Showing papers on "Angular velocity published in 2001"

Stellar evolution with rotation. VII. - Low metallicity models and the blue to red supergiant ratio in the SMC

Abstract: We calculate a grid of models with and without the eects of axial rotation for massive stars in the range of 9t o 60M and metallicity Z =0 :004 appropriate for the SMC. Remarkably, the ratios =crit of the angular velocity to the break{up angular velocity grow strongly during the evolution of high mass stars, contrary to the situation at Z =0 :020. The reason is that at low Z, mass loss is smaller and the removal of angular momentum during evolution much weaker, also there is an ecient outward transport of angular momentum by meridional circulation. Thus, a much larger fraction of the stars at lower Z reach break{up velocities and rotation may thus be a dominant eect at low Z. The models with rotation well account for the long standing problem of the large numbers of red supergiants observed in low Z galaxies, while current models with mass loss were predicting no red supergiants. We discuss in detail the physical eects of rotation which favour a redwards evolution in the HR diagram. The models also predict large N enrichments during the evolution of high mass stars. The predicted relative N{enrichments are larger at Z lower than solar and this is in very good agreement with the observations for A{type supergiants in the SMC.

Linear analysis of the Hall effect in protostellar disks

Abstract: The effects of Hall electromotive forces (HEMFs) on the linear stability of protostellar disks are examined. Earlier work on this topic focused on axial field and perturbation wavenumber geometry. Here we treat the problem more generally. Both axisymmetric and nonaxisymmetric cases are treated. Though seldom explicitly included in calculations, HEMFs appear to be important whenever Ohmic dissipation is. They allow for the appearance of electron whistler waves, and since these have right-hand polarization, a helicity factor is also introduced into the stability problem. This factor is the product of the components of the angular velocity and magnetic field along the perturbation wavenumber, and it is destabilizing when negative. An important finding of our more general calculation is that unless the field and angular velocity are exactly aligned, it is always possible to find destabilizing wavenumbers. HEMFs can destabilize any differential rotation law, even those with angular velocity increasing outward. Regardless of the sign of the angular velocity gradient, the maximum growth rate is always given in magnitude by the local Oort A value of the disk, as in the standard magnetorotational instability. The role of HEMFs may prove crucial to understanding how turbulence is maintained in the "low state" of eruptive disk systems.

Method and apparatus for motion tracking of an articulated rigid body

Abstract: The invention comprises a method of determining an orientation of a sensor, includes measuring a local magnetic field vector (507) and a local gravity vector (509) and using those measurements to determine the orientation of the sensor. Another embodiment comprises measuring a local magnetic field vector (507), a local gravity vector (509), and the angular velocity of the sensor (501). These three vectors are processed to determine the orientation of the sensor. Another embodiment comprises determining a local gravity vector (509) by providing an acceleration detector, moving the detector from a start point to an end point over a time period, and summing acceleration measurements over the time period. The total gravity vector is calculated using the summed acceleration measurements.

Direct numerical simulations of the Blandford–Znajek effect

Abstract: The time-dependent general relativistic equations of degenerate electrodynamics are solved numerically in order to study the mechanism of the electromagnetic extraction of the rotational energy of black holes. We performed a series of 2D runs for black holes with specific angular momentum, a, from 0.1 to 0.9 and for a monopole magnetic field assuming axisymmetry. In the inner region of the wind, the solution quickly settles to a steady state with an outgoing Poynting flux. In all cases the angular velocity of the magnetic field lines is almost half the angular velocity of the black hole. Thus, at least for the configuration considered, the Blandford–Znajek mechanism operates near its maximum power output.

On the relationship between joint angular velocity and motor cortical discharge during reaching.

Abstract: Single-unit activity in area M1 was recorded in awake, behaving monkeys during a three-dimensional (3D) reaching task performed in a virtual reality environment. This study compares motor cortical ...

Angular velocity sensor

Abstract: PROBLEM TO BE SOLVED: To reduce an error in an angular velocity output value by eliminating a driven vibration for a weight part from propagating to the direction of detection (hereafter called, unnecessary vibration) due to machining errors, in the case of a vibration type angular velocity sensor with a weight part displaceably supported by a beam part. SOLUTION: In order to suppress the weight part 3 from being driven to vibrate in directions other than a driving direction x, comb-teeth shaped electrodes 7, 7', 8, 8' for unnecessary vibration suppression are formed on the weight 3 side and on the base part 2 side as unnecessary vibration suppressing means for impressing static electric force in the direction of detection y on the weight part 3. A specified DC or AC voltage is placed between the movable electrodes 7, 7' and the fixed electrodes 8, 8' to generate the static electric force, thus causing the two sets of electrodes 7, 8, 7', 8' to attract each other.

Reciprocal angular acceleration of the ankle and hip joints during quiet standing in humans.

Abstract: Human quiet standing is often modeled as a single inverted pendulum rotating around the ankle joint, under the assumption that movement around the hip joint is quite small. However, several recent studies have shown that movement around the hip joint can play a significant role in the efficient maintenance of the center of body mass (COM) above the support area. The aim of this study was to investigate how coordination between the hip and ankle joints is controlled during human quiet standing. Subjects stood quietly for 30 s with their eyes either opened (EO) or closed (EC), and we measured subtle angular displacements around the ankle (θ a ) and hip (θ h ) joints using three highly sensitive CCD laser displacement sensors. Reliable data were obtained for both angular displacement and angular velocity (the first derivative of the angular displacement). Further, measurement error was not predominant, even among the angular acceleration data, which were obtained by taking the second derivative of the angular displacement. The angular displacement, velocity, and acceleration of the hip were found to be significantly greater (P<0.001) than those of the ankle, confirming that hip-joint motion cannot be ignored, even during quiet standing. We also found that a consistent reciprocal relationship exists between the angular accelerations of the hip and ankle joints, namely positive or negative angular acceleration of ankle joint is compensated for by oppositely directed angular acceleration of the hip joint. Principal component analysis revealed that this relationship can be expressed as: $$\ddot \theta _h = \gamma \ddot \theta _a $$ with γ=–3.15±1.24 and γ=–3.12±1.46 (mean ±SD) for EO and EC, respectively, where ' $$\ddot \theta $$ ' is the angular acceleration. There was no significant difference in the values of γ for EO and EC, and these values were in agreement with the theoretical value calculated assuming the acceleration of COM was zero. On the other hand, such a consistent relationship was never observed for angular displacement itself. These results suggest that the angular motions around the hip and ankle joints are not to keep the COM at a constant position, but rather to minimize acceleration of the COM.

Overcritical rotation of a trapped Bose-Einstein condensate.

Abstract: The rotational motion of an interacting Bose-Einstein condensate confined by a harmonic trap is investigated by solving the hydrodynamic equations of superfluids, with the irrotationality constraint for the velocity field. We point out the occurrence of an overcritical branch where the system can rotate with angular velocity larger than the oscillator frequencies. We show that in the case of isotropic trapping the system exhibits a bifurcation from an axisymmetric to a triaxial configuration, as a consequence of the interatomic forces. The dynamical stability of the rotational motion with respect to the dipole and quadrupole oscillations is explicitly discussed.

Effect of endpoint conditions on position and velocity near impact in tennis.

Abstract: Smoothing to obtain accurate position and velocity data near impacts in sport biomechanics studies is complicated by the accelerations of impact, endpoint effects and the smoothing technique used. Wrist goniometric data with two levels of random noise added were used to examine three endpoint modelling conditions for obtaining accurate position and velocity data at impact in the tennis forehand. The common approach of smoothing through impact created distortions of the position signal up to 100 ms before impact and resulted in consistent underestimations (-3.2%) of wrist angle and angular velocity (-67.9%) at impact. New linear and polynomial extrapolation conditions smoothed with all techniques provided lower root mean squared errors than the smoothing-through-impact condition, with discrete wrist positions at impact within 1.1% of the criterion data. Both the new linear and polynomial conditions can be used to make more accurate angular position and velocity estimates for tennis impacts, whereas the smo...

Accelerated diffusion in the centre of a vortex

Abstract: The spiral wind-up and diffusive decay of a passive scalar in circular streamlines is considered. An accelerated diffusion mechanism operates to destroy scalar fluctuations on a time scale of order P1/3 times the turn-over time, where P is a Peclet number. The mechanism relies on differential rotation, that is, a non-zero gradient of angular velocity. However if the flow is smooth, the gradient of angular velocity necessarily vanishes at the centre of the streamlines, and the time scale becomes greater. The behaviour at the centre is analysed and it is found that scalar there is only destroyed on a time scale of order P1/2. Related results are obtained for magnetic field and for weak vorticity, a scalar coupled to the stream function of the flow. Some exact solutions are presented.

Design of gyroscope-free navigation systems

Abstract: We examine the feasibility of designing a gyroscope-free inertial navigation system (INS) that uses only accelerometers to compute the linear and angular motions of a rigid body. The accelerometer output equation is derived to relate the linear and angular motions of a rigid body relative to a fixed inertial frame. A sufficient condition is given to determine if a configuration of accelerometers is feasible. If the condition is satisfied, the angular and linear motions can be computed separately using two decoupled equations of an input-output (I/O) dynamical system; a state equation for angular velocity and an output equation for linear acceleration. This simple computation scheme is derived from the corresponding dynamical system equations for a special cube configuration for which the angular acceleration is expressed as a linear combination of the accelerometer outputs.

Dynamic inversion-based adaptive/reconfigurable control of the X-33 on ascent

Abstract: A quaternion-based attitude control system is developed for the X-33 in the ascent flight phase. A nonlinear control law commands body-axis rotation rates that align the angular velocity vector with an Euler-axis defining the axis of rotation that takes the body-axis system into a desired-axis system. The magnitudes of the commanded body rates are determined by the magnitude of the rotation error The commanded body rates form the input to a dynamic inversion-based adaptive/reconfigurable control law. The indirect adaptive control portion uses online system identification to estimate the current control effectiveness matrix to update a control allocation module. The control allocation nominally operates in a minimum deflection mode; however, if a fault is detected, it can operate in a null-space injection mode that excites and decorrelates the effecters without degrading the vehicle response in order to enable online system identification. The overall system is designed to provide fault and damage tolerance for the X-33 on ascent. The baseline control law supports full envelope operation and eliminates trajectory dependent gain-scheduling that is typically found on this type of vehicle. Preliminary results are shown to demonstrate the feasibility of the approach.

Composite sensor device and method of producing the same

Abstract: A plane vibrator (5) of an angular velocity sensor (2) and a movable member (20) of an acceleration sensor (3) are provided in a spaced floating state on the same substrate (4). A lid (30) is formed so as to cover and be spaced from the upper side of the plane vibrator (5) and the movable member (20). A space defined by the substrate (4) and the lid (30) is sectioned into a angular velocity sensor space (33) and an acceleration sensor space (34) by use of a sectioning wall (36). The angular velocity sensor space (33) is hermetically sealed to be in the vacuum state. The acceleration sensor space (34) is hermetically sealed to be under atmospheric pressure. The plane vibrator (5) is vibrated at a high frequency and a large amplitude so that the angular velocity detection sensitivity is enhanced. The movable member (20), even if vibration of the plane vibrator (5) is transmitted thereto, is prevented from vibrating at a high frequency and a large amplitude, due to the damping effect of air. Thus, the acceleration detection sensitivity is enhanced.

Screw instability in black hole magnetospheres and a stabilizing effect of field-line rotation

Abstract: The screw instability of a magnetic field is a mechanism for prohibiting the generation of strongly twisted field lines on large scales If it can work in black hole magnetospheres, the global axisymmetric structure and the main process of energy release will be significantly influenced In this paper, we study the instability condition in the framework of the variational principle, paying special attention to the stabilizing effect due to field-line rotation against the screw-unstable modes satisfying the well-known Kruskal-Shafranov criterion The basic formulation for the stability analysis of rotating force-free fields in Kerr geometry is provided Then, for practical use of the analytical method, the stationary configuration is assumed to be cylindrical, and we treat the long-wave mode perturbations excited at large distances from the central black hole, where the strength of gravity becomes negligibly small This allows us to derive clearly a new criterion dependent on the rotational angular velocity of the magnetic field lines, and the implications of the results obtained for magnetic activities of jets driven by a black hole are briefly discussed

On the Number and Placement of Accelerometers for Angular Velocity and Acceleration Determination

Abstract: This paper identifies the minimum number of accelerometers nec-essary to measure rigid body acceleration. Notwithstanding thatonly 9 scalar unknowns must be identified, 12 devices compose aminimum set of transducers. This redundancy is necessary toavoid singularities in the equations. Conditions for the sensorplacement are given. It is also shown that when the determinationof the angular velocity is not required, a reduced set of 9 sensorscan be adopted. @DOI: 10.1115/1.1386649#

Angular velocity sensor

Abstract: PROBLEM TO BE SOLVED: To provide an angular velocity sensor with higher sensitivity and precision by obtaining a stable driving vibration as well as reducing influence of a mechanical coupling. SOLUTION: The angular velocity sensor is capable of detecting at least one angular velocity of one axial direction among three directional axses perpendicular to each other. The sensor is provided with a beam structure body suspended via an elastic beam on a substrate. The beam structure body is composed of a pair of driving frames and detection frames. As for the driving frames, each frame is supported at least by a pair of elastic beams, connected to both the sides of the connection part via a pair of driving beams, and vibrated toward the 1st or 2nd axial direction parallel to the substrate surface. The detection frames are connected by the connection part, arranged point to point symmetry to the 1st and/or 2nd axial direction regarding the center of the connection part, and provided with a pair of detection mass body suspended by a detection beam capable of vibrating toward detecting direction, and vibrates around the 3rd axis perpendicular to the substrate surface by vibration the driving frame. The displacement of the detection mass body to the 3rd axis direction generated by the angular velocity is detected by the detection electrode provided on the substrate. COPYRIGHT: (C)2005,JPO&NCIPI

Dispersion Reduction of a Direct-Fire Rocket Using Lateral Pulse Jets

Abstract: Impact point dispersion of a direct e re rocket can be drastically reduced with a ring of appropriately sized lateral pulse jets coupled to a trajectory tracking e ight control system. The system is shown to work well against uncertainty in the form of initial off-axis angular velocity perturbations as well as atmospheric winds. For an example case examined, dispersion was reduced by a factor of 100. Dispersion reduction is a strong function of the number of individual pulse jets, the pulse jet impulse, and the trajectory tracking window size. Proper selection of these parameters for a particular rocket and launcher combination is required to achieve optimum dispersion reduction. Forrelatively lowpulsejetimpulse, dispersion steadily decreasesasthenumberofpulsejetsisincreased or as the pulse jet impulse is increased. For a e xed total pulse jet ring impulse, a single pulse is the optimum pulse jet cone guration when the pulse jet ring impulse is small because the effect of a pulse on the trajectory of a rocket decreases as the round e ies downrange. Nomenclature CDD = e n cant roll moment aerodynamic coefe cient CLP = roll damping aerodynamic coefe cient CMQ = pitch damping aerodynamic coefe cient CNA = normal force aerodynamic coefe cient CX0 = zero yaw axial force aerodynamic coefe cient CX2 = yaw axial force aerodynamic coefe cient D = rocket reference diameter ethres = trajectory tracking window size L; M; N = total applied moments about rocket mass center expressed in the aft body reference frame nJ = number of individual lateral pulse jets nRXi ;nRYi , = ith main rocket motor direction cosines in the nRZi body frame p;q;r = components of the angular velocity vector of the projectile in the body reference frame T = P ° time constant TJi = ith lateral pulse jet thrust TRi = ith main rocket motor thrust t ¤ = time of the most recent pulse jet e ring u;v;w = components of the velocity vector of the mass center of the composite body in the body reference frame uA;vA;wA = components of the velocity of the mass center of the projectile with mean wind expressed in the body reference frame VA = magnitude of the velocity vector of the mass center of the projectile experienced with mean wind expressed in the body reference frame VMW;aeMW = magnitude and wind factor of the mean atmospheric wind expressed in the initial reference frame X;Y; Z = total applied force components in the aft body reference frame

Rotating Convection in f-Planes: Mean Flow and Reynolds Stress

Abstract: We study turbulent compressible convection under the influence of rotation in an f-plane configuration using numerical simulation. Our focus is on the behaviors of the mean flows and the Reynolds stress. A parametric study is conducted, using 36 computed cases with different energy fluxes, rotation rates (Ω), and inclinations of the rotation vector. The flux varies over a factor of 8; the Coriolis number ranges from 0 to approximately 7; the inclination of the rotation vector covers the range from 0 (at the pole) to π/2 (at the equator). The coverage of this piece of parameter space is rather full and dense, so that we do not need to base our discussions on extrapolations of sparsely distributed cases. Special attention is paid to obtaining statistical convergence of the Reynolds stress, a very slow process that consumes much computer time. The numerical results show that: (1) Even though the properties of the convection zones are different (efficient versus inefficient convection), the behavior of our cases has considerable similarity to that of the turbulent cases explored by Brummell et al. (2) Between the two studies, the most significant difference in flow behavior occurs in the mean zonal velocity at low Rossby numbers. While Brummell et al. found a "constant-with-depth profile in the bulk of the layer" (and two "boundary layers"), we find that the profile develops a prominent retrograde dip at the top of the convection zone. (3) We offer an explanation for the dip based on the vertical distribution of the vertical-meridional component of the Reynolds stress. This may have relevance for understanding the radial drop of the solar angular velocity near the Sun's surface. (4) When the rotation vector is perpendicular to the vertical direction (at the equator), the behavior of the system undergoes a qualitative jump from those with other rotation vector inclinations. A shear with a strain rate of -2Ω develops in the mean zonal velocity, independent of the size of the energy flux. (5) We have tabulated the maxima and minima of the mean horizontal velocities, the rms velocities, and correlations between different velocity components for all the cases. Behavioral trends of these quantities can be readily identified. (6) The correlation of the meridional and zonal velocity fluctuations, important in both theory and observation, is found to change its sign from negative to positive when the Rossby number drops past 1. (7) After the meridional momentum equation (which ignores minor effects due to a shell geometry) is averaged over longitude, depth, and time, the resulting equation relates the vertically averaged Reynolds stress to the rotation rate of a whole conical sheet of fluid at a specific latitude. Using our f-plane results to estimate the amount of driving generated by the turbulent Reynolds stress in the solar convection zone, we find that its role is quite insignificant and inadequate for producing the observed differential rotation. We conclude that the latitudinal gas pressure gradient and the global circulation play more important roles.

Axisymmetric flow of navier-stokes fluid in the whole space with non-zero angular velocity component

Abstract: We study axisymmetric solutions to the Navier-Stokes equations in the whole three-dimensional space. We find conditions on the radial and angular components of the velocity field which are sufficient for proving the regularity of weak solutions.

Classification of Algorithms for Angular Velocity Estimation

Abstract: Scanning the known algorithms for deriving the angular velocity vector from either vector measurements or attitude measurements, it is realized that the algorithms are divided into two categories, each category employing a different approach One category requires differentiation of the measurements, and one does not A superficial inspection of the two categories may lead to the conclusion that the two are not related to one another; however, a deeper examination reveals that the two are closely related In this paper the two categories are formulated in general terms, which enables the presentation of the connection between them The connection is demonstrated through examples

A large-eddy simulation of turbulent compressible convection: differential rotation in the solar convection zone

Abstract: We present the results of two simulations of the convection zone, obtained by solving the full hydrodynamic equations in a section of a spherical shell. The first simulation has cylindrical rotation contours (parallel to the rotation axis) and a strong meridional circulation, which traverses the entire depth. The second simulation has isorotation contours about mid-way between cylinders and cones, and a weak meridional circulation, concentrated in the uppermost part of the shell. We show that the solar differential rotation is directly related to a latitudinal entropy gradient, which pervades into the deep layers of the convection zone. We also offer an explanation of the angular velocity shear found at low latitudes near the top. A non-zero correlation between radial and zonal velocity fluctuations produces a significant Reynolds stress in that region. This constitutes a net transport of angular momentum inwards, which causes a slight modification of the overall structure of the differential rotation near the top. In essence, the thermodynamics controls the dynamics through the Taylor–Proudman momentum balance. The Reynolds stresses only become significant in the surface layers, where they generate a weak meridional circulation and an angular velocity ‘bump’.

A Nonlinear, Transient, Single-Cylinder Diesel Engine Simulation for Predictions of Instantaneous Engine Speed and Torque

Abstract: A non-linear, transient, single-cylinder diesel engine simulation has been developed for predictions of instantaneous engine speed and torque. The foundation of our model is a physically based, thermodynamic, steady-state diesel engine simulation (Assanis, D. N., and Heywood, J. B., 1986, Development and Use of a Computer Simulation of the Turbocompounded Diesel System for Engine Performance and Component Heat Transfer Studies, SAE Paper 860329), which has been comprehensively validated for various engine designs. The transient extension of the parent model represents the diesel engine as a non-linear, dynamic system. The instantaneous crank-shaft speed is determined from the solution of the engine-external load dynamics equation, where the engine torque is tracked on a crank-angle basis. Validation of the transient model during rapid engine acceleration shows that both the cyclic fluctuations in the instantaneous crank-shaft speed line and the overall engine response are in good agreement with experimental measurements. Predictions of single-cylinder engine starting reveals the importance of selecting the proper value of the engine moment of inertia in order to control the amplitude of angular velocity fluctuations and ensure stable engine operation. It is further shown that the variation in the inertial forces on the reciprocating components with speed has a dramatic impact on the instantaneous torque profile, and consequently on angular velocity fluctuations.

Adaptive control for z-axis MEMS gyroscopes

Abstract: An angular rate-sensing scheme for z-axis MEMS oscillatory gyroscopes, which is based on observer-based adaptive control, is presented. The proposed control scheme estimates the component of the angular velocity vector, which is orthogonal to the plane of oscillation of the gyroscope (z-axis), as well as compensates friction forces, and fabrication imperfections, which cause model parameter variations and the presence of off-diagonal terms in the system's stiffness and damping matrix. The convergence and resolution analysis shows that the proposed observer-based adaptive controlled scheme offers several advantages over conventional sensing strategies, including a larger operational bandwidth, producing no zero-rate output, the ability of self-calibration and a large robustness to parameter variations caused by fabrication defects and ambient conditions.

Flexible Spacecraft Reorientations Using Gimbaled Momentum Wheels

Abstract: We study the reorientations of flexible spacecraft using momentum exchange devices. A new concise form of the equations of motion for a spacecraft with gimbaled momentum wheels and flexible appendages is presented. The derivation results in a set of vector nonlinear first order differential equations with gimbal torques and spin axis torques as the control inputs. Feedback control laws which result in smooth reorientations are sought with the goal of minimizing structural excitations. We pay special attention to a class of maneuvers wherein the magnitude of the momentum in the wheel cluster is held constant, resulting in a so-called “stationary platform maneuver. “ The advantage of this maneuver is that the platform angular velocity remains small throughout, thereby reducing the excitation of the appendages.

Method for rollover detection for automotive vehicles with safety-related devices

Abstract: Method for rollover detection for automotive vehicles with safety-related devices, such as roll bars, (side) airbags and seat-belt tensioners. In a known method according to DE 196 09 717 A1, in which an angular rate sensor measures the angular velocity in each case around the vertical axis (yaw axis), the longitudinal axis and the transverse axis (pitch axis) of the vehicle, a rollover is detected when at least one of the measured angular velocities exceeds a defined threshold value (limit value). This publication further proposes calculating the rotational energy of the vehicle from the angular velocities, and indicating an impending rollover when the rotational energy exceeds a defined threshold. However, the disadvantage of this method is that false decisions cannot be excluded, when for example the vehicle is traveling over steep terrain or is subject to slow rolling motions while traveling around curves, especially into steep curves. According to the invention, starting from the initial position angle indicating the initial position of the vehicle, the integrated angular rate signal—as angle of rotation—is added so that the value proportional to the momentary inclination angle (in relation to the horizontal plane) can be compared to a trigger threshold which is a function of the angular rate. A safety-related device is triggered if this trigger threshold is exceeded by the cumulative value.