circulation transports angular momentum and changes the law of rotation of the star. The final state of rotation cannot be determined until the form of convection in a rotating star is better understood, but it is possible that the asymptotic state is closer to one of uniform angular momentum than uniform angular velocity. (auth)

Fluctuations in the Earth's Rate of Rotation Related to Changes in the Geomagnetic Dipole Field

Abstract: Relation between changes in the dipole field and those in the earth's rate of rotation has been examined for three different periods, 8000, 400 and 65 years, based on such various kind of data as those of archeomagnetism, observation of moon's longitudes and recent instrumental observations. It has been confirmed that fluctuation exists in the rate of rotation corresponding to the dipole change for these periods. The magnitude of the variation in the rotation to be related to the dipole change increases as the period decreases.Time variation in the drift velocity has also been examined for several features of the geomagnetic secular variation. It is very probable that a change in the drift velocity accompanied the 400 year period fluctuation in the earth's rotation.The results thus obtained are compared with a theoretical result. Except for the phase of the angular velocity of the mantle for 65 year period and the magnitude of the geomagnetic westward drift for 400 year period, the observed results are well accounted for by an electromagnetic coupling caused by a dipole change at the core-mantle boundary, provided that the electrical conductivity of the lower mantle is as large as 10-8emu.

X-ray diffraction apparatus

Abstract: An X-ray diffraction apparatus comprising means for rotating a specimen in the path of an X-ray beam and means for rotating a diffraction slit simultaneously with the specimen but at a lower angular velocity, so that the X-ray irradiated portion of the specimen remains substantially constant in size during such rotation

MAXWELL‐Theorie (in Medien) und Quantentheorie in einem rotierenden Bezugssystem

Abstract: On the basis of our 3-dimensional conceptions of the electromagnetic quantities [1] the MAXWELL theory is represented in a rotating frame of reference. For such a frame the MAXWELL equations obtain additional terms depending on the angular velocity (analogous to the CORIOLIS term etc. in NEWTONian mechanics). Using these results with the help of the DIRAC equation we investigate quantum mechanics in a rotating frame of reference. Also in this case we obtain interesting additional terms depending on the angular velocity. The need for such a theory is obvious for many reasons: 1. Our Earth is such a rotating laboratory. Later the rotation effects must not be neglected. 2. In magnetic resonance physics theoretical questions with respect to rotating systems are important. 3. Interesting statements result for a rotational JOSEPHSON effect of superconductors. — All our calculations are carried out up to the first order in the angular velocity.

Equilibrium attitude transitions of a three-rotor gyrostat in a circular orbit.

Abstract: ( ) Nomenclature —2m2/3(/1-/3)co0 =[3(/1-/3)/(/2-J2)] = angular momenta of rotors divided by co0 = inertia matrix of the gyrostat (including Rotors) — moments of inertia of the gyrostat about its principal axes == inertia matrix for rotors = moments of inertia of rotors Nos. 1, 2, 3 about their spin axes = column matrix whose components are the angular momenta of the rotors = angular momenta of rotors Nos. 1, 2, 3 about their spin axes = impulse control moments = constant control moments = time — the time for the transition process = column matrix whose components ulf u2, u3 are the control moments acting on the rotors Nos. 1, 2, 3 — principal axes of inertia for the gyrostat = pitch, yaw, and roll angles respectively = direction cosine matrix specifying the satellite orientation relative to the £ frame = axes of the orbital £ frame = direction cosine, one of the elements of the matrix 0 = column matrix whose components lf (j>2, 3 are the angular coordinates of rotors Nos. 1, 2, 3 = angular velocity matrix of the satellite = projections on the body axes xlt x2> x3 of the angular velocity of the satellite with respect to the inertial space (elements of co matrix) = magnitude of the angular velocity of the satellite in its orbit = over a variable, differentiation with respect to time

Method and apparatus for the no-contact measurement of velocities, changes in relative position, or displacement paths

Abstract: Light diffracting or dispersing properties of an object dividing a wave front in angular differently oriented wave fronts are used for no-contact optical velocity-, acceleration-, change in relative position- or displacement path measurements of said object movable relative to a measuring head. No systematic markings affecting light phase or amplitude on the measuring surface are disposed in the depth of field of imaging system. Measurements are made respectively to one coordinate associated to one of the six possible spatial degrees of freedom of motion. The object under test and an optical component yielding sharply defined angular relationship among different but combined wave fronts are conjugatedly disposed in the imaging system. Light modulations produced upon changing the relative position are photoelectrically converted into signals exhibiting a frequency change proportional to linear or angular velocity variation. The measurement is improved by using components having negligible light absorption, and determining angular relationship among the wave fronts. Light fluxes from interaction among partial wave fronts containing information concerning the object movement, derived from solid angle areas of equal modulation phase are converted separately into photoelectrical signals having sinusoidally varying modulation characteristics with the respective measuring coordinate. The modulation period cycles are half as long as the statistical spatial frequency components of the object under test. The light energy proportions are split off from and outside the solid angle area of the illumination aperture. The electric signals produced are evaluated as direct or carrier-frequency signals with respect to the measured qualities desired.

Secular Stability of Rapidly Rotating Stars of Arbitrary Structure.

Abstract: The aim of the present paper will be to utilize Poincare's criteria to investigate secular stability of self-gravitating configurations, of arbitrary structure, in the state of rapid rotation. The potential energy, a knowledge of which is necessary for application of these criteria, will be determined by an extension of Clairaut's method; and its evaluation in terms of suitably chosen generalized coordinates carried out explicitly to quantities of fourth order in superficial oblateness, for configurations of arbitrary internal structure. The method employed can, moreover, clearly be extended to attain accuracy of any order — at the expense of mere manipulative work which lends itself to machine automation; and the angular velocity of axial rotation can be an arbitrary function of position as well as of the time. An application of our results to homogeneous configurations in rigig-body rotation will be undertaken to demonstrate that our method, when applied to a case for which a closed solution exists, leads to results which are consistent with it.

Viscous effects in rapidly rotating stars with application to white-dwarf models. III - Further numerical results

Abstract: Improved viscous evolutionary sequences of differentially rotating, axisymmetric, nonmagnetic, zero-temperature white-dwarf models are constructed using the relativistically corrected degenerate electron viscosity. The results support the earlier conclusion that angular momentum transport due to viscosity does not lead to overall uniform rotation in many interesting cases. Qualitatively different behaviors are obtained, depending on how the total mass M and angular momentum J compare with the M and J values for which uniformly rotating models exist. Evolutions roughly determine the region in M and J for which models with a particular initial angular momentum distribution can reach carbon-ignition densities in 10 b.y. Such models may represent Type I supernova precursors.

Dynamic passivation of a spinning and tumbling satellite using free-flying teleoperators.

Abstract: A satellite will generally have some initial angular motion. Before the satellite can be retrieved, it will be necessary to null its angular rates. A method is presented for nulling the simultaneous angular rates for cylindrical and near-cylindrical satellites. It is assumed that there are no external torques acting on the satellite initially. A model is being fabricated to verify the analysis. The analysis shows that it is feasible to null the spin and tumble rates for cylindrical and near-cylindrical satellites with an arm attached to a remote manipulator unit.

Radiation reaction for a rotating sphere with rigid surface charge

Abstract: Radiation reaction in classical electrodynamics is studied using as a simple model a rotating sphere with rigid surface charge. Because of the transparent geometric nature of the problem, we obtain an exact integral expression for the “self-torque”, which depends causally and linearly on the angular speed. This leads to a linear equation of motion, which does not have any runaway solutions, as long as no negative mechanical moment-of-inertia is added to the system. The results are illustrated with a few examples corresponding to predetermined motions and external torques.

Acoustic device for measuring rotation rates

Abstract: An acoustic sensing device for measuring the angular velocity of a spherical body; preferably comprised of at least one input transducer and at least one output transducer. The acoustic wave column traverses the periphery of the spherical body from the input transducer to the output transducer when the spherical body is rotated. The rate of rotation is determined by the output signal received by the output transducer.

Stroboscopic celestial scanner

Abstract: Apparatus employing a plurality of radiation sensors mounted in a rotating body, and successively enabled to sense radiation as their fields of view sweep across a radiation source emitting radiation too faint to be separable from the background noise by conventional means By summing the signals from the sensors, the signal-to-noise ratio can be sufficiently improved to allow an accurate determination of the angular position of the body with respect to the radiation source, and the angular velocity of the rotating body In a preferred embodiment, the sensors are grouped into pairs having adjacent fields of view, and each pair is enabled separately as their combined fields of view sweep across adjacent but non-overlapping areas which, together contain the radiation source The difference in output signals between the sum of the signals from the left-hand sensors and the sum of the signals from the right-hand sensors is a measure of the angular position and velocity of the rotating body with respect to the radiation source at the time each pair of sensors were enabled

Angular velocity measuring apparatus using ionized gas in an endless loop

Abstract: Gyroscopic apparatus is disclosed in which the reference element employed in measuring angular velocity comprises a moving stream of ionized gas. An ion collector is disposed in a conduit in which the gas stream moves and changes in angular velocity of the conduit relative to the gas stream are determined by sensing changes in ion collection.

Method of measuring moment of inertia

Abstract: The method for measuring torque described is based upon the fact that angular velocity omega and angular acceleration Alpha are independent dynamical variables at any given time. Thus, for any given omega , a simultaneous determination of Alpha and omega can be utilized for a determination of power. The method of measurement requires a negligible perturbation of the rotating system. It is easily susceptible to modification over a wide range of variations.

Precision turntable rotation in a vacuum atmosphere

Abstract: Fluid from a hydraulic pressure source is utilized to rotate and support a turntable in a vacuum chamber Signals representative of the rotational velocity of the turntable are utilized to control the hydraulic pressure of the fluid rotating the turntable

A preliminary study on the relation between the great earthquakes of china and the secular variation of the angular velocity of rotation of the earth

Abstract: The additional force field on the earth crust produced by the variation of the angular velocity of the Earth's rotation is opposite in direction when the velocity increases or decreases.On account of this fact,in this paper we attempt to examine whether the effect on earthquake occurrences is also opposite,when the velocity increases or decreases.By marking the signs of the increase or decrease of the angular velocity of the Earth's rotation at the earthquakes epicentres on a geological tectonic map,we notice that in certain types of tectonic zones,the earthquakes always oc-curre when the velocity of rotation increases and few or almost no earthquake occurre when,the velocity decreases,and in some other types of tectonic zones,the case is just the opposite.We conclude that great earthquakes are possibly related to the variation of the angular velocity of the Earth's rotation.

Long-term motion in a restricted problem of rotational motion

Abstract: A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the long-term effects of gravity-gradient torque and orbital evolution on the rotational motion of a triaxial, rigid satellite The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass The orbit, which has a constant inclination, is constrained to precess and spin with constant rates The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order in n/ω0, where n is the orbital mean motion of the center of mass and ω0 is a reference value of the magnitude of the satellite’s rotational angular velocity The differential equations derivable from the transformed Hamiltonian are integrable and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals Geometrical aspects of the long-term rotational motion are discussed and a comparison of theoretical results with observations is made

The motion and stability of a dual-spin satellite during the momentum wheel spin-up maneuver.

Abstract: The stability of a dual-spin satellite system during the momentum wheel spin-up maneuver is treated both analytically and numerically. The dual-spin system consists of: a slowly rotating or despun main-body; a momentum wheel (or rotor) which is accelerated by a torque motor to change its initial angular velocity relative to the main part to some high terminal value; and a nutation damper. A closed form solution for the case of a symmetrical satellite indicates that when the nutation damper is physically constrained for movement (i.e. by use of a mechanical clamp) the magnitude of the vector sum of the transverse angular velocity components remains bounded during the wheel spin-up under the influence of a constant motor torque. The analysis is extended to consider such effects as: the motion of the nutation damper during spin-up; a non-uniform motor torque; and the effect of a non-symmetrical mass distribution in the main spacecraft and the rotor. An approximate analytical solution using perturbation techniques is developed for the case of a slightly asymmetric main spacecraft.

Experiment on Relativistic Rigidity of a Rotating Disk

Abstract: : Several theories have suggested the possibility that the space-time metric of a rotating disk could be nonstatic as well as non-Euclidean. These, and also a theory of optical aberration based on the Thomas precession of vectors, predict a (real or apparent) decrease in angular velocity with radius, even in an ideally 'rigid' disk, with a rim lag time period of alpha v squared/c squared, where v is rim speed, c is light speed, and alpha is a constant between 1 and 1/6, depending on the theory. A spinning-disk experiment was done at the Naval Ordnance Laboratory (NOL) over a four-month period of continuous rotation to look for such effects.