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Showing papers on "Angular velocity published in 2004"


Journal ArticleDOI
TL;DR: In this paper, the Geneva stellar evolution code was used to model the pre-supernova evolution of rotating massive stars, and it was shown that the effects of rotation on pre-Supernova structures are significant between 15 and 30 M�.
Abstract: We describe the latest developments of the Geneva stellar evolution code in order to model the pre-supernova evolution of rotating massive stars. Rotating and non-rotating stellar models at solar metallicity with masses equal to 12, 15, 20, 25, 40 and 60 Mwere computed from the ZAMS until the end of the core silicon burning phase. We took into account meridional circulation, secular shear instabilities, horizontal turbulence and dynamical shear instabilities. We find that dynamical shear instabilities mainly smoothen the sharp angular velocity gradients but do not transport angular momentum or chemical species over long distances. Most of the differences between the pre-supernova structures obtained from rotating and non-rotating stellar models have their origin in the effects of rotation during the core hydrogen and helium burning phases. The advanced stellar evolutionary stages appear too short in time to allow the rotational instabilities considered in this work to have a significant impact during the late stages. In particular, the internal angular momentum does not change significantly during the advanced stages of the evolution. We can therefore have a good estimate of the final angular momentum at the end of the core helium burning phase. The effects of rotation on pre-supernova models are significant between 15 and 30 M� . Indeed, rotation increases the core sizes (and the yields) by a factor ∼1.5. Above 20 M� , rotation may change the radius or colour of the supernova progenitors (blue instead of red supergiant) and the supernova type (IIb or Ib instead of II). Rotation affects the lower mass limits for radiative core carbon burning, for iron core collapse and for black hole formation. For Wolf-Rayet stars (M > 30 M� ), the pre-supernova structures are mostly affected by the intensities of the stellar winds and less by rotational mixing.

286 citations


Proceedings ArticleDOI
01 Jan 2004
TL;DR: The proposed quaternion-based feedback control scheme for exponential attitude stabilization of a four-rotor vertical take-off and landing (VTOL) aerial robot known as the quadrotor aircraft shows that the model-independent PD controller provides asymptotic stability for the problem.
Abstract: In this paper, we propose a quaternion-based feedback control scheme for exponential attitude stabilization of a four-rotor vertical take-off and landing (VTOL) aerial robot known as the quadrotor aircraft. The proposed controller is based upon the compensation of the Coriolis and gyroscopic torques and the use of a PD/sup 2/ feedback structure, where the proportional action is in terms of the quaternion vector and the two derivative actions are in terms of the airframe angular velocity and the quaternion velocity. We also show that the model-independent PD controller, where the proportional action is in terms of the quaternion vector and the derivative action is in terms of the airframe angular velocity, without compensation of the Coriolis and gyroscopic torques, provides asymptotic stability for our problem. Simulation results are also provided to show the effectiveness of the proposed controller.

253 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered solutions with conformal symmetry of the static, spherically symmetric gravitational field equations in the vacuum in the brane world scenario, and they considered the behavior of the angular velocity of a test particle moving in a stable circular orbit.
Abstract: We consider solutions with conformal symmetry of the static, spherically symmetric gravitational field equations in the vacuum in the brane world scenario. By assuming that the vector field generating the symmetry is nonstatic, the general solution of the field equations on the brane can be obtained in an exact parametric form, with the conformal factor taken as parameter. As a physical application of the obtained solutions we consider the behavior of the angular velocity of a test particle moving in a stable circular orbit. In this case the tangential velocity can be expressed as a function of the conformal factor and some integration constants only. For a specific range of integration constants, the tangential velocity of the test particle tends, in the limit of large radial distances, to a constant value. This behavior is specific to galactic rotation curves and is explained usually by invoking the hypothesis of dark matter. The limiting value of the angular velocity of the test particle can be obtained as a function of the baryonic mass and radius of the galaxy. The behavior of the dark radiation and dark pressure terms is also considered in detail, and it is shown that they can be expressed in terms of the rotational velocity of a test particle. Hence all the predictions of the present model can be tested observationally. Therefore the existence of the nonlocal effects, generated by the free gravitational field of the bulk in a conformally symmetric brane, may provide an explanation for the dynamics of the neutral hydrogen clouds at large distances from the galactic center.

146 citations


Patent
12 Oct 2004
TL;DR: An angular velocity sensor has two masses which are laterally disposed in an X-Y plane and indirectly connected to a frame as discussed by the authors, and the two masses are linked together by a linkage such that they necessarily move in opposite directions along Z.
Abstract: An angular velocity sensor has two masses which are laterally disposed in an X-Y plane and indirectly connected to a frame. The two masses are linked together by a linkage such that they necessarily move in opposite directions along Z. Angular velocity of the sensor about the Y axis can be sensed by driving the two masses into Z-directed antiphase oscillation and measuring the angular oscillation amplitude thereby imparted to the frame. In a preferred embodiment, the angular velocity sensor is fabricated from a bulk MEMS gyroscope wafer, a cap wafer and a reference wafer. In a further preferred embodiment, this assembly of wafers provides a hermetic barrier between the masses and an ambient environment.

133 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of stellar rotation on the carbon ignition in a carbon-oxygen white dwarf accreting CO-rich matter was studied, and it was shown that the critical carbon ignition rate for the off-center ignition is not significantly changed by the effects of rotation, however, the mass coordinate of the ignition layer and the mass of the white dwarf at the ignition are larger than those for the corresponding nonrotating model.
Abstract: We study the effect of stellar rotation on the carbon ignition in a carbon-oxygen white dwarf accreting CO-rich matter. Including the effect of the centrifugal force of rotation, we have calculated evolutionary models up to the carbon ignition for various accretion rates. The rotational velocity at the stellar surface is set to the Keplerian velocity. The angular velocity in the stellar interior is determined by taking into account the transport of angular momentum due to turbulent viscosity. We have found that an off-center carbon ignition occurs even when the effect of stellar rotation is included if the accretion rate is sufficiently high; the critical accretion rate for the off-center ignition is hardly changed by the effect of rotation. Rotation, however, delays the ignition, i.e., the mass coordinate of the ignition layer and the mass of the white dwarf at the ignition are larger than those for the corresponding nonrotating model. The result supports our previous conclusion that a double-white dwarf merger would not be a progenitor of a Type Ia supernova (SN Ia).

131 citations


Journal ArticleDOI
TL;DR: In this paper, a parametric analysis of the magnetic field and rotation of a massive stellar core was performed, and the authors found that the combination of rotation and magnetic field can lead to a jetlike prompt explosion in the direction of the rotational axis, which would not be produced by either of them alone.
Abstract: Hydrodynamics of the rotational collapse of strongly magnetized massive stellar cores has been studied numerically. Employing simplified microphysics and a two-dimensional nonrelativistic MHD code, we have performed a parametric research with respect to the strength of magnetic field and rotation, paying particular attention to the systematics of dynamics. We assume initially that the rotation is almost uniform and the magnetic field is constant in space and parallel to the rotation axis. The initial angular velocity and magnetic field strength span 1.7-6.8 rad s-1 and × 1012 G, respectively. We have found that the combination of rotation and magnetic field can lead to a jetlike prompt explosion in the direction of the rotational axis, which would not be produced by either of them alone. The range of the maximum angular velocity and field strength is 2.3 × 10-3 to 5.8 × 10-4 rad s-1 and 2.3 × 1015 to 5.6 × 1016 G, respectively, at the end of computations. Although the results appear to be consistent with those by LeBlanc & Wilson and Symbalisty, the magnetic fields behind the shock wave, not in the inner core, are the main driving factor of the jet in our models. The fields are amplified by the strong differential rotations in the region between the shock wave and the boundary of the inner and outer cores, enhanced further by the lateral matter motions induced either by an oblique shock wave (for a strong shock case) or possibly by the MRI (magnetorotational instability)-like instability (for a weak shock case). We have also calculated the gravitational wave forms in the quadrupole approximation. Although the wave form from a nonrotating magnetic core is qualitatively different from those from rotating cores, the amplitude is about an order of magnitude smaller. Otherwise, we have found no substantial difference in the first burst of gravitational waves among the magnetized and nonmagnetized models, since the bounce is mainly driven by the combination of the matter pressure and the centrifugal force.

97 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied the local stability of stratified, differentially rotating fluids to axisymmetric perturbations in the presence of a weak magnetic field and of finite resistivity, viscosity, and heat conductivity.
Abstract: We study the local stability of stratified, differentially rotating fluids to axisymmetric perturbations in the presence of a weak magnetic field and of finite resistivity, viscosity, and heat conductivity. This is a generalization of the Goldreich-Schubert-Fricke (GSF) double-diffusive analysis to the magnetized and resistive, triple-diffusive case. Our fifth-order dispersion relation admits a novel branch that describes a magnetized version of multidiffusive modes. We derive necessary conditions for axisymmetric stability in the inviscid and perfect-conductor (double-diffusive) limits. In each case, rotation must be constant on cylinders and angular velocity must not decrease with distance from the rotation axis for stability, irrespective of the relative strength of viscous, resistive, and heat diffusion. Therefore, in both double-diffusive limits, solid-body rotation marginally satisfies our stability criteria. The role of weak magnetic fields is essential to reach these conclusions. The triple-diffusive situation is more complex, and its stability criteria are not easily stated. Numerical analysis of our general dispersion relation confirms our analytic double-diffusive criteria but also shows that an unstable double-diffusive situation can be significantly stabilized by the addition of a third, ostensibly weaker, diffusion process. We describe a numerical application to the Sun's upper radiative zone and establish that it would be subject to unstable multidiffusive modes if moderate or strong radial gradients of angular velocity were present.

87 citations


Patent
Wook Chang1, Dong Yun Kim1, Kyoung-ho Kang1, Eun-Seok Choi1, Won-Chul Bang1 
17 Jun 2004
TL;DR: In this paper, a 3D input apparatus and a method for precisely detecting a position of the input apparatus are presented. But, the 3D inputs are assumed to be fixed, and the position restoration unit is assumed to determine a position by integrating the second velocity.
Abstract: Provided are a 3D input apparatus and method for precisely detecting a position of the 3D input apparatus. The 3D input apparatus includes a sensor package which measures a first velocity an acceleration, and an angular velocity of the 3D input apparatus in a relative body coordinate system; a posture information generating unit, which generates posture information of the 3D input apparatus using the measured acceleration and angular velocity; a velocity transformation unit, which transforms the measured first velocity into a second velocity in an absolute coordinate system using the posture information; and a position restoration unit, which determines a position of the 3D input apparatus by integrating the second velocity.

86 citations


Patent
02 Jul 2004
TL;DR: In this paper, the authors proposed a control mode switch from the positional control to the electric current control and a torque, the direction of which is reverse to a direction of the motor rotation is generated by the motor, so that the motor rotating speed can be reduced and the collision energy can be alleviated.
Abstract: When either a command value or an actually measured value is appropriately selected as an angular velocity used for the frictional torque calculation, the frictional compensation can be made valid at all times in both the case in which a robot is actively operated according to an angular velocity command and the case in which the robot is passively operated being pushed by an external force. In the case where a motor rotating direction and a collision direction are reverse to each other after a collision has been detected, the control mode is switched from the positional control to the electric current control and a torque, the direction of which is reverse to the direction of the motor rotation is generated by the motor, so that the motor rotating speed can be reduced and the collision energy can be alleviated. After that, when the motor rotating speed is reduced to a value not more than the setting value, the control mode is switched to the compliance control and the distortion caused in a reduction gear is dissolved. On the other hand, in the case where the motor rotating direction and the collision direction are the same, the control mode is directly switched from the positional control to the compliance control without passing through the electric current control. When the robot is operated whole following a collision force, the collision force can be alleviated.

82 citations


Journal ArticleDOI
TL;DR: It has been shown that a self-similar solution is possible when the free stream angular velocity and the angular velocity of the cone vary inversely as a linear functions of time.

80 citations


Proceedings ArticleDOI
27 Sep 2004
TL;DR: By integrating the measured gravity and geomagnetic field with the local angular velocity using Sigma-Points Kalman Filters (SPKFs), the stability and the robustness of estimating the absolute orientation are improved over either sensor alone.
Abstract: In this paper, we develop an absolute orientation estimation device equipped with a wireless network. Accelerometers and magnetometers are used to measure the gravity and the geomagnetic field respectively. Gyroscope sensors are used to measure the local angular velocity. The geomagnetic field varies according to the environment. Therefore the device can obtain the information about the magnetic field through the wireless network. The orientation estimation task can be also requested to the other computers with the wireless network. By integrating the measured gravity and geomagnetic field with the local angular velocity using Sigma-Points Kalman Filters (SPKFs), the stability and the robustness of estimating the absolute orientation are improved over either sensor alone. We also propose an estimation method which excludes the effect of motion and magnetic disturbances for the accurate estimation.

Journal ArticleDOI
TL;DR: In this article, the angular expansion velocity in the sky is compared to the radial velocity of gas measured spectroscopically, and it is shown that for typical PNe the pattern velocity is 20 to 30% larger than the material velocity.
Abstract: The distances to individual wind-driven bubbles such as Planetary Nebulae (PNe) can be determined using expansion parallaxes: the angular expansion velocity in the sky is compared to the radial velocity of gas measured spectroscopically. Since the one is a pattern velocity, and the other a matter velocity, these are not necessarily the same. Using the jump conditions for both shocks and ionization fronts, I show that for typical PNe the pattern velocity is 20 to 30% larger than the material velocity, and the derived distances are therefore typically 20 to 30% too low. I present some corrected distances and suggest approaches to be used when deriving distances using expansion parallaxes.

Proceedings ArticleDOI
28 Sep 2004
TL;DR: The proposed Kalman filter obtains a non-drifting orientation estimate with improved resolution by incorporating the motion dynamics of the instrument during microsurgery and models the angular velocity drift explicitly as extra dynamic states.
Abstract: This paper presents the theory and modeling of a quaternion-based augmented state Kalman filter for real-time orientation tracking of a handheld microsurgical instrument equipped with a magnetometer-aided all-accelerometer inertial measurement unit (IMU). The onboard sensing system provides two complementary sources of orientation information. The all-accelerometer IMU provides a high resolution but drifting angular velocity estimate, while the magnetic north vector is combined with the estimated gravity vector to yield a non-drifting but noisy orientation estimate. Analysis of the dominant stochastic noise components of the sensors and derivation of the noise covariance are presented. The proposed Kalman filter obtains a non-drifting orientation estimate with improved resolution by incorporating the motion dynamics of the instrument during microsurgery and models the angular velocity drift explicitly as extra dynamic states.

Journal ArticleDOI
R. Arlt, V. Urpin1
TL;DR: In this paper, the authors investigated the nonlinear evolution of the vertical shear instability in accretion discs using three-dimensional hydrodynamic simulations and found that a vertical dependence of the angular velocity destabilizes the disc and leads to the generation of velocity fluctuations enhancing the angular momentum transport.
Abstract: The nonlinear evolution of the vertical shear instability in accretion discs is investigated using three-dimensional hydrodynamic simulations. A vertical dependence of the angular velocity destabilizes the disc and leads to the generation of velocity fluctuations enhancing the angular momentum transport. The instability emerges in the numerical models for large radial perturbation wave numbers. The growth time is a few tens of orbital revolutions.

Journal ArticleDOI
TL;DR: In this article, a first-order approximation coupling model is presented to analyze the dynamics of rotating flexible beam system, which is based on the Hamilton theory and the finite element discretization method.

Patent
03 Aug 2004
TL;DR: In this article, a method and apparatus for controlling a brushless DC motor over a wide range of angular speeds is presented Analog magnetic sensors provide continuous signal measurements related to the rotor angular position at a sample rate independent of rotor angular speed.
Abstract: A method and apparatus for controlling a brushless DC (BLDC) motor over a wide range of angular speeds is presented Analog magnetic sensors provide continuous signal measurements related to the rotor angular position at a sample rate independent of rotor angular speed In one embodiment, analog signal measurements are subsequently processed using an arctangent function to obtain the rotor angular position The arctangent may be computed using arithmetic computation, a small angle approximation, a polynomial evaluation approach, a table lookup approach, or a combination of various methods In one embodiment, the BLDC rotor is used to drive a Roots blower used as a compressor in a portable mechanical ventilator system

Journal ArticleDOI
TL;DR: In this paper, the authors studied the steady solutions of Euler-Poisson equations in bounded domains with prescribed angular velocity and showed that the radius of a rotating spherically symmetric star is uniformly bounded independent of the central density.
Abstract: In this paper, we study the steady solutions of Euler-Poisson equations in bounded domains with prescribed angular velocity. This models a rotating Newtonian star consisting of a compressible perfect fluid with given equation of state P=eSργ. When the domain is a ball and the angular velocity is constant, we obtain both existence and non-existence theorems, depending on the adiabatic gas constant γ. In addition we obtain some interesting properties of the solutions; e.g., monotonicity of the radius of the star with both angular velocity and central density. We also prove that the radius of a rotating spherically symmetric star, with given constant angular velocity and constant entropy, is uniformly bounded independent of the central density. This is physically striking and in sharp contrast to the case of the non-rotating star. For general domains and variable angular velocities, both an existence result for the isentropic equations of state and non-existence result for the non-isentropic equation of state are also obtained.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the possibility of measuring stellar differential rotation for solar-type stars through asteroseismology, and proposed a method to estimate differential rotation based on the realization that the m =± 1a ndm =± 2 components of quadrupole oscillations can be observed simultaneously in asterosesismology.
Abstract: The variation of rotation with latitude is poorly known on stars other than the Sun. Several indirect techniques, photometric and spectroscopic, have been used to search for departure from rigid rotation for sufficiently fast rotators. Here we investigate the possibility of measuring stellar differential rotation for solar-type stars through asteroseismology. Rotationally split frequencies of global oscillation provide information about rotation at different latitudes depending on the azimuthal order, m, of the mode of pulsation. We present a method to estimate differential rotation based on the realization that the m =± 1a ndm =± 2 components of quadrupole oscillations can be observed simultaneously in asteroseismology. Rotational frequency splittings can be inverted to provide an estimate of the difference in stellar angular velocity between the equator and 45 ◦ latitude. The precision of the method, assessed through Monte Carlo simulations, depends on the value of the mean rotation and on the inclination angle between the rotation axis and the line of sight.

Proceedings ArticleDOI
26 Apr 2004
TL;DR: In this paper, a modified generalized GF-INS algorithm based on four or more vector (triaxial) accelerometers is presented, which can serve in lieu of more expensive and less reliable angular rate gyros in vehicle moment controls and inclinometers in anti-theft systems.
Abstract: Modern automotive electronic control and safety systems, including air-bags, anti-lock brakes, anti-skid systems, adaptive suspension, and yaw control, rely extensively on inertial sensors. Currently, each of these sub-systems uses its own set of sensors, the majority of which are low-cost accelerometers. Recent developments in MEMS accelerometers have increased the performance limits of mass-produced accelerometers far beyond traditional automotive requirements; this growth trend in performance will soon allow the implementation of a gyro-free inertial navigation system (GF-INS) in an automobile, utilizing its existing accelerometer network. We propose, in addition to short-term aid to GPS navigation, a GF-INS can also serve in lieu of more expensive and less reliable angular rate gyros in vehicle moment controls and inclinometers in anti-theft systems. This work presents a modified generalized GF-INS algorithm based on four or more vector (triaxial) accelerometers. Historically, GF-INS techniques require strategically-placed accelerometers for a stable solution, hence inhibiting practical implementations; the vector-based GF-INS allows much more flexible system configurations and is more computationally efficient. An advanced attitude estimation technique is presented, utilizing coupled angular velocity terms that emerged as a result of the intrinsic misalignment of real vector accelerometers; this technique is void of singularity problems encountered by many prior researchers and is particularly useful when error due to the integration of angular accelerations is prominent, such as in low-speed systems or long-duration navigations. Furthermore, an initial calibration method for the vector-based GF-INS is presented. In the experimental setup, four vector accelerometers, based on Analog Devices accelerometers, are assembled into a portable, one cubic-foot, rigid structure, and the data is compared with that of a precision optical position tracking system. Finally, the feasibility of a GF-INS implementation in an automobile is assessed based on experimental results.

Journal ArticleDOI
TL;DR: Dobaczewski and Dudek as discussed by the authors describe the new version (v2.08i) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock problem by using the Cartesian deformed harmonic-oscillator basis.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the evolution of rigidly and differentially rotating protoneutron stars during the first twenty seconds of their life and found that the scale of variation of the angular velocity in a newly born neutron star is of the order of 7−10 km.
Abstract: We investigate the evolution of rigidly and differentially rotating protoneutron stars during the first twenty seconds of their life. We solve the equations describing stationary axisymmetric configurations in general relativity coupled to a finite temperature, relativistic equation of state, to obtain a sequence of quasi-equilibrium configurations describing the evolution of newly born neutron stars. The initial rotation profiles have been taken to mimic the situation found immediately following the gravitational collapse of rotating stellar cores. By analyzing the output of several models, we estimate that the scale of variation of the angular velocity in a newly born neutron star is of the order of 7−10 km. We obtain the maximum rotation frequency that can be reached as the protoneutron stars deleptonizes and cools down, as well as other relevant parameters such as total angular momentum or the instability parameter |T/W|. Our study shows that imposing physical constraints (conservation of baryonic mass and angular momentum) and choosing reasonable thermodynamical profiles as the star evolves gives results consistent with the energetics of more complex simulations of non-rotating protoneutron stars. It appears to be unlikely that newly born protoneutron stars formed in nearly axisymmetric core collapses reach the critical angular velocity to undergo the bar mode instability. They could, however, undergo secular or low |T/W| rotational instabilities a few seconds after birth, resulting in a strong emission of gravitational waves retarded with respect to the neutrino luminosity peak. We also found that the geometry of strongly differentially rotating protoneutron stars can become toroidal-like for large values of the angular velocity, before reaching the mass shedding limit.

Journal ArticleDOI
TL;DR: In this paper, the velocity fluctuations present in macroscopically homogeneous suspensions of neutrally buoyant non-Brownian spheres undergoing simple shear flow, and their dependence on the microstructure developed by the suspensions, are investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics simulations.
Abstract: The velocity fluctuations present in macroscopically homogeneous suspensions of neutrally buoyant non-Brownian spheres undergoing simple shear flow, and their dependence on the microstructure developed by the suspensions, are investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics simulations. We show that, in the dilute limit, the standard deviation of the velocity fluctuations (the so-called suspension temperature) is proportional to the volume fraction, in both the transverse and the flow directions, and that a theoretical prediction, which considers only the hydrodynamic interactions between isolated pairs of spheres, is in good agreement with the numerical results at low concentrations. We also simulate the velocity fluctuations that would result from a random hard-sphere distribution of spheres in simple shear flow, and thereby investigate the effects of the microstructure on the velocity fluctuations. Analogous results are discussed for the fluctuations in the angular velocity of the suspended spheres. In addition, we present the probability density functions for all the linear and angular velocity components, and for three different concentrations, showing a transition from a Gaussian to an exponential and finally to a stretched exponential functional form as the volume fraction is decreased.The simulations include a non-hydrodynamic repulsive force between the spheres which, although extremely short range, leads to the development of fore–aft asymmetric distributions for large enough volume fractions, if the range of that force is kept unchanged. On the other hand, we show that, although the pair distribution function recovers its fore–aft symmetry in dilute suspensions, it remains anisotropic and that this anisotropy can be accurately predicted theoretically from the two-sphere solution by assuming the complete absence of any permanent doublets of spheres.We also present a simple correction to the analysis of laser-Doppler velocimetry measurements, which substantially improves the interpretation of these measurements at low volume fractions even though it involves only the angular velocity of a single sphere in the vorticity direction.Finally, in an Appendix, we show that, in the dilute limit, the whole velocity autocorrelation function can be predicted using again only two-particle encounters.

Journal ArticleDOI
TL;DR: A method is presented for fast estimation of the angular rate of a tumbling spacecraft in a low-Earth orbit from sequential readings of Earth’s magnetic field from an extended Kalman filter, based on the assumption that the inertial geomagnetic field vector does not significantly change during the short sampling time.
Abstract: A method is presented for fast estimation of the angular rate of a tumbling spacecraft in a low-Earth orbit from sequential readings of Earth’s magnetic field Useful as a backup algorithm in cases of rate gyro malfunctions or during the initial acquisition phase, the estimator consists of an extended Kalman filter, based on the assumption that the inertial geomagnetic field vector does not significantly change during the short sampling time As the external disturbance torque is neglected, an analytic solution of Euler’s equations can be used in the filter’s propagation phase, allowing a significant savings of computation time compared to numerical integration of Euler’s equations Contrary to most existing angular rate estimators, the spacecraft’s attitude is neither used nor estimated within the proposed algorithm Moreover, the body-referenced geomagnetic field observations are not differentiated with respect to time as an external prefiltering procedure but are directly processed by the filter This processing gives rise to a colored effective measurement noise, which is properly handled via approximate Markov modeling and application of Bryson and Henrikson’s reduced-order filtering theory A simulation study employing a standard tenth-order International Geomagnetic Reference Field model is presented to demonstrate the performance of the algorithm

Journal ArticleDOI
TL;DR: In this paper, the rotational dynamics of disk accretion around a strongly magnetized neutron star with an aligned dipole field were investigated, and the authors obtained a prescription for the dynamical viscosity of such magnetically modified solutions for a Keplerian disk.
Abstract: We investigate the rotational dynamics of disk accretion around a strongly magnetized neutron star with an aligned dipole field. The magnetospheric field is assumed to thread the disk plasma both inside and outside the corotation radius. As a result of disk-star interaction, the magnetic torque on the disk affects the structure of accretion flow to yield the observed spin-up or spin-down rates for a source of given fastness, magnetic field strength, and mass accretion rate. Within the model we obtain a prescription for the dynamical viscosity of such magnetically modified solutions for a Keplerian disk. We then use this prescription to find a model solution for the rotation rate profile throughout the entire disk, including the non-Keplerian inner disk. We find that the non-Keplerian angular velocity transition region is not necessarily narrow for a source of given spin state. The boundary layer approximation, as in the standard magnetically threaded disk model, holds only in the case of dynamical viscosity decreasing all the way to the innermost edge of the disk. These results are applied to several observed disk-fed X-ray pulsars that have exhibited quasi-periodic oscillations (QPOs). The QPO frequencies provide a constraint on the fastness parameter and enable one to determine uniquely the width of the angular velocity transition zone for each source within model assumptions. We discuss the implications of these results on the value of the critical fastness parameter for a magnetized star in spin equilibrium. Applications of our model are also made with relevant parameters from recent numerical simulations of quasi-stationary disk-magnetized star interactions.

Journal ArticleDOI
TL;DR: In this article, the general spinning motion of an axisymmetric rigid body on a horizontal table is analyzed, allowing for slip and friction at the point of contact P. The governing dynamical system is six-dimensional, and trajectories of the system are computed in projection in a three-dimensional subspace; these start near unstable fixed points and (in the case of viscous friction) end at stable fixed points.
Abstract: The general spinning motion of an axisymmetric rigid body on a horizontal table is analysed, allowing for slip and friction at the point of contact P. Attention is focused on the case of spheroids (prolate or oblate), and particularly on spheroids whose density distribution is such that the centre-of-mass and centre-of-volume coincide. Four classes of fixed points (i.e. steady states) are identified, and the linear stability properties in each case are determined, assuming viscous friction at P. The governing dynamical system is six-dimensional. Trajectories of the system are computed, and are shown in projection in a three-dimensional subspace; these start near unstable fixed points and (in the case of viscous friction) end at stable fixed points. It is shown inter alia that a uniform prolate spheroid set in sufficiently rapid spinning motion with its axis horizontal is unstable, and its axis rises to a stable steady state, at either an intermediate angle or the vertical, depending on the initial angular velocity. These computations allow an assessment of the circumstances under which the condition described as ‘gyroscopic balance’ is realized. Under this condition, the evolution from an unstable to a stable state is greatly simplified, being described by a first-order differential equation. Oscillatory modes which are stable on linear analysis may be destabilized during this evolution, with consequential oscillations in the normal reaction R at the point of support. The computations presented here are restricted to circumstances in which R remains positive.

Journal ArticleDOI
TL;DR: In this paper, the authors present results for 2D models of rapidly rotating main sequence stars for the case where the an-gular velocity Ω is constant throughout the star.
Abstract: We present results for 2-dimensional models of rapidly rotating main sequence stars for the case where the an- gular velocity Ω is constant throughout the star. The algorithm used solves for the structure on equipotential surfaces and iteratively updates the total potential, solving Poisson's equation by Legendre polynomial decomposition; the algorithm can readily be extended to include rotation constant on cylinders. We show that this only requires a small number of Legendre polynomials to accurately represent the solution. We present results for models of homogeneous zero age main sequence stars of mass 1, 2, 5, 10 Mwith a range of angular velocities up to break up. The models have a composition X = 0.70, Z = 0.02 and were computed using the OPAL equation of state and OPAL/Alexander opacities, and a mixing length model of convection modified to include the effect of rotation. The models all show a decrease in luminosity L and polar radius Rp with increasing angular velocity, the magnitude of the decrease varying with mass but of the order of a few percent for rapid rotation, and an increase in equatorial radius Re. Due to the contribution of the gravitational multipole moments the parameter Ω 2 R 3/GM can exceed unity in very rapidly rotating stars and Re/Rp can exceed 1.5.

Patent
28 Apr 2004
TL;DR: In this paper, the dynamic matrix sensitivity of an inertia sensor is measured with a motion generating machine or a vibrating table for inducing a translational or rotary motion, an acceleration measuring unit, an angular velocity measuring unit or angular acceleration measuring units, an output device for fetching an output from the unit, one or, pre light reflectors, a displacement measuring device for seizing a multidimensional motion by using a laser interferometer radiating light from a plurality of directions to the light reflector, a data processing unit for processing a data indicating the state of motion
Abstract: A device for measuring the dynamic matrix sensitivity of an inertia sensor is provided with a motion generating machine or a vibrating table for inducing a translational or rotary motion, an acceleration measuring unit, an angular velocity measuring unit or angular acceleration measuring unit, an output device for fetching an output from the unit, one or, pre light reflectors, a displacement measuring device for seizing a multidimensional motion by using a laser interferometer radiating light from a plurality of directions to the light reflectors, a data processing unit for processing a data indicating the state of motion and obtained from the displacement measuring unit, and a displaying device to display or a transmitting device to transmit the output of the data processing unit and the output of the acceleration measuring unit, angular velocity measuring unit or angular acceleration measuring unit. Since the accelerometer is exposed to acceleration in every conceivable direction and possibly fails to find a correct value of acceleration as encountered by the conventional one-dimensional calibration, it is actually calibrated by applying acceleration from all possible directions thereto.

Patent
07 Dec 2004
TL;DR: In this article, the angular velocity sensor for detecting an angular velocity for detecting movement amounts and for controlling postures of vehicles, airplanes, cameras, and the like is provided with a piezoelectric vibrator, a temperature compensation function generating section, an oscillation section, a synchronous pulse forming section, and a Coriolis output detection section.
Abstract: The angular velocity sensor for detecting an angular velocity for detecting movement amounts and for controlling postures of vehicles, airplanes, cameras, and the like. The angular velocity sensor is provided with a piezoelectric vibrator, a temperature compensation function generating section, a correction coefficient setting section, an oscillation section, a synchronous pulse forming section, and a Coriolis output detection section. If an angular velocity is applied to the piezoelectric vibrator vibrating in a specific direction being driven by the oscillator section, a Coriolis force acts on the piezoelectric vibrator, and a vibration is generated which is perpendicular to the vibration in a specific direction. An electric charge generated by this vibration is detected at the detection electrode of the piezoelectric vibrator. The detected electric charge is converted to a voltage at the Coriolis output detection section, and a temperature compensation is performed, and further, the output is detected and a DC component is extracted. After that, a DC detecting signal having high stability without being influenced by factors such as the ambient temperature, power supply voltage fluctuations and unevenness in circuit devices is output from the Coriolis output detection section.

Journal ArticleDOI
TL;DR: A semi-similar solution of an unsteady mixed convection flow over a rotating cone in a rotating viscous fluid has been obtained when the free stream angular velocity and the angular velocity of the cone vary arbitrarily with the time.

Proceedings ArticleDOI
16 Nov 2004
TL;DR: In this paper, the Taylor-Proudman theorem is applied to a rapidly rotating cylindrical annulus and two possible options for minimizing these end-effects are presented: simply taking a very long cylinder, and splitting the end-plates into a series of differentially rotating rings.
Abstract: We present numerical simulations of the flow in a rapidly rotating cylindrical annulus. We show that at the rotation rates relevant to the magneto‐rotational instability, the flow is strongly constrained by the Taylor‐Proudman theorem. As a result, it is controlled almost entirely by the end‐plates. We then consider two possible options for minimizing these end‐effects, namely (i) simply taking a very long cylinder, and (ii) splitting the end‐plates into a series of differentially rotating rings. Regarding option (i), we show that the cylinder would have to be hundreds of times as long as it is wide before end‐effects become unimportant in the interior. Since this is clearly not feasible, we turn to option (ii), and show that in order to obtain a smooth angular velocity profile, the end‐plates would have to be split into around ten rings. If the end‐plates are split into fewer rings, perhaps 3–5, the angular velocity profile will not be smooth, but will instead consist of a series of Stewartson layers at the boundaries from one ring to the next. We suggest therefore that the instabilities one obtains in this system will be the familiar Kelvin‐Helmholtz instabilities of these Stewartson layers, rather than the magneto‐rotational instability. At best, one might hope to obtain the MRI superimposed on these Kelvin‐Helmholtz modes. Any subsequent interpretation of results is thus likely to be quite complicated.