Showing papers on "Rotation published in 1976"

The boundary problems of physical geodesy

Abstract: The purpose of this paper is to discuss the determination of the figure of the earth and its gravity field from astrogeodetic and gravimetric data (By gravity we mean the resultant of the attractive force of the masses of the earth, also called gravitation, and the centrifugal force of the earth's rotation) Let us recall that at the surface of the earth: (a) astronomic observations allow one to determine the direction of the gravity vector G; (b) gravimetric measurements give the length I GI of the gravity vector; (c) levelling combined with gravimetric measurements gives the differential of the gravity potential W, and thus yields W apart from an additive constant We assume the measured data G and W corrected for, say, the gravitational interaction with the moon, the sun and the planets, for the precession of the earth, and so on, so that we have the following idealized situation:

Ligament length patterns, strength, and rotational axes of the knee joint.

Abstract: Using intact fresh specimens, the cruciate ligament lengths for positions of flexion and internal-external rotation were computed using a non-invasive technique; using photographic methods, the centers of transverse rotation on the tibia and the direction of the flexion axis were also obtained. The anterior cruciate was found to be particularly effective in restraining internal tibial rotation; the ability of the posterior cruciate to restrain external rotation, however, depended strongly on the transverse axis location. Ligament length changes during flexion were found to be small in the absence of rotary torque and anteroposterior forces. The average internal rotation occurring during flexion was 37 degrees, half of which took place during the first 15 degrees of flexion. Ultimate rupture strengths of approximately 60 kh for the cruciates were measured, with stiffnesses of 16 kg/mm.

Perceptual illusion of rotation of three-dimensional objects.

Abstract: Perspective views of the same three-dimensional object in two orientations, when presented in alternation, produced an illusion of rigid rotation. The minimum cycle duration required for the illusion increased linearly with the angular difference between the orientations and at the same slope for rotations in depth and in the picture plane.

The Passive Influence of the Oceans upon the Rotation of the Earth

Abstract: A general theory is developed which allows the exact numerical computation of the static equilibrium response of a non-rotating spherically symmetric Earth model covered by thin oceans with geometrically irregular coastlines to the action of an imposed static tidal or centrifugal potential. The theory is self-consistent, and takes into account the gravitational self-attraction of the oceans and the elastic-gravitational response of the Earth model to both the applied potential and the equilibrium oceanic tidal load on the surface. The results are used to determine the influence of an equilibrium pole tide on the free period and the associated rotational eigenfunction of the Chandler wobble. If the pole is globally well represented by this equilibrium approximation, its effect is to increase the Chandler wobble period by 27·6 days. It is shown that a fully self-consistent theory of the rotation of an Earth model with oceans predicts that changes in spin and wobble will be coupled, and that the Chandler wobble should, as a result, be accompanied by an associated periodic change in the length of day. The consequences of spin-wobble coupling are explored quantitatively, and found to be slight.

On the structure and stability of rapidly rotating fluid bodies in general relativity. I. The numerical method for computing structure and its application to uniformly rotating homogeneous bodies

Abstract: A new numerical method for computing the structure of rapidly rotating fluid bodies in general relativity is presented. The method is a Henyey-type relaxation method of the kind previously used by Stoeckly in Newtonian theory. It permits the construction of accurate models for fluid bodies with various strengths of relativity and various amounts of uniform or differential rotation. The method is used to construct sequences of uniformly rotating homogeneous bodies, the relativistic analogs of the classical Maclaurin spheroids. The results reveal that, in contrast to the Newtonian sequence, most, and probably all, of the relativistic sequences terminate at nonzero ratios of proper polar radius to proper equatorial radius where centrifugal and gravitational accelerations balance at the equator. Other relativistic effects, including those associated with the formation of regions within which observers must rotate relative to infinity, are discussed. The computational results provide a foundation for a speculative discussion of stability and a scenario for the possible evolution of contracting bodies. Emerging from this are suggestions that relativistic effects might channel the contraction of a highly relativistic body toward a nearly spherical, rather than a disklike, configuration, and that black holes might generally not be near the extreme Kerr limit whenmore » they initially form. The computational results are also applied to uniformly rotating neutron stars in order to obtain rough estimates of their rotational energies, their moments of inertia, and the percent by which uniform rotation can increase the maximum-mass limit above its nonrotating value. For equations of state yielding a maximum mass approx.1.3 M/sub sun/ in the nonrotating limit, this latter percent increase is estimated to be approx.15 percent if attention is restricted to completely stable objects and approx.30 percent if no stability restrictions are imposed. (AIP)« less

Flow-through centrifuge

Abstract: A flow-through centrifuge free of rotating seals. The centrifuge includes a frame having three spaced apart horizontal plates which carry a central bowl, a countershaft and a tube-supporting hollow shaft. A motor is arranged to drive the frame at an angular velocity of ω. The countershaft is driven by a stationary pulley on the motor and drives the bowl at an angular velocity of 2ω. The motion of the countershaft is also transferred to the tube-supporting hollow shaft by a pulley coupling having a ratio which effects rotation of the hollow shaft, with respect to the frame, at an angular velocity of -ω.

Unusually High Barriers to Rotation Involving the Tetrahedral Carbon Atom

Abstract: Rotation about CC single bonds in suitably substituted compounds gives rise to rotational isomers (also called rotamers) which can be isolated if the barrier to rotation is high enough. The present article considers derivatives of triptycene and fluorene whose barriers to rotation are of the order of 30 kcal/mol.

Singularity methods for elastostatics

Abstract: By distributing the concentrated singularities such as a Kelvin doublet along the axis of symmetry we describe the displacement field, in an elastic medium, for various modes of rotation and translation for a rigid prolate and oblate spheroid. The limiting cases of a sphere, a slender body and a thin circular disk are also discussed. All the solutions are presented in a closed form.

Oscillation, Nutation and Wobble of an Elliptical Rotating Earth with Liquid Outer Core

Abstract: We have constructed a general first-order theory describing those small oscillations of a rotating elliptical earth that are affected by the presence of a liquid outer core The theory is applicable to free core oscillations and earth tides Care has been taken to include the effects of the wobble or nutation due to the rotation of the outer core relative to the solid earth On the basis of the theory the free spheroidal modes of degree 2 and order 1 have been investigated We have searched for and listed undertones with periods less than 28 hr No upper limit to the eigenperiods has been detected It is shown that stable, unstable and neutral polytropic cores are capable of free oscillation At a period close to the sidereal day the spheroidal mode is accompanied by rigid rotation of the liquid outer core with respect to the solid earth This is the well-known diurnal wobble of the Earth It appears probable that the diurnal wobble is one of a class of similar wobbles that involve large toroidal motions in the outer core Finally, the amplitudes of the 18·6-yr principal nutations has been computed Excellent agreement is found with observed values

Possible effects of internal rotation in low-mass stars

Abstract: The influence of internal rotation on the evolution of a 0.85M ⊙ star is investigated by the construction of model sequences. Rotation is treated by a simple one-dimensional approximation. The calculations assume solid-body rotation on the zero-age Main Sequence, followed by conservation of angular momentum in shells. The 4 cases considered have the initial angular velocities 0,2×10−4, 6×10−4, and 8×10−4/sec. All cases but the last are followed to helium ignition. Compared with the non-rotating case, the rotating models are older at Main-Sequence turnoff, develop fast-spinning central regions on the red-giant branch, and ignite helium at higher surface luminosities and at larger helium-core masses. The increases in the last two quantities are roughly proportional to the square of the initial angular velocity. The 6×10−4 case is followed through the helium core flash to the zero-age horizontal branch. Under the assumption of spherical symmetry, the non-central ignition of helium leads to a sequence of flashes of decreasing amplitude occurring progressively closer to the center. The flashes are weaker than those encountered in previous studies and do not produce mixing.

Tool for connecting and disconnecting well pipe

Abstract: A combination tool including a power slip, spinner unit and torque wrench, all mounted movably to a common support structure adjacent a well. The assembly is operable to first support the lower of two successive sections of pipe in the power slip, and then turn the upper section relative to the lower one to screw the pipes together or apart, with the major portion of the rotation being effected by the spinner, and the final high torque make-up rotation or initial joint breaking rotation being produced by the torque wrench.

Windmill plant for generating energy

Abstract: Windmill or solar plant for generating electric energy having a transmission in the form of an epicyclic gear transmission with sun wheel and planet wheels, the sun wheel of which is connected to the generator shaft, and the planet wheels being coupled with a regulator motor having two directions of rotation as well as a variable speed of rotation, the ring gear being driven directly or indirectly by the windmill or driving shaft.

Spin and statistics

Abstract: An exchange operator is defined in terms of rotation and displacement operators This operator contains a rotation around the z axis that produces a factor (−1)2s in front of the wave function By postulating that such a rotation must produce the same value for the wave function if the particles are identical, we obtain the usual connection between spin and statistics Particle states lying in the irreducible representations of the three‐dimensional rotation group are seen to allow only Fermi and Bose statistics

Effect of rotation on thermal instability of a viscoelastic fluid

Abstract: The thermal instability of a layer ofOldroyd fluid acted on by a uniform rotation is considered. The rotation is found to have destabilizing as well as stabilizing effect under certain conditions in contrast to that of a Maxwell fluid where it has a destabilizing effect. The analytic conditions for non-existence of overstability are investigated.

Angular momentum diffusion and the initiation of cyclones

Abstract: IT is possible to explain1,2 the intensification of a cyclone vortex once the stream lines in a weak depression close around a core of higher vorticity, but it is less clear how the process starts. Scorer3 proposed that convection might diffuse angular momentum within a field of initially uniform rotation to localised regions, thereby concentrating cyclonic vorticity. Experiments failed to demonstrate the effect4–7, and although strong vortices could be produced through the breaking of inertial waves8, the effects were open to misinterpretation. We present here new experimental results showing that first, angular momentum or relative vorticity can be diffused at a rate comparable with the diffusion of relative velocity (turbulent ‘viscosity’). This distinctive property seems to be intrinsic to weak turbulence in rotation, and can be parameterised very simply. Second, such diffusion occurs only when the turbulence is sufficiently weak to be constrained by rotation to an essentially two-dimensional structure. This might explain the failure of earlier experiments. Our results could have many applications to geophysics, including tropical cyclogenesis.

Optical scanning apparatus with two mirrors rotatable about a common axis

Abstract: Apparatus for scanning the field of view of an optical objective. A primary mirror is mounted for rotation about a spin axis. A secondary mirror supports an electrical motor magnet and is mounted for rotation about the spin axis. A non-rotating stator is mounted behind the secondary mirror and supports the electric motor coils. The primary and secondary mirrors are canted slightly out of perpendicularity with the spin axis. The primary and secondary mirrors and the electric motor stator are fully gimbaled for tracking a target. The scanning patterns of the primary and secondary mirrors combine to scan a rosette pattern across a sensor.

Vertical axis wind turbines

Abstract: A vertical axis wind turbine comprises one or more aerofoil section blades attached to a support structure. The blade has at least one part thereof which is acted on by centrifugal forces as the blade rotates with the support structure and thereby caused to increase its angle of inclination to the said vertical axis when the speed of rotation increases beyond the normal operating range, whereby the rate of increase of rotational speed with wind speed is reduced.

Apparatus for conveying and turning articles

Abstract: Apparatus for conveying and rotating articles 90° while being conveyed along a predetermined path with rotation being achieved by contacting a forward corner of the article for pivoting it partially as the extending side will be grasped by a side-facing belt to complete rotation and propel the article forward.

Progressive cavity drive train

Abstract: An improved drive train for a progressive cavity device is disclosed. The progressive cavity device has a rotor, a stator, means for fluid to enter between said stator and rotor, and means for fluid to exit therefrom. The rotor is adapted to roll with respect to the stator. The improved drive train comprises means attached to the rotor, for rotation substantially about a single axis, whereby the rolling of said rotor and the rotational motion about said single axis are directly connected and are at different speeds. At least a portion of said means attached to the rotor is aligned with the true center of the rotor.

Toroidal plasma rotation in axisymmetric and slightly nonaxisymmetric systems

Abstract: The relaxation of toroidal plasma rotation in the intermediate and collisional regimes has been calculated. The present results connect smoothly to previous results for the banana and collisional regimes. Small magnetic field ripples lead to a nonambipolar ion flux which may significantly affect toroidal rotation in all three regimes. This has also been calculated.

The slow motion of a sphere in a second-order fluid

Abstract: The slow motion of a rigid sphere in a viscoelastic fluid is studied. Variations of the velocity gradient of the undisturbed fluid motion over the dimension of the sphere are neglected. Considering only rheologically slow flows the equations of a second-order fluid are employed. The resulting hydrodynamic force and couple are calculated and shown to be fundamentally different from the corresponding results in a Newtonian fluid: for the force a coupling is found not only for translation and rotation but also for translation and a pure straining motion. For the torque only a coupling between rotation and a pure straining motion exists. It is demonstrated that by means of this coupling the two material parameters can be obtained individually. Furthermore any lateral migration of a sphere in a vertical Poiseuille flow would immediately unmask the fluid as a non-Weissenberg fluid.

Apparatus and method for indicating condition of a rotating body

Abstract: Apparatus and method particularly adapted for detecting over and/or under inflated conditions in a wheel structure of the type comprised of a pneumatic tire mounted on a wheel rim. A generator unit is mounted to the wheel generally coaxial of the axis of wheel rotation and is constructed such that the generator rotor is operably journalled within the generator stator in a manner facilitating rotation of the rotor independently of the remainder of the generator unit and wheel itself. One side of the rotor is weighted so that as the wheel and generator unit are rotated, the rotor disposition remains generally stationary due to the influence of gravity forces on the weighted area. The relative rotation thus achieved between stator and rotor causes a voltage to be induced in the stator field winding which is utilized to energize a small radio transmitter mounted on the wheel with the generator unit. Pressure sensing means communicating with the tire controls energization of the transmitter in response to a predetermined tire pressure condition. The transmitted radio signal is then received by a receiving unit spaced remote from the wheel to cause energization of convenient indicating means located in the vehicle to show that the predetermined air pressure condition has been detected.

Effect of vibrations on the internal rotation barrier in ethane

Abstract: The effect on the ethane internal rotation barrier of (1) zero‐point vibrational averaging and (2) distortions in equilibrium geometry during internal rotation is determined. We find that the (previously ignored) averaging term is 374±90 cal/mole which is substantially larger, and opposite in sign, to the distortion correction of −161±20 cal/mole. The isotope shift, other experimental tests, and some important implications of our results are discussed.

On the Dragging of the Plane of Polarization of Light Propagating in a Rotating Medium

Abstract: The rotation of the plane of polarization of light propagating along the axis of rotation of a rotating dielectric medium, as recently measured by Jones (I976), is examined by means of the usual formalism of the electrodynamics of a moving medium. The treatment goes beyond that of Fermi (I923) in including the effects of dispersion. It is found that the optical rotation includes a 'dragging coefficient' (1/np) (ng - 1/np) (where ng and no are the group and phase refractive indices of the medium respectively) equal to that found for 'aether drag' in the transverse case or in the longitudinal case for a fluid medium with fixed boundaries. In the preceding paper, Jones (I976) has reported the results of his experiments to observe the 'dragging' of the plane of polarization of light propagating along the axis of rotation of a rotating dielectric medium. As argued by Jones, such an effect may be anticipated by analogy with the Fresnel 'aether drag' in a uniformly moving medium. However, only one theoretical treatment of the situation seems to have been published (Fermi I923) and it does not consider the effect of dispersion. It is the purpose of this note to re-examine the theory of the effect (to first order in v/c) and to include some discussion of dispersion. We begin by considering the electrodynamics of a moving medium, and to do so introduce two frames of reference: the 'rest frame' with respect to which the medium moves with velocity v; and the 'moving frame' with respect to which the medium is at rest. In either frame Maxwell's equations (in Gaussian units) for a dielectric medium with no free charges are

The effect of rotation on electrohydrodynamic instability

Abstract: The effect of uniform rotation on the onset of convective instability in a dielectric fluid confined between two horizontal planes under the simultaneous action of a vertical ac electric field and a vertical temperature gradient is considered. Applying linear perturbation theory and approximations analogous to the usual Boussinesq approximations, an equation of tenth order is derived. Under somewhat artificial boundary conditions, this equation is solved exactly and the eigenvalue equation is obtained. It is shown that (1) the principle of the exchange of stabilities is valid for most dielectric fluids; (2) the Coriolis force has an inhibiting effect on the onset of instability even if the electrical effect is taken into account; (3) as the speed of rotation increases the coupling between the two agencies causing instability (electrical force and buoyancy) becomes tighter.

Wind driven electric power plant

Abstract: A wind driven power plant for the generation of electric power comprising a rotor, a shield, and a fin mounted on a vertical, central shaft, the fin and shield adjustably interconnected via a cog and gear track arrangement affording variable relative alignment of the fin and shield to position the shield relative to the wind. A constant rotor rotation rate is achieved by varying the masking thereof by the shield to compensate for wind speed variations. A hydraulic rotation rate control system senses the rotation rate of the rotor and generates a signal permitting the adjustment of the relative orientation of the fin and the shield. The rotor is coupled to a conventional electric generator for the generation of electric power.