Showing papers on "Angular velocity published in 1981"

Turbulent Wind and Its Effect on Flight

Abstract: = components of (W— WA) in FB or FA = components of Wm FE = velocity of airplane mass centre relative toFA = reference steady value of V = local velocity of the air relative to the Earth = mean value of W, velocity of frame FA = state vector = dX/du, etc., classical stability derivatives = wavelength, 27T/Q, = rms value of stochastic variable indicated by subscript = vector separating two points in FA = angular velocity of airplane relative to FE = local angular velocity of air relative to E = wave number vector in FA = matrix of three-dimensional spectrum functions = matrix of two-dimensional spectrum functions = matrix of one-dimensional spectrum functions = Laplace transform = transpose of matrix = ensemble average = complex conjugate Reference Frames FE:(xE,yE,zE)

On the coronae of rapidly rotating stars. I - The relation between rotation and coronal activity in RS CVn systems

Abstract: Soft X-ray observations are presented of a nearly complete sample of RS Canum Venaticorum systems taken with the Einstein X-ray Observatory. It is shown that the quiescent coronal activity, as measured by the ratio of the X-ray to bolometric flux, is directly proportional to the angular velocity of the star with the active chromosphere in these systems. This relation is found to hold over two decades in angular velocity. It is also found that the stellar surface gravity has no obvious influence on the ratio of the X-ray luminosity to the bolometric luminosity over two decades in surface gravity. It is pointed out that the linear relation between the ratio of the X-ray luminosity to the bolometric luminosity on the one hand, and the angular velocity, on the other, holds important implications for dynamo theories of the generation of stellar magnetic fields.

Rotation of the inner core

Abstract: We cannot observe the magnetic field inside the earth's core directly, but there is likely to be a large toroidal part of 10–100 Gauss which, together with the dipole component, could produce a magnetic torque on the inner core that tends to rotate it. Estimates based on dynamo calculations give torques of 1019 N m which is large enough to accelerate the inner core to the westward drift velocity of 0.2° per year within a few days. Presumably some equilibrium has been reached in which the inner core rotates with constant angular velocity and experiences no net torque. This rotation should have significant consequences for dynamo calculations because it is a very effective method of stretching field lines, and its helps to drive differential rotation in the liquid outer core. The core is modeled by two solid spheres permeated by a uniform field of 5 Gauss representing the dipole. The inner sphere is free to rotate relative to the outer sphere. When a torque of 1019 N m is applied to the inner sphere it reaches equilibrium with a steady angular velocity corresponding to a rotation period of 2300 years, which is similar to the westward drift speed, and a toroidal field of about 100 Gauss is induced. The inner sphere can also undergo toroidal oscillations with a period of about 10 years which may be related to the observed secular variation.

Mechanism for generating power from wave motion on a body of water

Abstract: A mechanism for generating power from wave motion on a body of water. The mechanism includes a buoyant body which is adapted to float on a body of water and to roll and pitch in response to the wave motion of the water. A gyro-wave energy transducer is mounted on the buoyant body for translating the pendulum-like motions of the buoyant body into rotational motion. The gyro-wave energy transducer includes a gimbal comprised of first and second frames, with the first frame being pivotally mounted to the second frame and the second frame being pivotally mounted to the buoyant body. A gyroscope is mounted to the first frame for rotation about an axis perpendicular to the axes of rotation of the first and second frames. A motor/generator is coupled to the gyroscope for maintaining a controlled rotational velocity for the gyroscope. Transferring members are associated with one of the first and second frames for transferring torque of one of the first and second frames to the gyroscope about an axis that is perpendicular to that of the gyroscope which results in rotation of the other of the first and second frames. An electrical generator is responsive to the relative rotational movement of the first and second frames for generating electrical energy. A storage battery is mounted on the buoyant body for storing and releasing electrical energy and is operatively coupled to the motor/generator and the electrical generator. A control circuit is associated with the generator and the motor/generator unit of the gyroscope and is responsive to the time rate of change of current produced by the generator for controlling the rotational velocity of the gyroscope in order to maintain maximum power output from the electrical generator.

Symmetric Missile Dynamic Instabilities

Abstract: _ / Magnus moment \ V */2PSlVpd / = axial and transverse moments of inertia = amplitudes of the two yaw model arms for a symmetric missile = trim angle magnification factor = reference length = mass -XYZ components of the missile's angular velocity = reference area = dynamic stability factor = 2c0/d0o gyroscopic stability factor = (op) /4C^ = time = magnitude of the missile velocity = missile-fixed axes, the X axis along the longitudinal axis of the missile, positive forward = nonspinning aeroballistic axes = angles of attack and sideslip in the missilefixed system = circular limit motion radius = polar angle of £ = K j / K j ( j = l , 2 ) = value of \j for a linear Magnus moment = the complex angle of attack in the missile-fixed system = 0 4ict = be i9

Reorientational correlation functions for computer-simulated liquids of tetrahedral molecules

Abstract: Molecular dynamics simulations have been carried out on fluids of tetrahedral molecules for several sets of temperatures and pressures. The results were analysed to give reorientational and angular velocity autocorrelation functions. It was found that these could be related by a cumulant expansion in powers of the angular velocity and rotation operators. This type of analysis is likely to prove simple and useful for relating orientational correlation functions to the angular velocity correlation function in dense fluids where reorientation is hindered.

Solar rotation measurements at Mount Wilson. II - Systematic instrumental effects and the absolute rotation rate

Abstract: Possible sources of systematic error in solar Doppler rotational velocities are examined. Scattered light is shown to affect the Mount Wilson solar rotation results, but this effect is not enough to bring the spectroscopic results in coincidence with the sunspot rotation. Interference fringes at the spectrograph focus at Mount Wilson have in two intervals affected the rotation results. It has been possible to correlate this error with temperature and thus correct for it. A misalignment between the entrance and exit slits is a possible source of error, but for the Mount Wilson slit configuration the amplitude of this effect is negligibly small. Rapid scanning of the solar image also produces no measurable effect.

Some exact results for rotational correlation functions at short times

Abstract: Expressions are derived for several of the coefficients in the Taylor series expansion for rotational correlation functions in powers of time. Classical ensembles of symmetric tops, spherical tops, and linear molecules are treated. Coriolis coupling terms are included in the coefficients for the angular correlation functions of symmetric tops; and angular velocity correlations are discussed as well as orientational correlation functions. Expressions are obtained for the first three non-zero coefficients of the orientational correlation functions for hindered rotors (up to and including t 6). Formal expressions are obtained for all coefficients of freely rotating molecules, and a number of these expressions are explicitly evaluated. A gaussian approximation to the memory function is proposed for the angular velocity correlation function; curves calculated from the resulting expression are compared with several simulated correlation functions.

Process and an apparatus for measuring an angle

Abstract: The angle which two members enclose with respect to an axis of rotation about which they are rotatable with respect to each other is measured by placing a rotating mark carrier on one of two members. The carrier has marks disposed thereon at a certain distance apart in the direction of rotation. A first sensor is attached to the same member as the mark carrier and a second sensor is attached to the other member. The sensors emit a signal corresponding to each of the passing marks, which signal is fed to a measuring and evaluating circuit. The circuit has an identification circuit which identifies the marks belonging to the signals emitted by the sensors, a time measuring unit which measures the time distances of the signals emitted by the sensors and a calculation and storage circuit which, after receiving a corresponding command signal, calculates and stores the angular distances, with respect to a zero point of the angular measurements. The measurement is taken between the marks from the time distance values for signals assigned to identified marks and coming from the various sensors; from stored calibrating values for the absolute angular distances of identified marks; and from the instantaneous angular velocity of the mark carrier; said calculation and storage circuit, upon subsequent rotations of the mark carrier, calculates the instantaneous angle between the two members from the time distance values for signals assigned to identified marks and coming from the various sensors, and from the stored angular distances of these marks, the angular distances being with respect to the zero point of the angular measurement, and from the instantaneous angular velocity of the mark carrier.

Linear stability of rotating Hagen-Poiseuille flow

Abstract: Linear stability of rotating Hagen-Poiseuille flow has been investigated by an orthonormal expansion technique, confirming results by Pedley and Mackrodt and extending those results to higher values of the wavenumber |α|, the Reynolds number R, and the azimuthal index n. For |α| [gsim ] 2, the unstable region is pushed to considerably higher values of R and the angular velocity, Ω. In this region, the neutral stability curves obey a simple scaling, consistent with the unstable modes being centre modes. For n = 1, individual neutral stability curves have been calculated for several of the low-lying eigenmodes, revealing a complicated coupling between modes which manifests itself in kinks, cusps and loops in the neutral stability curves; points of degeneracy in the R, Ω plane; and branching behaviour on curves which circle a point of degeneracy.

Rotational modes in a slowly and uniformly rotating star

Abstract: A perturbation method is derived forr-modes in a slowly and uniformly rotating star. In contrast to previous studies, the perturbation of the gravitational potential is included in the perturbation method. On the assumption that the effects of the centrifugal force are taken into account in the equilibrium model up to the second order in the angular velocity, an eigenvalue problem of sixth-order in the radial coordinate is derived that allows one to determine the zeroth-order toroidal displacement field and the third-order term in the expansion of the eigenfrequency. Furthermore, another eigenvalue problem is derived that governs the first-order toroidal displacement field and the fourth-order term in the expansion of the eigenfrequency. This second eigenvalue problem is also of the sixth-order in the radial coordinate. It is shown that the third-order term in the expansion of the eigenfrequency is real, and that the fourth-order term is zero.

Magnetic fields in late-type stars

Abstract: Observations show that magnetic activity in late-type stars is correlated with rotation rates and that there is a discontinuous change in behavior at a critical rotation period. This can be explained as a consequence of a transition from convection in rolls parallel to the rotation axis to normal convection cells as the angular velocity is decreased.

On the dynamic behavior of the wobblestone

Abstract: The wobblestone is a generalized form of a top with distinct inertias and a nonspherical surface at the point of contact to the horizontal plane on which it moves. Some wobble-stones exhibit a curious property of allowing steady rotation about the vertical principal inertia axis only when rotated in one direction, while other wobblestones exhibit repeated reversals of the direction of rotation after being spun. Here, nonlinear equations governing the motion of a wobblestone are derived assuming no slippage at the point of contact to the supporting rigid plane, which corresponds to a conservative model. The equations are formulated in a manner suitable for numerical integration. The major observed properties of the motion of these asymmetrical tops are demonstrated in numerical simulations. The results lead to a better understanding of their complex and fundamentally nonlinear motion.

Normal modes of oscillation for rotating stars. I - The effect of rigid rotation on four low-order pulsations

Abstract: Some normal modes of rotating stars can be computed numerically without having to assume a slow angular velocity. This can be done by solving directly on a two-dimensional grid the linearized dynamical equations governing adiabatic oscillations. In this paper, the effects of rigid rotation on four axisymmetric modes are found for several equiblibrium systems including polytropes and a 15 M/sub sun/ stellar model. It is shown that even a small rotation changes significantly the space dependence of the eigenfunctions.

Linear Stability Theory of Boundary Layer along a Cone Rotating in Axial Flow

Abstract: A linear stability theory is treated for an incompressible laminar boundary layer along a cone rotating about its axis of symmetry with a constant angular speed in an external forced flow field. Small perturbations are assumed to be of spiral vortices. This leads to one set of perturbation equations including an order of magnitude (δ1/R0), where δ1 denotes a displacement thickness of the boundary layer, calculated from a velocity component in the meridional section, and R0 is a local radius of the cone at instability. A numerical procedure for solving the eigenvalue problem is shown. As an example, calculations are carried out for a cone having a total included angle of 30° at a rotating speed ratio 3, where the rotating speed ratio is defined as the ratio of the circumferential velocity at the cone surface to the external flow velocity at the outer edge of the boundary layer. From stability diagrams obtained herein, critical Reynolds number, spiral angle and the associated eigenvalues are determined. The critical Reynolds number is compared with an experiment.

The Fokker–Planck–Langevin model for rotational Brownian motion. III. Symmetric top molecules

Abstract: The general series expansion for the angular velocity–orientation conditional probability density for a fluid composed of symmetric top molecules is derived, and expressions for the reorientational correlation functions, correlation times, spectral densities, angular velocity correlation functions, and the correlation times relevant to magnetic relaxation via spin–rotational interactions are presented. Numerical calculations of the reorientational correlation functions, memory functions, spectral densities, and correlation times indicate that these properties are sensitive to the anisotropy of the angular velocity correlations produced by an anisotropic friction tensor in the rotational Langevin equation.

Process and an apparatus for measuring the angular velocity of a rotating member

Abstract: The instantaneous angular velocity of a rotating shaft or the like is translated from the relative rotation of a mark carrier, having a scale of marks, and a sensing device. A series of signals are produced and processed in a calibrating run and thereafter in a series of operating runs. In the calibrating run, the time distance of the sensed signals between at least one pair of the marks is measured and from it a calibrating value is calculated corresponding to the absolute angular distance between the marks and thereafter stored. During the operation runs, the instantaneous time distance of the sensed signals between the marks is measured and the instantaneous velocity is obtained by comparing it with the stored calibrating value.

Induced rotation with concentric patterns.

Abstract: Duncker (1929) described induced rotation of a radial-line pattern when a concentric, enclosing annulus pattern rotated. This observation has not, so far, been confirmed or extended. Six experiments are described. The results from Experiments 1 and 2 showed that the frequency with which induced rotation is reported during standard observation periods is not affected by either angular velocity up to 15 deg/sec or unpatterned gaps up to 5 deg wide between the inner and outer patterns. Experiment 3 confirmed that the strength of the effect can be satisfactorily measured by cancellation of induced movement. Experiments 4–6 showed that induced rotation is very weak or absent when the inner disk rotates and the concentric annulus is stationary, increases in velocity as the number of radial lines in the rotating annulus increases by up to half the number in the stationary disk, and is only slightly stronger when the area of contrast between moving and stationary lines is poorly resolved in the peripheral visual field. The results are considered in terms of the resolution in perception of displacement ambiguity between moving and stationary elements.

Shaft position synchronization means for multiple synchronous induction motors

Abstract: The exact shaft angle position synchronization of two or more ordinary synchronous induction motors is provided. One motor, serving as the master, is powered directly from a source of alternating current. Each additional motor, which may be of a different size or type, is slaved to the intrinsic rotational speed of the master through the inherent electrical speed synchronization wrought by being excited by a common alternating current power source. Each slave motor is further synchronized by this invention to attain, and subsequently hold, an exact angular shaft position relative to the master. The position of the master and each slave motor shaft position is constantly measured, thereby producing several trains of electrical pulses which are compared. When an error exists, an electrical signal is produced which acts with the a.c. excitation applied to the slave motor so as to controllably retard its rotational velocity, thereby causing the angular shaft position to the slave motor to slip, or be retarded, relative to the angular position of the master motor shaft. When the angle of the slave has slipped sufficiently, and generally less than 360 degrees, the pulse train produced by the master and the slave achieve momentary coincidence and the electrical retardation of the slave motor ceases. The subsequent result is a mechanical synchronization of the angular shaft position of each motor, which is then maintained in that useful relationship by the nature of their common speed synchronization with the alternating current source frequency.

Equilibrium figures for beta Lyrae type disks

Abstract: Accumulated evidence for a geometrically and optically thick disk in the ..beta.. Lyrae system has now established the disk's basic external configuration. Since the disk has been constant in its main properties over the historical interval of ..beta.. Lyrae observations and also seems to have a basically well-defined photosphere, it is now time to being consideration of its sturcture. Here, we compute equilibrium figures for self-gravitating disks around stars in binary systems as a start toward eventual computation of complete disk models. A key role is played by centrifugally limited rotation of the central star, which would naturally arise late in the rapid phase of mass transfer. Beta Lyrae is thus postulated to be a double-contact binary, which makes possible nonarbitrary separation of star and disk into separate structures. The computed equilibrium figures are three-dimensional, as the gravitation of the second star is included. Under the approximation that the gravitational potential of the disk is that of a thin wire and that the local disk angular velocity is proportional to u/sup n/ (u = distance from rotation axis), we comptue the total potential and locate equipotential surfaces. The centrifugal potential is written in a particularly convenient form which permits onemore » to change the rotation law discontinuously (for example, at the star-disk coupling point) while ensuring that centrifugal potential and centrifigual force are continuous functions of position. With such a one-parameter rotation law, one can find equilibrium disk figures with dimensions very similar to those found in ..beta.. Lyrae, but considerations of internal consistency demand at least a two-parameter law.« less

Ball rolling on a turntable: Analog for charged particle dynamics

Abstract: For a ball to roll without slip across the surface of a rotating platform, a frictional force of the form Aωd×v is required, where A is a known constant, ωd is the platform’s angular velocity, and v is the particle’s velocity relative to inertial space. Since this force is of the same form as that experienced by a charged particle moving through a magnetic field, the ball executes only closed circular orbits. Other similarities to the charged particle problem are easily demonstrated: for example, drift velocities are produced normal to any external force lying in the plane of the disk, and an adiabatic invariant can be defined for the case when the disk changes its spin rate.

Application of unsteady airfoil theory to rotary wings

Abstract: A clarification is presented on recent work concerning the application of unsteady airfoil theory to rotary wings. The application of this theory may be seen as consisting of four steps: (1) the selection of an appropriate unsteady airfoil theory; (2) the resolution of that velocity which is the resultant of aerodynamic and dynamic velocities at a point on the elastic axis into radial, tangential and perpendicular components, and the angular velocity of a blade section about the deformed axis; (3) the expression of lift and pitching moments in terms of the three components; and (4) the derivation of explicit expressions for the components in terms of flight velocity, induced flow, rotor rotational speed, blade motion variables, etc.

The electromagnetic torque on axially symmetric rotating metal cylinders and spheres

Abstract: The torque is calculated on an electrically resistive rotating cylinder and sphere through which a current is fed by means of sliding contacts. The torque on a rotating cylinder is proven to vanish identically for arbitrary angular velocity. The torque on the sphere is shown to vanish up to second order in an expansion with the angular velocity as the expansion parameter. The nonzero torque in first order found by Gruenberg is shown to be due to an algebraic error.

Correcting a widespread error concerning the angular velocity of a rotating rigid body

Abstract: In obtaining the instantaneous angular velocity of a rotating rigid body, a large number of standard textbooks uses an incorrect argument by only considering the rate of change of the Euler angles but disregarding the simultaneous rate of change of the corresponding time‐dependent rotation axes. Therefore, a correct and concise derivation of this quantity for a rather general case is given, which also reveals that the usual simple formula does not at all arise as the erroneous textbook reasoning suggests, but as a consequence of certain generalized commutation relations satisfied by Euler rotations.

The orientation of the solar rotation axis from Doppler velocity observations

Abstract: Mt. Wilson observations of solar velocity fields have been examined for evidence that the rotation axis of the nonmagnetic gas at the solar surface is oriented differently that the axis found by Carrington (1863) from sunspot observations. No difference is found with accuracy of 0.15 in the angle of inclination of the axis to the ecliptic.