Showing papers on "Angular velocity published in 1968"
TL;DR: In this article, the transform fault concept is extended to a spherical surface, where the motion of one block relative to another block may then be described by a rotation of a rigid crustal blocks relative to the other block.
Abstract: The transform fault concept is extended to a spherical surface. The earth's surface is considered to be made of a number of rigid crustal blocks. It is assumed that each block is bounded by rises (where new surface is formed), trenches or young fold mountains (where surface is being destroyed), and great faults, and that there is no stretching, folding, or distortion of any kind within a given block. On a spherical surface, the motion of one block (over the mantle) relative to another block may then be described by a rotation of one block relative to the other block. This rotation requires three parameters, two to locate the pole of relative rotation and one to specify the magnitude of the angular velocity. If two adjacent blocks have as common boundaries a number of great faults, all of these faults must lie on ‘circles of latitude’ about the pole of relative rotation. The velocity of one block relative to the other must vary along their common boundary; this velocity would have a maximum at the ‘equator’ and would vanish at a pole of relative rotation.
The motion of Africa relative to South America is a case for which enough data are available to critically test this hypothesis. The many offsets on the mid-Atlantic ridge appear to be compatible with a pole of relative rotation at 62°N (±5°), 36°W (±2°). The velocity pattern predicted by this choice of pole roughly agrees with the spreading velocities determined from magnetic anomalies. The motion of the Pacific block relative to North America is also examined. The strike of faults from the Gulf of California to Alaska and the angles inferred from earthquake mechanism solutions both imply a pole of relative rotation at 53°N (±3°), 53°W (±5°). The spreading of the Pacific-Antarctic ridge shows the best agreement with this hypothesis. The Antarctic block is found to be moving relative to the Pacific block about a pole at 71°S (±2°), 118°E (±5°) with a maximum spreading rate of 5.7 (±0.2) cm/yr. An estimate of the motion of the Antarctic block relative to Africa is made by assuming closure of the Africa-America-Pacific-Antarctica-Africa circuit and summing the three angular velocity vectors for the cases above.
1,106 citations
TL;DR: The theory of marginal convection in a uniformly rotating, self-gravitating, fluid sphere, of uniform density and containing a uniform distribution of heat sources, is developed to embrace modes of convection which are asymmetric with respect to the axis of rotation.
Abstract: The theory of marginal convection in a uniformly rotating, self-gravitating, fluid sphere, of uniform density and containing a uniform distribution of heat sources, is developed to embrace modes of convection which are asymmetric with respect to the axis of rotation It is shown that these modes are the most unstable, except for the smallest Taylor numbers, T (a measure of the rotation rate); ie for any T and o) (Prandtl number), the lowest Rayleigh number (a measure of the temperature gradients in the sphere) is associated with an asymmetric motion This is demonstrated both by an expansion method suitable for small T, and by asymptotic theory for T oo For large T, the eigenmode most easily excited is small in amplitude everywhere except near a cylindrical surface, of radius about half that of the sphere, and coaxial with the diameter parallel to the angular velocity vector
338 citations
TL;DR: The analysis and experiments in this paper are restricted to the flow between two coaxial, infinite disks, one rotating and one stationary, and the results of numerical calculations show that many solutions can exist for a given Reynolds number Ωl2/v (Ω is the angular velocity of the rotating disk and I is the spacing between the two disks).
Abstract: The analysis and experiments in this paper are restricted to the flow between two coaxial, infinite disks, one rotating and one stationary. The results of numerical calculations show that many solutions can exist for a given Reynolds number Ωl2/v (Ω is the angular velocity of the rotating disk and I is the spacing between the two disks). Out of a greater number of possible solutions, three solution branches have been identified; the branches correspond to one-, two- and three-flow cells in the meridional plane.The one-cell branch has been accorded detailed treatment. Within this branch there are two subbranches. The first, now well documented in the literature, includes solutions from zero to infinite Reynolds number. The latter limiting case is characterized by an inward-flowing boundary layer on the stationary disk and an outward-flowing boundary layer on the rotating disk. In between is a core flow rotating with a constant angular velocity. The second sub-branch of the single-cell flows, apparently unknown heretofore, begins with an infinite Reynolds number, decreases to a minimum and then increases to an infinite Reynolds number again. The first infinite Reynolds number limit again corresponds to two boundary-layer flows separated by a core flow with constantangular velocity opposite in direction to the angular velocity of the rotating disk. The second limiting case of infinite Reynolds number is the free-disk solution of von Karman (1921). Asymptotic solutions have been obtained which more fully describe the nature of this flow as the Reynolds number increases.The second part of the paper presents experimental measurements corresponding to the Reynolds number range 0–100. Profiles were measured with a hot-wire anemometer. The measurements are in agreement with the first, one-cell branch of solutions. A semi-quantitative evaluation of edge effects is obtained.
191 citations
TL;DR: In this article, the exact field equations for the metric of axially symmetric, stationary rotating bodies in general relativity are applied to calculate, to first order in the angular velocity of rotation (without restriction to weak gravitational fields), the rotation of the inertial frame induced by an incompressible fluid sphere, and by concentric mass shells.
Abstract: The exact field equations for the metric of axially symmetric, stationary rotating bodies in general relativity are exhibited. They are applied to calculate, to first order in the angular velocity of rotation (but without restriction to weak gravitational fields), the rotation of the inertial frame induced by an incompressible fluid sphere, and by concentric mass shells. In addition, the effect of the exterior field of rotating bodies on light rays is discussed. The results of this paper appear qualitatively to agree with some of Mach’s ideas on the origin of inertia.
76 citations
TL;DR: In this article, an experimental and theoretical study of the complicated disturbance (Taylor column) due to the slow relative motion between a spherical, or short cylindrical, rigid object and an incompressible fluid of low viscosity in which the object is immersed, when the motion of an object is that of steady revolution with angular speed Ω rad/see about an axis (the Z-axis) whose perpendicular distance from the centre of the object, was described.
Abstract: This paper describes an experimental and theoretical study of the complicated disturbance (Taylor column) due to the slow relative motion between a spherical, or short cylindrical, rigid object and an incompressible fluid of low viscosity in which the object is immersed, when the motion of the object is that of steady revolution with angular speed Ω rad/see about an axis (the Z-axis) whose perpendicular distance from the centre of the object, , is much greater than a typical linear dimension of the object, L, and the undisturbed fluid motion is one of steady rotation about the same axis with angular speed (Ω+Uϑ/R) and zero relative vorticity (i.e. d(Uϑ R)/dR = 0). It extends earlier experimental work on Taylor columns to systems of sufficiently large axial dimensions for Z variations in the disturbance pattern to be perceptible. Over the ranges of Rossby and Ekman numbers (based on L) covered by the experiments, namely e = 1·89 × 10−3 to 2·36 ×10−1 and γ = 1·30 × 10−3 to 2·03 × 10−2 respectively, the axis of the Taylor column is found to trail in the downstream direction at a small angle ϕ = tan−1 (Ke) to the line parallel to the Z-axis through the centre of the object, where K = (1·54 ± 0·04) for a sphere. The variation with Z of the amplitude of the disturbance is roughly linear and the scale-length of this variation, Zc, is close to L/γ¼ over the limited range of γ covered by the experiments.The experimental value of K is remarkably close to the theoretical value derived by Prof. Lighthill in the appendix, where he applies his general linear theory of waves generated in a dispersive system by travelling forcing effects to the problem of describing a Taylor column at large distances from the moving object when the fluid is inviscid and unbounded.
60 citations
TL;DR: In this article, the results of a theoretical treatment are presented for the slow flow of a viscous fluid through a circular cylinder within which a small spherical particle is confined, where the sphere is situated in an arbitrary position within the cylinder, rotates with an arbitrary constant angular velocity and moves at constant velocity parallel to the wall.
Abstract: The results of a theoretical treatment are presented for the slow flow of a viscous fluid through a circular cylinder within which a small spherical particle is confined. The sphere is situated in an arbitrary position within the cylinder, rotates with an arbitrary constant angular velocity and moves at constant velocity parallel to the wall. Approximate expressions are presented which give the frictional force, torque, and permanent pressure drop caused by the presence of this obstacle in the original Poiseuillian field of flow.An eccentricity function for the torque on a sphere in a circular cylinder was evaluated numerically. It can be used to predict the wall-effect for the torque as well as the angular velocity with which a ‘dense’ spherical particle will rotate. Expressions are presented which predict the angular velocity of ‘dense’ as well as neutrally buoyant hydrodynamically supported spherical particles.
44 citations
TL;DR: In this paper, a closed form solution for the linearized problem of the diffraction of Kelvin waves by a sharp bend on a rotating earth was obtained. But the solution was not suitable for the case where the wave is transmitted around the bend without change of amplitude, and the amplitude is in general reduced for the special angles π/(2n + 1).
Abstract: A closed form solution is obtained for the linearized problem of the diffraction of Kelvin waves by a sharp bend on a rotating earth. It is shown that for the frequency ω of the incoming wave less than f, where ½f is the angular velocity of rotation, the wave is transmitted around the bend without change of amplitude. For ω > f the amplitude is in general reduced but is unaltered for the special angles π/(2n + 1). For these special angles the solution is obtained in elementary terms.
33 citations
TL;DR: Rotational velocity estimates by observers during angular acceleration, noting vestibular function interpretation.
Abstract: Rotational velocity estimates by observers during angular acceleration, noting vestibular function interpretation
26 citations
TL;DR: In this paper, the shape of a drop of incompressible fluid held together by the action of surface tension and made to rotate about an axis is determined, the effect of gravity being neglected.
Abstract: The shape of a drop of incompressible fluid held together by the action of surface tension and made to rotate about an axis is determined, the effect of gravity being neglected. Two distinct problems are investigated. In the first an isolated drop of liquid in the form of a surface of revolution is considered. At zero angular speed the drop is spherical and with increasing angular momentum the oblateness increases until a maximum angular speed is reached (where the total mechanical potential is a minimum) beyond which a new linear series of equilibrium forms emerges. A solution in the form of a toroid is also found.
23 citations
TL;DR: In this article, the authors considered laminar axially symmetric flow and heat transfer between two horizontal disks which rotate around a common axis with a common angular velocity, where the temperatures of both disks are constant with that of the upper disk being hotter.
21 citations
TL;DR: In this paper, the authors systematically expanded the Larmor radius ordering for a collisionless plasma in an axial magnetic field Bz(x, y, t), where the magnetic field variation is a direct result of finite plasma pressure (β ∼ 1).
Abstract: The distribution function is systematically expanded in the finite Larmor radius ordering scheme for a collisionless plasma in an axial magnetic field Bz(x, y, t), where the magnetic field variation is a direct result of finite plasma pressure (β ∼ 1). Fluid equations are evaluated in both the guiding‐center frame and the center‐of‐mass frame. These equations are complicated by the velocity dependent ∇B drift which prevents strict closure of the moment equations. The effect of finite β is to include further terms in the stress tensor and in the energy equation in the form of a heat flux. An alternative derivation by a direct moment expansion is included. From these fluid equations the mechanism for producing radial differential rotation is rigorously shown. Secondly the stability of a rotating theta pinch is studied showing two finite β effects which can contribute to stability. The first is due to the increase in diamagnetic angular velocity (a result of creating a magnetic well) and the second due to th...
TL;DR: Matrix form of kinematical differential equations for rotating bodies described by Euler-Rodrigues parameter, deriving time derivatives as mentioned in this paper, is used to derive time derivatives of rotating bodies.
Abstract: Matrix form of kinematical differential equations for rotating bodies described by Euler-Rodrigues parameter, deriving time derivatives
TL;DR: In this paper, the solution of the time dependent flow due to the impulsive starting of a single infinite disk from rest is obtained numerically for the entire history of the transient.
Abstract: The solution of the time dependent flow due to the impulsive starting of a single infinite disk from rest is obtained numerically for the entire history of the transient The primary tangential velocity exhibits a single overshoot of its steady value while the growth of the secondary flows is monotonic The overshoot is seen to be a direct consequence of the lag in the development of the secondary flows An analytical solution is obtained for a related linearized problem: The angular velocity of an infinite disk, initially rotating with an infinite environment, is perturbed The oscillatory decays to the steady state, which occur in both unbounded and bounded linearized analyses, are discussed in relation to the overshoot in the impulsively started disk problem
Patent•
19 Sep 1968
TL;DR: In this article, a disk formed with peripheral notches or magnetic regions forms the input of an acceleration-measuring device, which produces a pulse train for which a pulse shaper ensures pulses of equal duration and amplitude, the frequency being proportional to angular velocity.
Abstract: A disk formed with peripheral notches or magnetic regions forms the input of an acceleration-measuring device. As the disk turns these notches or magnetic regions are scanned by a pickup coil, thereby producing a pulse train for which a pulse shaper ensures pulses of equal duration and amplitude, the frequency being proportional to angular velocity. The signal is then averaged. The average is integrated in two consecutive equal time periods and the difference of the two resulting integrals is obtained by an algebraically operating summing amplifier, the difference being equal to the angular acceleration.
TL;DR: In this article, the complete set of equations for the two-fluid model of a fully ionized plasma, the parameters of which depend on two spatial dimensions and time, is solved by a computer program.
Abstract: The complete set of equations for the two‐fluid model of a fully ionized plasma, the parameters of which depend on two spatial dimensions and time, is solved by a computer program. This program is applied to the problem of plasma rotation in a theta pinch caused by transverse multipole fields. The results show that the plasma does not rotate like a cylindrical rigid body, rather the velocity varies strongly with azimuth. Moreover, the rotation changes direction along the radius. Therefore, transfer of angular momentum from outside is not necessary for the existence of rotation. Even in small transverse fields (B ∼ 500 G) the rise time for the angular velocity is of the order of 10−7 sec and very short compared with those obtained from previous theoretical models.
TL;DR: It was concluded that adaptation evident in responses to the longer duration stimuli is a real phenomenon and of potential significance as one form of disorientation.
Abstract: The exponent of 1.0 found previously for numerical magnitude estimates of angular velocity during passive rotation was validated by auditory cross-modality estimates. Acceleration intensities ranged from 3°/sec2 to 24°/sec2, with durations varying from 10 sec to 80 sec. It was concluded that adaptation evident in responses to the longer duration stimuli is a real phenomenon and of potential significance as one form of disorientation.
TL;DR: In this article, the conservation of mass, energy, and momentum of viscous flow inside a heterogeneous, compressible, rotating fluid configuration, in which the coefficient of viscosity is an arbitrary function of radial distance, and the rotation is about a fixed z axis with angular velocity ω.
TL;DR: In this paper, the axisymmetric velocity and temperature profiles near a cooled infinite disk rotating at the same angular velocity as its infinite environment were analyzed under conditions under which the product of the Prandtl number coefficient of thermal expansion and temperature difference is order one or larger.
Patent•
04 Dec 1968
TL;DR: In this paper, the angular velocity of the velocity vector of the steerable body is proportional to the angular velocities of the line of sight and an apparatus for carrying out the method is presented.
Abstract: A method of spatial proportional navigation in which the angular velocity of the velocity vector of the steerable body is proportional to the angular velocity of the line of sight and an apparatus for carrying out the method wherein the position and direction of the angular velocity vector is chosen in such a manner that the plane of rotation of the velocity vector of the steerable body or of the steerable body itself contains the velocity vector V2* of the collision or constant bearing course, and that the actual course is pursued with the least possible positioning in the collision course.
TL;DR: In this paper, a theoretical analysis is made of the flow of a conducting viscous and incompressible fluid through a straight pipe of circular cross-section flowing under a constant pressure gradient.
Abstract: A theoretical analysis is made of the flow of a conducting viscous and incompressible fluid through a straight pipe of circular cross-section flowing under a constant pressure gradient. The pipe is rotated about an axis perpendicular to it and also there is imposed a uniform magnetic field transverse to the motion. It is assumed for the purpose of mathematical analysis, the angular velocity about the axis of rotation, is small. A solution is developed by successive approximations in ascending powers of the Hartmann number, the first approximation corresponds to the non-magnetic case, formulated and 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 in the non-magnetic case. An expression for the induced electric potential difference and sensitivity has been obtained.
TL;DR: In this article, the stability of a drop of incompressible fluid held together by the action of surface tension and made to rotate rigidly about an axis is determined, the effect of gravity being neglected.
Abstract: The stability of a drop of incompressible fluid held together by the action of surface tension and made to rotate rigidly about an axis is determined, the effect of gravity being neglected. Two distinct problems are investigated. In the first is considered an isolated drop in the form of a surface of revolution and the manner in which its stability changes with angular speed is investigated. At zero angular speed, where the drop is spherical, infinitesimal disturbances are shown to be stable and beyond a certain critical angular speed a new linear series of equilibrium forms emerges, the original series becoming unstable.
TL;DR: In this article, the effect of injection or suction from the disk surface on heat and mass transfer confficients was investigated for a disk rotating in a uniform forced stream, where the mass transfer parameter Hw was expressed by Hw=(Ww/U) Rsr1/2, Rer=Ur/V where ω is the rotating angular velocity, a constant obtained for the three dimensional stagnation flow and λ the resultant angular velocity in the presence of an axial forced flow.
Abstract: This paper deals with a theoretical investigation on the effect of injection or suction from the disk surface on heat and mass transfer confficients. That is, the basic differential equations for the velocity and temperature (or concentration) fields are solved numerically by means of the electronic computer for a disk rotating in a uniform forced stream. Especially, referring to the applcation to the transpiration cooling, the following conclusion is considered to be of interest. The flow around a rotating disk has a character of three dimensional boundary layer. Therefore, the velocity relative to a rotating disk, i.e. u=λγ{λ=(α2+ω2)1/2} may be used as the main stream velocity. Then, the mass transfer parameter Hw is expressed by Hw=(Ww/U) Rsr1/2, Rer=Ur/V where ω is the rotating angular velocity, a the constant obtained for the three dimensional stagnation flow and λ the resultant angular velocity in the presence of an axial forced flow. This relation corresponds qualitatively to that for the flow in a boundary layer over a flat plate with injection which has been analized by Hartnett et al.
Patent•
21 May 1968
TL;DR: In this article, a cross-rate sensor is provided for use with a moving vehicle, such as an elongated space vehicle, which undergoes both spinning and coning motion, and the angular position of the rotatable sensor relative to the vehicle can be used to phase the torques provided by a thrust-producing nozzle mounted on the vehicle to reduce and eventually eliminate the coning motions.
Abstract: A cross-rate axis sensor is provided for use with a moving vehicle, such as an elongated space vehicle, which undergoes both spinning and coning motion. The sensor which may be rotatably mounted about the longitudinal axis of the vehicle continually aligns itself with the instantaneous direction of transverse angular velocity or cross-rate axis of the vehicle due to coning motion, and the angular position of the rotatable sensor relative to the vehicle can be used to phase the torques provided by a thrust-producing nozzle mounted on the vehicle to reduce and eventually eliminate the coning motion. The sensor includes a rotatively driven momentum wheel, the axis of rotation of which continuously follows the cross-rate axis, and a cylindrical member rotatably mounted about an axis parallel to the vehicle axis of the elongation within the vehicle and having a hollow interior within which the momentum wheel is rotatably mounted as a gyroscope element in a balanced single degree of freedom gimbal system.
TL;DR: In this article, a control law for the stabilization of spacecraft angular velocity is presented, which minimizes both the time required to drive the angular velocity of the spacecraft to zero and the integral of the square of the norm of the angular momentum.
Abstract: A now procedure for the synthesis of a control law for the stabilization of spacecraft angular velocity is presented. This control law approximately minimizes both the time required to drive the angular velocity of the spacecraft to zero and the integral of the square of the norm of the angular momentum. Synthesis of the control law in feedback form is discussed. In a computer simulation, results obtained by use of the proposed control are shown to compare favourably with those obtained by use of the optimal control.
01 Mar 1968
TL;DR: In this article, the angular velocity and the stator and rotor currents in direct and quadrature axis were assumed as state variables and the state equations of the generalized machine, in a stationary reference framework, were derived.
Abstract: It is shown that the state-variable approach may be used conveniently in connection with generalized electric machine theory. This requires that the angular velocity and the stator and rotor currents in direct and quadrature axis be assumed as state variables. With these assumptions the state equations of the generalized machine, in a stationary reference framework, are easily derived.
TL;DR: In this article, a back-to-back connection of two gyros per axis is proposed to eliminate some of the errors due to cross coupling between the components of vehicle angular rates and accelerations.
Abstract: A back-to-back connection of two gyros per axis is suggested that eliminates some of the errors due to cross coupling between the components of vehicle angular rates and accelerations. In particular, the error due to output axis angular acceleration, the anisoinertia error, and the spin reference axis rectification error theoretically vanish. Use of redundant and identical strapdown systems for the purpose of obtaining higher reliability makes this connection practical.
TL;DR: In this article, the authors used the second-order theory of rotating polytropes to study rotational effects up to terms of the order ω 4, where ω is the angular velocity of rotation.
01 Jun 1968