Showing papers on "Angular velocity published in 1998"

Helioseismic Studies of Differential Rotation in the Solar Envelope by the Solar Oscillations Investigation Using the Michelson Doppler Imager

Abstract: The splitting of the frequencies of the global resonant acoustic modes of the Sun by large-scale flows and rotation permits study of the variation of angular velocity Ω with both radius and latitude within the turbulent convection zone and the deeper radiative interior. The nearly uninterrupted Doppler imaging observations, provided by the Solar Oscillations Investigation (SOI) using the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft positioned at the L1 Lagrangian point in continuous sunlight, yield oscillation power spectra with very high signal-to-noise ratios that allow frequency splittings to be determined with exceptional accuracy. This paper reports on joint helioseismic analyses of solar rotation in the convection zone and in the outer part of the radiative core. Inversions have been obtained for a medium-l mode set (involving modes of angular degree l extending to about 250) obtained from the first 144 day interval of SOI-MDI observations in 1996. Drawing inferences about the solar internal rotation from the splitting data is a subtle process. By applying more than one inversion technique to the data, we get some indication of what are the more robust and less robust features of our inversion solutions. Here we have used seven different inversion methods. To test the reliability and sensitivity of these methods, we have performed a set of controlled experiments utilizing artificial data. This gives us some confidence in the inferences we can draw from the real solar data. The inversions of SOI-MDI data have confirmed that the decrease of Ω with latitude seen at the surface extends with little radial variation through much of the convection zone, at the base of which is an adjustment layer, called the tachocline, leading to nearly uniform rotation deeper in the radiative interior. A prominent rotational shearing layer in which Ω increases just below the surface is discernible at low to mid latitudes. Using the new data, we have also been able to study the solar rotation closer to the poles than has been achieved in previous investigations. The data have revealed that the angular velocity is distinctly lower at high latitudes than the values previously extrapolated from measurements at lower latitudes based on surface Doppler observations and helioseismology. Furthermore, we have found some evidence near latitudes of 75° of a submerged polar jet which is rotating more rapidly than its immediate surroundings. Superposed on the relatively smooth latitudinal variation in Ω are alternating zonal bands of slightly faster and slower rotation, each extending some 10° to 15° in latitude. These relatively weak banded flows have been followed by inversion to a depth of about 5% of the solar radius and appear to coincide with the evolving pattern of torsional oscillations reported from earlier surface Doppler studies.

Axial instability of rotating relativistic stars

Abstract: Perturbations of rotating relativistic stars can be classified by their behavior under parity. For axial perturbations (r-modes), initial data with negative canonical energy is found with angular dependence eim for all values of m ≥ 2 and for arbitrarily slow rotation. This implies instability (or marginal stability) of such perturbations for rotating perfect fluids. This low m-instability is strikingly different from the instability to polar perturbations, which sets in first for large values of m. The timescale for the axial instability appears, for small angular velocity Ω, to be proportional to a high power of Ω. As in the case of polar modes, viscosity will again presumably enforce stability except for hot, rapidly rotating neutron stars. This work complements Andersson's numerical investigation of axial modes in slowly rotating stars.

Further passivity results for the attitude control problem

Abstract: In this paper we establish passivity for the system which describes the attitude motion of a rigid body in terms of minimal three-dimensional kinematic parameters. In particular, we show that linear asymptotically stabilizing controllers and control laws without angular velocity measurements follow naturally from these passivity properties. The results of this paper extend similar results for the case of the (nonminimal) Euler parameters.

Fluid particle model

Abstract: We present a mechanistic model for a Newtonian fluid called fluid particle hydrodynamics. By analyzing the concept of ``fluid particle'' from the point of view of a Voronoi tessellation of a molecular fluid, we propose a heuristic derivation of a dissipative particle dynamics algorithm that incorporates shear forces between dissipative particles. The inclusion of these noncentral shear forces requires the consideration of angular velocities of the dissipative particles in order to comply with the conservation of angular momentum. It is shown that the equilibrium statistical mechanics requirement that the linear and angular velocity fields are Gaussian is sufficient to construct the random thermal forces between dissipative particles. The proposed algorithm is very similar in structure to the (isothermal) smoothed particle hydrodynamics algorithm. In this way, this work represents a generalization of smoothed particle hydrodynamics that incorporates consistently thermal fluctuations and exact angular momentum conservation. It contains also the dissipative particle dynamics algorithm as a special case. Finally, the kinetic theory of the dissipative particles is derived and explicit expressions for the transport coefficients of the fluid in terms of model parameters are obtained. This allows us to discuss resolution issues for the model.

Estimation of Angular Velocity and Acceleration from Shaft-Encoder Measurements

Abstract: This paper suggests a Kalman-filter approach to the estimation of angular velocity and acceleration from (quantized) shaft-encoder measurements Finite-difference estimates deteriorate as sampling rates are increased For small sampling periods, we show that the filtering problem is the dual of the cheap control problem, and we jus tify the use of all-integrator models We investigate Kalman filtering with constant sampling rate, and also with measurements triggered by encoder pulses Simulation and experimental results are given

Multi-element micro gyro

Abstract: A micro-gyro device is disclosed combining a first element (20) which oscillates linearly in a plane along a first direction (y), and second element (24) which oscillates linearly in the same plane along a second direction (x) perpendicular to the first direction, so arranged that Coriolis force is transmitted from one element to the other without any substantial transfer of motion of either element to the other in its own direction of motion In other words, the masses of the two elements (20, 24) operate independently of one another, providing improved performance, and individual adjustability to compensate for any manufacturing imprecision The rate axis, around which is measured angular speed of the micro-gyro device due to exterior forces, is perpendicular to the plane of the first and second elements (20, 24) The presently-preferred device combines an outer rectangular ring (20), which oscillates along the drive direction, with an inner plate (24), which oscillates along the sensing direction, whenever external rotating motion occurs about the rate axis A unitary micro-gyro structure is disclosed in which a monolithic substrate (28) supports three micro-gyro devices (102, 104, 106), each of which measures angular speed of the structure around a different rate axis, which is perpendicular to each of the other two rate axes

MHD Unsteady Free Convection Flow past a Vertical Porous Plate

Abstract: The present work is concerned with unsteady 2-dimensional laminar free convection flow of an incompressible, viscous, electrically conducting (Newtonian or polar) fluid through a porous medium bounded by an infinite vertical plane surface of constant temperature. A uniform magnetic field acts perpendicular to the surface which absorbs the fluid with a suction velocity varying periodically with time about a non-zero constant mean value. The equations of conservation of mass, momentum, angular velocity, and energy, which govern the flow and heat transfer problem, are solved analytically using regular perturbation techniques. The effects of material parameters such as Grashof number, Prandtl number, permeability parameter, suction parameter, and magnetic parameter on the velocity, angular velocity, and temperature are discussed. Numerical results are presented graphically and discussed.

Angular velocity sensor

Abstract: PROBLEM TO BE SOLVED: To realize an angular velocity sensor by which a stress is hard to concentrate in a connection part when the sensor is operated and when a disturbance acceleration is applied, by which the breakdown strength of a spring and that of comb teeth are enhanced and whose durability is high. SOLUTION: The angular velocity sensor is provided with a plurality of sensor constituent elements which are composed of at least a support frame 1. The elements are composed of a support substrate 10 which is fixed to the support frame 1. The elements are composed of two first vibrating bodies 2 which are coupled to the support frame 1 via suspension springs 3. The elements are composed of coupling springs 4 which couple the two first vibrating bodies 2. The elements are composed of second vibrating bodies 5 which are coupled to the first respective vibrating bodies 2 via vibrating springs 6. The elements are composed of moving comb teeth 9 which are coupled to the second vibrating bodies 5. The elements are composed of fixed electrodes 7 which are fixed to the support substrate 10. The elements are composed of fixed comb teeth 8 which are coupled to the fixed electrodes 7. In any of the sensor constituent elements, a part which is coupled to at least one other sensor constituent element is formed in an arc shape.

Sliding mode control of the x-33 vehicle in launch and re-entry modes *

Abstract: This work develops a sliding mode controller for the X-33 vehicle in launch and re-entry mode. The resulting controller utilizes two-loop sliding mode controller and provides robust, de-coupled tracking of both the required angular velocity profiles and the desired vehicle orientation angles. The motion in sliding of both the angular velocity and the orientation angles is described by linear de-coupled homogeneous vector valued differential equations with desired eigenvalues placement. An optimal control allocation algorithm is employed to allocate torque commands into end- effector deflection commands, which are executed by the actuators. Simulation of the X-33 vehicle in launch and re-entry modes demonstrated accurate, robust, de- coupled tracking performance. provides robust de-coupled multivariable tracking of the desired X-33 vehicle re-entry profiles. A sliding mode control system was designed and analyzed for the WB001 reusable launch vehicle design"*'5. This work develops a sliding mode controller (SMC) for the X-33 launch and re-entry modes. The design consists of two basic steps. First, the required angular velocity profile is determined in the outer (guidance) loop such that the given vehicle mission angle profiles are followed if the angular velocity profile is tracked. This is achieved by designing an outer-loop SMC for the kinematics equation of angular motion and taking the angular velocity as the virtual control input. Second, a suitable inner-loop SMC is designed for the dynamic equation of motion such that the required angular velocity profile is tracked. The inner-loop SMC produces control signals in terms of roll, pitch and yaw torque commands. The inner loop transient response must be much faster than the outer loop response. A control allocation algorithm is employed to allocate torque commands into end- effector deflection commands, which are executed by the actuators. The resulting two-loop SMC provides robust, de-coupled tracking of both the angular velocity profiles and the desired vehicle mission angle profiles and takes full advantage of the cascade form of the equations of motion. The motion in sliding of both the angular velocity and the mission angles is described by linear de-coupled homogeneous vector valued differential equations with desired eigenvalues placement. Simulation results demonstrating the substantive effectiveness of this controller design for the X-33 launch and re-entry modes and utilizing realistic desired angular profiles provided in table lookup format are presented.

Innermost stable circular orbits around relativistic rotating stars

Abstract: We investigate the innermost stable circular orbit (ISCO) of a test particle moving on the equatorial plane around rotating relativistic stars such as neutron stars. First, we derive approximate analytic formulas for the angular velocity and circumferential radius at the ISCO making use of an approximate relativistic solution which is characterized by arbitrary mass, spin, mass quadrupole, current octapole and mass ${2}^{4}$-pole moments. Then, we show that the analytic formulas are accurate enough by comparing them with numerical results, which are obtained by analyzing the vacuum exterior around numerically computed geometries for rotating stars of polytropic equation of state. We demonstrate that contribution of mass quadrupole moment for determining the angular velocity and, in particular, the circumferential radius at the ISCO around a rapidly rotating star is as important as that of spin.

Differential Rotation and Meridional Flow for Fast-rotating Solar-Type Stars

Abstract: Observations indicate that normalized surface differential rotation decreases for fast-rotating stars, that is, | ΔΩ |/Ω ∝ Ω-0.3. An increase of | ΔΩ |/Ω is provided, however, by the current Reynolds stress theory of differential rotation in stellar convection zones, without the inclusion of meridional flow. We compute both the pole-equator difference of the surface angular velocity and the meridional drift for various Taylor numbers to demonstrate that the inclusion of meridional flow in the computations for fast rotation yields a systematic reduction of the resulting differential rotation. Our model's adiabatic and density-stratified convection zone, with stress-free surfaces and a thickness of 0.3 stellar radii, yields the relation | ΔΩ |/Ω ∝ Ω-(0.15 ... 0.30) for stars with faster rotation than the Sun, in agreement with previous observations. If the Coriolis number rather than the Taylor number is varied, we find a maximum differential rotation of 20%. For stars with fast rotation, exponents of up to n' 0.4 are found. All rotation laws exhibit superrotating equators.

Unsteady flow over a stretching surface with a magnetic field in a rotating fluid

Abstract: The effect of the magnetic field on the unsteady flow over a stretching surface in a rotating fluid has been studied. The unsteadiness in the flow field is due to the time–dependent variation of the velocity of the stretching surface and the angular velocity of the rotating fluid. The Navier–Stokes equations and the energy equation governing the flow and the heat transfer admit a self–similar solution if the velocity of the stretching surface and the angular velocity of the rotating fluid vary inversely as a linear function of time. The resulting system of ordinary differential equations is solved numerically using a shooting method. The rotation parameter causes flow reversal in the component of the velocity parallel to the strerching surface and the magnetic field tends to prevent or delay the flow reversal. The surface shear stresses along the stretching surface and in the rotating direction increase with the rotation parameter, but the surface heat transfer decreases. On the other hand, the magnetic field increases the surface shear stress along the stretching surface, but reduces the surface shear stress in the rotating direction and the surface heat transfer. The effect of the unsteady parameter is more pronounced on the velocity profiles in the rotating direction and temperature profiles.

Aerodynamics of the curve-ball : an investigation of the effects of angular velocity on baseball trajectories

Abstract: In this dissertation the aerodynamic force and initial conditions of pitched baseballs are estimated from high-speed video data. Fifteen parameters are estimated including the lift coefficient, drag coefficient and the angular velocity vector using a parameter estimation technique that minimizes the residual error between measured and estimated trajectories of markers on the ball’s surface and the center of mass of pitched baseballs. Studies are carried out using trajectory data acquired from human pitchers and, in a more controlled environment, with a pitching machine. In all 58 pitch trajectories from human pitchers and 20 pitching machine pitches with spin information are analyzed. In the pitching machine trials four markers on the ball are tracked over the first 4 ft (1.22 m) and the center of mass of the ball is tracked over the last 13 ft (3.96 m) of flight. The estimated lift coefficients are compared to previous measured lift coefficients of Sikorsky (Alaways & Lightfoot, 1998) and Watts & Ferrer (1987) and show that significant differences exists in the lift coefficients of twoand four-seam curve balls at lower values of spin parameter, S . As S increased the twoand four-seam lift coefficients merge becoming statistically insignificant. The estimated drag coefficients are compared to drag coefficients of smooth spheres and golf-balls and show that these data sets bound the drag-coefficient of the baseball. Finally, it is shown that asymmetries of the ball associated with the knuckleball can influence the trajectory of the more common curve and fastball.

Control device of leg type moving robot

Abstract: PROBLEM TO BE SOLVED: To appropriately control the actual floor reaction by detecting the actual floor reaction to calculate the moment around the center point, determining the amount of rotation to correct the target position and/or posture so that the position and/or posture of the leg part is rotated, and to displace the joint of a robot. SOLUTION: A two-foot walking robot 1 is provided with a joint on a leg part link 2. A six-axis force sensor 44 is mounted on a foot joint, the three- direction components of the force and the moment are measured, and presence/ absence of landing of a foot part and the floor reaction are detected. An inclination sensor 60 is installed on an upper body 24 to detect the inclination and the angular velocity. A rotary encoder to detect an amount of the rotation is provided on an electric motor for a joint. First and second arithmetic units are provided in a control unit 26, and the first arithmetic unit calculates the angular displacement command of the joint, and feeds it to a RAM. The second arithmetic unit reads the measured value to detect the command from the RAM, calculates the control value, and outputs it to the electric motor. The floor reaction can be appropriately controlled without generating the interference.

Stellar Evolution with Arbitrary Rotation Laws. III. Convective Core Overshoot and Angular Momentum Distribution

Abstract: Intermingled two-dimensional hydrodynamic and two-dimensional stellar evolution calculations are presented for two 8.75 M☉ models, one nonrotating and one rotating with a zero-age main sequence surface equatorial rotational velocity of 200 km s-1. The first calculation of the rotating model was made assuming no convective core overshooting and enforcing solid-body rotation in the convective core. Hydrodynamic simulations at various stages of core hydrogen burning indicate that neither of these assumptions is true. Overshooting to a distance equivalent to about 0.35 pressure scale heights is found, and there is some evidence that the distance in terms of the pressure scale height increases slightly in later stages of core hydrogen burning. This is not a claim that the pressure scale height is a relevant parameter for determining overshooting distances. The dynamic calculations also show that the rotation rate in the convective core is approximately constant on cylinders and that the rate may be expressed as a power law in the distance from the rotation axis, as long as there is a cutoff at small distances. Two more evolutionary sequences, one rotating and one not, were calculated utilizing these results. The largest effects are produced from the overshooting and are esssentially those found by previous researchers. However, the angular momentum distribution in the interior at the end of core hydrogen burning is significantly different for this second case than for the one assuming solid-body rotation in the convective core. The primary differences are that the horizontal variation in the rotation rate is much larger and that the rotation rate near the center is much higher in the second case.

Closed-form integrator for the quaternion (euler angle) kinematics equations

Abstract: The invention is embodied in a method of integrating kinematics equations for updating a set of vehicle attitude angles of a vehicle using 3-dimensional angular velocities of the vehicle, which includes computing an integrating factor matrix from quantities corresponding to the 3-dimensional angular velocities, computing a total integrated angular rate from the quantities corresponding to a 3-dimensional angular velocities, computing a state transition matrix as a sum of (a) a first complementary function of the total integrated angular rate and (b) the integrating factor matrix multiplied by a second complementary function of the total integrated angular rate, and updating the set of vehicle attitude angles using the state transition matrix. Preferably, the method further includes computing a quanternion vector from the quantities corresponding to the 3-dimensional angular velocities, in which case the updating of the set of vehicle attitude angles using the state transition matrix is carried out by (a) updating the quanternion vector by multiplying the quanternion vector by the state transition matrix to produce an updated quanternion vector and (b) computing an updated set of vehicle attitude angles from the updated quanternion vector. The first and second trigonometric functions are complementary, such as a sine and a cosine. The quantities corresponding to the 3-dimensional angular velocities include respective averages of the 3-dimensional angular velocities over plural time frames. The updating of the quanternion vector preserves the norm of the vector, whereby the updated set of vehicle attitude angles are virtually error-free.

Adaptive robust tracking for flexible spacecraft in presence of disturbances

Abstract: The paper deals with trajectory tracking for a flexible spacecraft, subject to a gravity-gradient disturbance, under parameter uncertainties. The controls are gas jets and reaction wheels, and the measured variables describe the attitude and angular velocity of the rigid part. The flexible dynamics is treated as an additional disturbance acting on a rigid structure. First, an adaptive control is designed with only the gravity-gradient disturbance acting on the spacecraft; second, it is proved to be effective also in the presence of disturbance due to the flexibility, provided that appropriate robustness conditions on the controller gains are satisfied. These conditions use partial knowledge of the parameters describing the elastic dynamics. Simulations show the good performance of such control scheme and demonstrate its applicability even in the presence of input saturation.

Optimal control on Lie groups with applications to attitude control

Abstract: In this paper we solve a class of optimal control problems on Lie groups in the sense that we derive differential equations which the optimal controls must satisfy. These results are applied to the attitude control of a spacecraft modeled as a rigid body. Specifically, we derive control laws (both in open-loop and closed-loop form) to maneuver the spacecraft between two given rotational states in finite time. The laws are such that a cost functional measuring the over-all angular velocity during the spacecraft’s motion is minimized. They do not require recourse to numerical methods and hence can be easily implemented in an on-board attitude control system. After dealing with a three-axis controlled spacecraft we also discuss the case that only torques about two principal axes of an axisymmetric spacecraft can be exerted.

Method for monitoring the work cycle of mobile machinery during material removal

Abstract: The invention is a method for monitoring a work cycle of a mobile machine (102) on a land site (104). The mobile machine (102) has a bucket (106) and a body (108) that is adapted to rotate about a fixed point of reference. The method includes the steps of determining an angular velocity of the body (108), determining the body (108) is stopped based on the angular velocity, determining a duration of time the body (108) is stopped, and determining the work cycle in response to the duration of time the body (108) is stopped.

Torsional delayed resonator with velocity feedback

Abstract: This paper concerns a vibration absorption scheme, which is called the delayed resonator (DR). Torsional vibration cases are considered here for the first time with the new scheme. The angular velocity which is a commonly measurable state for rotating systems, is fed back with a controlled time delay, as opposed to the position and acceleration of the earlier studied translational vibration cases, some interesting distinctions of this control law are highlighted. Analytical and experimental findings are presented to show how the method of DR absorption can be adapted on an electric drive setting. The stability analysis is also reviewed for the entire system, including the DR absorber and the original oscillatory structure. Encouraging agreement between analytical and experimental findings are reported.

Determination of zero-angular-velocity output level for angular velocity sensor

Abstract: A technique for determining a gyro zero voltage is provided. A gyroscope ("gyro") 19 is installed in an automobile as a component of an on-board navigation system. The gyro 19 outputs a voltage representing an angular velocity of the vehicle. The gyro 19 output voltage representing zero angular velocity ("gyro zero voltage") is determined by first determining when the vehicle is stationary based upon the amount of noise in the output voltage of the gyro 19. When the vehicle is determined to be stationary, the gyro zero voltage is measured.

Normal Modes of Oscillation for Rotating Stars. V. A New Numerical Method for Computing Nonradial Eigenfunctions

Abstract: This paper is a progress report on my efforts to develop a robust numerical scheme for computing eigenmodes of arbitrary order at arbitrary rotation rates. The slowly pulsating B stars and the line-profile variables on the upper main sequence provide the main impetus for the work. Consequently, the focus here is on the gravity modes responsible for these variables rather than on pressure modes. Unfortunately, the g-modes are harder to compute in general because their oscillation periods can be longer than the rotation periods of high-mass stars, which makes them more sensitive to the effects of inertial forces. The standard technique for calculating the nonradial modes of spherical stellar models is generalized to two dimensions. The four dependent variables are the radial and latitudinal components of the Lagrangian displacement together with the Eulerian pressure and gravitational potential perturbations, all evaluated on level surfaces and normalized to have nonzero values on the boundaries. The integration in polar angle is replaced by numerical differentiation which is performed by various techniques involving Fourier, Legendre, or Chebyshev transforms. For the radial integrations, two numerical schemes are explored. One involves explicit Runge-Kutta integration inward and outward with fitting at an intermediate level surface. The other is an implicit, finite-difference method that does not require an initial trial solution. Each has advantages and disadvantages, but both ultimately fail for the same reason—small numerical errors in the θ-derivatives of eigenfunctions that are being distorted by growing high-order spherical harmonic components that are mixed in by rotation. Lack of convergence appears when the ratio Ω/σ of angular velocity and mode frequency exceeds about 0.5. This makes high-order g-modes (n > 15) in the presence of large rotation inaccessible with the methods proposed here. Nevertheless, it is possible to conclude that rapid rotation and large radial order suppress the pressure perturbations but enhance the horizontal motions especially near the surface and the equatorial plane. In fact, this trend is sufficiently clear and persistent that it should be possible to model the line profiles of the observationally relevant modes without actually computing them exactly.

Error analysis of direction cosines and quaternion parameters techniques for aircraft attitude determination

Abstract: Matrix differential equations for the determination of aircraft attitude orientation and the associated errors equations are developed in a four-dimensional space for both the direction cosines and quaternion parameter approaches. In this four-dimensional space, the corresponding algorithms, using accumulated gyro outputs, are developed and evaluated for the case of classical coning motion with time-varying angular velocity direction vector. Computation using symbolic algebra is considered in finding a closed-form solution for error propagation for a time-varying angular velocity direction vector. Examining the coning motion case shows that the true (analytic) scale and skew errors generated by the gyro drift are negligibly small in the direction cosines approach. Further, the true (analytic) scale errors in the quaternion technique are smaller than the computed (numerical) errors. Graphically illustrated are the true and computed errors in both the direction cosines and quaternion techniques for comparison.