Showing papers on "Angular velocity published in 2011"

Geologically current motion of 56 plates relative to the no-net-rotation reference frame

Abstract: NNR-MORVEL56, which is a set of angular velocities of 56 plates relative to the unique reference frame in which there is no net rotation of the lithosphere, is determined. The relative angular velocities of 25 plates constitute the MORVEL set of geologically current relative plate angular velocities; the relative angular velocities of the other 31 plates are adapted from Bird (2003). NNR-MORVEL, a set of angular velocities of the 25 MORVEL plates relative to the no-net rotation reference frame, is also determined. Incorporating the 31 plates from Bird (2003), which constitute 2.8% of Earth's surface, changes the angular velocities of the MORVEL plates in the no-net-rotation frame only insignificantly, but provides a more complete description of globally distributed deformation and strain rate. NNR-MORVEL56 differs significantly from, and improves upon, NNR-NUVEL1A, our prior set of angular velocities of the plates relative to the no-net-rotation reference frame, partly due to differences in angular velocity at two essential links of the MORVEL plate circuit, Antarctica-Pacific and Nubia-Antarctica, and partly due to differences in the angular velocities of the Philippine Sea, Nazca, and Cocos plates relative to the Pacific plate. For example, the NNR-MORVEL56 Pacific angular velocity differs from the NNR-NUVEL1A angular velocity by a vector of length 0.039 ± 0.011° a−1 (95% confidence limits), resulting in a root-mean-square difference in velocity of 2.8 mm a−1. All 56 plates in NNR-MORVEL56 move significantly relative to the no-net-rotation reference frame with rotation rates ranging from 0.107° a−1 to 51.569° a−1.

Power screwdriver having rotary input control

Abstract: A power tool includes an output shaft configured to rotate about a longitudinal axis, a motor drivably connected to the output shaft to impart rotary motions thereto, and a rotational motion sensor spatially separated from the output shaft and operable to determine the user-imparted rotational motion of the power tool with respect to the longitudinal axis. A controller is electrically connected to the rotational motion sensor and the motor. The controller determines angular velocity of the power tool about the axis, rotational displacement of the power tool about the axis, and/or a direction of the rotational displacement using input from the rotational motion sensor. The controller then controls the motor according to the angular velocity, the rotational displacement, and/or the direction of the rotational displacement.

Rotation Speed of the First Stars

Abstract: We estimate the rotation speed of Population III (Pop III) stars within a minihalo at z∼ 20 using a smoothed particle hydrodynamics (SPH) simulation, beginning from cosmological initial conditions. We follow the evolution of the primordial gas up to densities of 1012 cm−3. Representing the growing hydrostatic cores with accreting sink particles, we measure the velocities and angular momenta of all particles that fall on to these protostellar regions. This allows us to record the angular momentum of the sinks and estimate the rotational velocity of the Pop III stars expected to form within them. The rotation rate has important implications for the evolution of the star, the fate encountered at the end of its life, and the potential for triggering a gamma-ray burst (GRB). We find that there is sufficient angular momentum to yield rapidly rotating stars (≳1000 km s−1, or near break-up speeds). This indicates that Pop III stars likely experienced strong rotational mixing, impacting their structure and nucleosynthetic yields. A subset of them was also likely to result in hypernova explosions and possibly GRBs.

Fault-Tolerant Attitude Control for Flexible Spacecraft Without Angular Velocity Magnitude Measurement

Abstract: S INCE some catastrophic faults or failures may be induced due to the aging or damage of actuators and sensors during the mission of a spacecraft, those faults would lead to performance degradation of the spacecraft attitude control system or even result in the specified aerospacemission failure. Therefore, fault tolerance of the spacecraft attitude control system is one of the key issues that needs to be addressed. With a view to tackle such a challenge, fault-tolerant control (FTC) has received considerable attention in order to enhance the spacecraft reliability and to guarantee the attitude control performance [1–5]. In [5], an adaptive FTC is developed for the flexible spacecraft attitude tracking system where the persistent bounded disturbances, unknown inertia parameter, and even two types of reaction wheel faults are successfully accommodated. Indeed, the aforementioned approaches offer many attractive conceptual features, but at the same time they are derived based on the availability of direct and exact measurements of both the angular velocity and the attitude orientation. It is important to note, however, that when it comes to practical implementation, the angular velocity measurements are not always available because of either cost limitations or implementation constraints. Motivated from such a practical consideration, it is therefore highly desirable to develop partial state feedback attitude control strategies with spacecraft angular velocity measurements eliminated. The issue has been addressed in the literature by using observer-based control [6,7], Lyapunov-based control [8,9], and variable structure control [10] under normal operation of spacecraft. In this work, we provide solutions to two different problems of the flexible spacecraft attitude control system. The first problem consists of developing a control law to perform a attitude stabilization maneuver without angular velocity magnitude. In contrast with the velocity-free control schemes available in the literature, the presented approach can guarantee the attitude control performance be greatly robust to external disturbances and unknown inertia parameters. The second problem solved is the casewhere both loss of control effectiveness and additive fault occur in actuators simultaneously, but the attitude still requires stabilization with high resolution. To the best knowledge of the authors, this study is the first attempt to deal with fault-tolerant attitude stabilization control for flexible spacecraft with the angular velocity magnitude eliminated. The Note is organized as follows. Section II presents the mathematical model and attitude control problems formation of a flexible spacecraft under normal and faulty actuator conditions. Section III presents the proposed fault-tolerant attitude stabilization controller without velocity magnitude in the presence of two types of actuator faults. Simulation results to demonstrate various features of the proposed scheme are given in Sec. IV followed by conclusions in Sec. V.

Engineering Notes Fault-Tolerant Attitude Control for Flexible Spacecraft Without Angular Velocity Magnitude Measurement

Abstract: S INCE some catastrophic faults or failures may be induced due to the aging or damage of actuators and sensors during the mission of a spacecraft, those faults would lead to performance degradation of the spacecraft attitude control system or even result in the specified aerospacemission failure. Therefore, fault tolerance of the spacecraft attitude control system is one of the key issues that needs to be addressed. With a view to tackle such a challenge, fault-tolerant control (FTC) has received considerable attention in order to enhance the spacecraft reliability and to guarantee the attitude control performance [1–5]. In [5], an adaptive FTC is developed for the flexible spacecraft attitude tracking system where the persistent bounded disturbances, unknown inertia parameter, and even two types of reaction wheel faults are successfully accommodated. Indeed, the aforementioned approaches offer many attractive conceptual features, but at the same time they are derived based on the availability of direct and exact measurements of both the angular velocity and the attitude orientation. It is important to note, however, that when it comes to practical implementation, the angular velocity measurements are not always available because of either cost limitations or implementation constraints. Motivated from such a practical consideration, it is therefore highly desirable to develop partial state feedback attitude control strategies with spacecraft angular velocity measurements eliminated. The issue has been addressed in the literature by using observer-based control [6,7], Lyapunov-based control [8,9], and variable structure control [10] under normal operation of spacecraft. In this work, we provide solutions to two different problems of the flexible spacecraft attitude control system. The first problem consists of developing a control law to perform a attitude stabilization maneuver without angular velocity magnitude. In contrast with the velocity-free control schemes available in the literature, the presented approach can guarantee the attitude control performance be greatly robust to external disturbances and unknown inertia parameters. The second problem solved is the casewhere both loss of control effectiveness and additive fault occur in actuators simultaneously, but the attitude still requires stabilization with high resolution. To the best knowledge of the authors, this study is the first attempt to deal with fault-tolerant attitude stabilization control for flexible spacecraft with the angular velocity magnitude eliminated. The Note is organized as follows. Section II presents the mathematical model and attitude control problems formation of a flexible spacecraft under normal and faulty actuator conditions. Section III presents the proposed fault-tolerant attitude stabilization controller without velocity magnitude in the presence of two types of actuator faults. Simulation results to demonstrate various features of the proposed scheme are given in Sec. IV followed by conclusions in Sec. V.

Vortex structures of rotating spin-orbit-coupled Bose-Einstein condensates

Abstract: We consider the quasi-two-dimensional two-component Bose-Einstein condensates with Rashba spin-orbit (SO) coupling in a rotating trap. The rotation angular velocity couples to the mechanical angular momentum, which contains a noncanonical part arising from SO coupling. The effects of an external Zeeman term favoring spin polarization along the radial direction is also considered, which has the same form as the noncanonical part of the mechanical angular momentum. The rotating condensate exhibits a variety of rich structures by varying the strengths of the trapping potential and interaction. With a strong trapping potential, the condensate exhibits a half-quantum vortex-lattice configuration. Such a configuration is driven to the normal one by introducing the external radial Zeeman field. In the case of a weak trap potential, the condensate exhibits a multidomain pattern of plane-wave states under the external radial Zeeman field.

Formation of black hole and accretion disk in a massive high-entropy stellar core collapse

Abstract: We present the first numerical result of fully general relativistic axisymmetric simulations for the collapse of a rotating high-entropy stellar core to a black hole and an accretion disk. The simulations are performed taking into account the relevant microphysics. We adopt as initial conditions a spherical core with constant electron fraction (Ye = 0.5) and entropy per baryon s = 8 kB , and angular velocity is superimposed. In the early phase, the core collapses in a homologous manner. Then it experiences a weak bounce due to the gas pressure of free nucleons. Because the bounce is weak, the core eventually collapses to a black hole. Subsequent evolution depends on initial angular velocity. When the rotation is not fast, a geometrically thin (but optically thick) accretion disk is formed, and shock waves are formed in the inner part of the disk. For the moderately rotating case, the thin accretion disk eventually expands to become a geometrically thick torus after sufficient accumulation of the thermal energy is generated at the shocks. Furthermore, convection occurs inside the torus. Neutrino luminosities vary violently with time because of the convective motion. For the rapidly rotating case, by contrast, a geometrically thick torus is formed soon after the black hole formation, and the convective activity is weak due to the presence of an epicyclic mode.

Rotational intermittency and turbulence induced lift experienced by large particles in a turbulent flow.

Abstract: The motion of a large, neutrally buoyant, particle freely advected by a turbulent flow is determined experimentally. We demonstrate that both the translational and angular accelerations exhibit very wide probability distributions, a manifestation of intermittency. The orientation of the angular velocity with respect to the trajectory, as well as the translational acceleration conditioned on the spinning velocity, provides evidence of a lift force acting on the particle.

Optimal Taylor-Couette turbulence

Abstract: Strongly turbulent Taylor-Couette flow with independently rotating inner and outer cylinders with a radius ratio of \eta = 0.716 is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux Nu_\omega(Ta, a) as a function of the Taylor number Ta and the angular velocity ratio a = -\omega_o/\omega_i in the large-Taylor-number regime 10^{11} \lesssim Ta \lesssim 10^{13}. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux Nu_\omega(Ta, a) = f(a)Ta^\gamma, with an amplitude f(a) and an exponent \gamma. The data are consistent with one effective exponent \gamma = 0.39\pm0.03 for all a. The amplitude of the angular velocity flux f(a) = Nu_\omega(Ta, a)/Ta^0.39 is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of a_opt = 0.33\pm0.04. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and identify the radial position r_n of the neutral line. While for moderate counter-rotation -0.40 \omega_i \lesssim \omega_o < 0, the neutral line still remains close to the outer cylinder and the probability distribution function (p.d.f.) of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the p.d.f. of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view for all these various results.

Swing analyzing apparatus

Abstract: A swing analyzing apparatus includes at least an angular velocity sensor, an impact detection section, an angular velocity information calculation section, and an impact state judgment section. The impact detection section detects the timing of impact in a swing of a sporting good. The angular velocity information calculation section calculates at least one of the amount of change in angular velocity with respect to a predetermined axis in a predetermined period after the impact timing and the greatest value of the angular velocity based on data outputted form the angular velocity sensor. The impact state judgment section judges the state of impact based on the result calculated by the angular velocity information calculation section.

Convection and differential rotation properties of G and K stars computed with the ASH code

Abstract: The stellar luminosity and depth of the convective envelope vary rapidly with mass for G-and K-type main sequence stars. In order to understand how these properties influence the convective turbulence, differential rotation, and meridional circulation , we have carried out 3D dynamical simulations of the interiors of rotating main sequence stars, using the anelastic spherical harmonic (ASH) code. The stars in our simulations have masses of 0.5, 0.7, 0.9, and 1.1 M , corresponding to spectral types K7 through G0, and rotate at the same angular speed as the sun. We identify several trends of convection zone properties with stellar mass, exhibited by the simulations. The convective velocities, temperature contrast between up-and downflows, and meridional circulation velocities all increase with stellar luminosity. As a consequence of the trend in convective velocity, the Rossby number (at a fixed rotation rate) increases and the convective turnover timescales decrease significantly with increasing stellar mass. The 3 lowest mass cases exhibit solar-like differential rotation, in a sense that they show a maximum rotation at the equator and minimum at higher latitudes, but the 1.1 M case exhibits anti-solar rotation. At low mass, the meridional circulation is multi-cellular and aligned with the rotation axis; as the mass increases, the circulation pattern tends toward a unicellular structure covering each hemisphere in the convection zone.

Modelling the rotational evolution of solar-like stars: the rotational coupling time-scale

Abstract: We investigate the rotational evolution of solar-like stars with a focus on the internal angular momentum transport processes. The double zone model, in which the star’s radiative core and convective envelope are assumed to rotate as solid bodies, is used to test simple relationships between the core-envelope coupling timescale, �c, and rotational properties, like the envelope angular velocity or the differential rotation at the core-envelope interface. The trial relationships are tested by fitting the model parameters to available observations via a Monte Carlo Markov Chain method. The synthetic distributions are tested for compatibility with their observational counterparts by means of the standard Kolmogorov-Smirnov (KS) test.

Real-Time Upper Limb Motion Estimation From Surface Electromyography and Joint Angular Velocities Using an Artificial Neural Network for Human–Machine Cooperation

Abstract: A current challenge with human-machine cooperation systems is to estimate human motions to facilitate natural cooperation and safety of the human. It is a logical approach to estimate the motions from their sources (skeletal muscles); thus, we employed surface electromyography (SEMG) to estimate body motions. In this paper, we investigated a cooperative manipulation control by an upper limb motion estimation method using SEMG and joint angular velocities. The SEMG signals from five upper limb muscles and angular velocities of the limb joints were used to approximate the flexion-extension of the limb in the 2-D sagittal plane. The experimental results showed that the proposed estimation method provides acceptable performance of the motion estimation [normalized root mean square error (NRMSE) ;0.9] under the noncontact condition. From the analysis of the results, we found the necessity of the angular velocity input and estimation error feedback due to physical contact. Our results suggest that the estimation method can be useful for a natural human-machine cooperation control.

Ambulatory Estimation of Knee-Joint Kinematics in Anatomical Coordinate System Using Accelerometers and Magnetometers

Abstract: Knee-joint kinematics analysis using an optimal sensor set and a reliable algorithm would be useful in the gait analysis. An original approach for ambulatory estimation of knee-joint angles in anatomical coordinate system is presented, which is composed of a physical-sensor-difference-based algorithm and virtual-sensor-difference-based algorithm. To test the approach, a wearable monitoring system composed of accelerometers and magnetometers was developed and evaluated on lower limb. The flexion/extension (f/e), abduction/adduction (a/a), and inversion/extension (i/e) rotation angles of the knee joint in the anatomical joint coordinate system were estimated. In this method, since there is no integration of angular acceleration or angular velocity, the result is not distorted by offset and drift. The three knee-joint angles within the anatomical coordinate system are independent of the orders, which must be considered when Euler angles are used. Besides, since there are no physical sensors implanted in the knee joint based on the virtual-sensor-difference-based algorithm, it is feasible to analyze knee-joint kinematics with less numbers and types of sensors than those mentioned in some others methods. Compared with results from the reference system, the developed wearable sensor system is available to do gait analysis with fewer sensors and high degree of accuracy.

Effects of anisotropic winds on massive star evolution

Abstract: Context. Whenever stars rotate very rapidly, such that Ω/Ωcrit > 0.7 where Ω crit is the Keplerian angular velocity of the star accounting for its deformation, radiative stellar winds are enhanced in polar regions. This theoretical prediction has now been confirmed by interferometric observations of rapidly rotating stars. Aims. Polar winds remove less angular momentum than spherical winds, thus allow the star to retain more angular momentum. We quantitatively assess the importance of this effect. Methods. We first use a semi-analytical approach to estimate the variation in the angular momentum loss when the rotation parameter increases. We then compute complete 9 M ⊙ stellar models at very high angular velocities (starting on the ZAMS with Ω/Ω crit = 0.8 and reaching the critical velocity during the main sequence) with and without radiative wind anisotropies. Results. When wind anisotropies are accounted for, the angular-momentum loss rate is reduced by less than 4% for Ω/Ω crit < 0.9 relative to the case for spherical winds. The reduction amounts to at most 30% when the star is rotating near the critical velocity. These values result from two counteracting effects: on the one hand, polar winds reduce the loss of angular momentum, and on the other hand, surface deformations imply that the mass that is lost at high co-latitude is lost at a larger distance from the rotational axis and thus removes more angular momentum. Conclusions. In contrast to previous studies that neglected surface deformations, we show that the radiative wind anisotropies have a relatively modest effect on the evolution of the angular momentum content of rapidly rotating stars.

Constrained Angular Motion Estimation in a Gyro-Free IMU

Abstract: In this paper, we present an extended Kalman filter (EKF)-based solution for the estimation of the angular motion using a gyro-free inertial measurement unit (GF-IMU) built of twelve separate mono-axial accelerometers. Using such a GF-IMU produces a vector, which we call the angular information vector (AIV) that consists of 3D angular acceleration terms and six quadratic terms of angular velocities. We consider the multiple distributed orthogonal triads of accelerometers that consist of three nonplanar distributed triads equally spaced from a central triad as a specific case to solve. During research for the possible filter schemes, we derived equality constraints. Hence we incorporate the constraints in the filter to improve the accuracy of the angular motion estimation, which in turn improves the attitude accuracy (direction cosine matrix (DCM) or quaternion vector).

Angle Estimation of Simultaneous Orthogonal Rotations from 3D Gyroscope Measurements

Abstract: A 3D gyroscope provides measurements of angular velocities around its three intrinsic orthogonal axes, enabling angular orientation estimation. Because the measured angular velocities represent simultaneous rotations, it is not appropriate to consider them sequentially. Rotations in general are not commutative, and each possible rotation sequence has a different resulting angular orientation. None of these angular orientations is the correct simultaneous rotation result. However, every angular orientation can be represented by a single rotation. This paper presents an analytic derivation of the axis and angle of the single rotation equivalent to three simultaneous rotations around orthogonal axes when the measured angular velocities or their proportions are approximately constant. Based on the resulting expressions, a vector called the simultaneous orthogonal rotations angle (SORA) is defined, with components equal to the angles of three simultaneous rotations around coordinate system axes. The orientation and magnitude of this vector are equal to the equivalent single rotation axis and angle, respectively. As long as the orientation of the actual rotation axis is constant, given the SORA, the angular orientation of a rigid body can be calculated in a single step, thus making it possible to avoid computing the iterative infinitesimal rotation approximation. The performed test measurements confirm the validity of the SORA concept. SORA is simple and well-suited for use in the real-time calculation of angular orientation based on angular velocity measurements derived using a gyroscope. Moreover, because of its demonstrated simplicity, SORA can also be used in general angular orientation notation.

Cross-Range Scaling Algorithm for ISAR Images Using 2-D Fourier Transform and Polar Mapping

Abstract: This paper proposes a new method that solves the problem of inverse synthetic aperture radar image cross-range scaling by estimating the rotational velocity (RV) using the expansion-rotation-scale relationship between two range-Doppler (RD) images. This method is composed of three steps. The first step is preprocessing to construct 2-D Fourier transform images and initial polar-mapped images. In this step, two RD images are 2-D Fourier transformed to avoid the necessity of finding the rotation center; then, the transformed images are polar mapped with identical polar grids to convert rotation into translation in the θ-direction only. The second step is a coarse search that finds the angular shift that provides the maximum correlation between two polar images. The angular shift found is used as the initial relative rotation angle (RA), and the initial relative scaling factor (RSF) is calculated using the RV which is equal to the angular shift divided by the time delay between the images. The third step is the optimization of the relative RA using the Nelder-Mead approach, with the RSF updated using the relative RA derived during each iteration. In simulations using a Mig-25 aircraft, composed of ideal point scatterers, and the measured data from a Boeing 747-400, the targets were properly rescaled in the range-cross-range domain due to the accurate estimation of the RV.

Application and analysis of functionally graded piezoelectrical rotating cylinder as mechanical sensor subjected to pressure and thermal loads

Abstract: The exact thermoelastic analysis of a functionally graded piezoelectrical (FGP) rotating cylinder is investigated analytically. The cylinder is subjected to a combination of electrical, thermal, and mechanical loads simultaneously. The structure is a simplified model of a rotational sensor or actuator. The basic governing differential equation of the system is obtained by using the energy method. A novel term, named as the additional energy, is introduced to exact the evaluation of the energy functional. The solution to the governing differential equation is presented for two types of boundary conditions including free rotating and rotating cylinders exposed to the inner pressure. The effect of the angular velocity is investigated on the radial distribution of various components. The mentioned structure can be considered as a sensor for measuring the angular velocity of the cylinder subjected to the pressure and temperature. The obtained results indicate that the electrical potential is proportional to the angular velocity.

Design, analysis and experiment of a novel ring vibratory gyroscope

Abstract: This work presents the design, analysis, simulation and experiment of a novel ring vibratory gyroscope based on piezoelectric effect. The gyroscope has a simple millimeter-scale resonator which comprises of a metallic structure and eight piezoelectric elements. The piezoelectric elements attached to the metallic structure excite the primary mode of the resonator, sense the second mode caused by Coriolis force and output signal proportional to input angular velocity. A theoretical analysis on the proposed gyroscope is performed using the AMM method and DM method for the forced vibration solution of active mode and sense mode with the inclusion of the Coriolis force coupling. The sensitivity of the gyroscope and its dependence on some geometry parameters are obtained. The working principle is validated by using FEM simulation. The metallic structure of the prototypal gyroscope was machined by precision turning and electrical charge technologies, as a result, the adherence process of the piezoelectric elements is simplified and the positioning precision is improved, which ensures the high axial symmetry of the resonator. A prototypal gyroscope is selected for practical experiments. The natural frequencies of active mode and sense mode of the prototype are close, the frequency split is 0.06 Hz, and the quality factor is approximately 5000 in atmosphere. Therefore, the gyroscope can work properly without a vacuum package. A control circuit was specially designed to activate the resonator and readout the angular velocity signal. The performance of the gyroscope is characterized on a precision rate table. The experimentally obtained scale factor is 65.5 mV/°/s, the nonlinearity is 1323 ppm in range of ±150°/s, the angle random walk is about 0.05°/h1/2, and the zero-bias instability is about 1.5°/h at room temperature. There is a good linear relation between the sensing voltage and the angular velocity, suggesting that the novel ring vibratory gyroscope is a good candidate for low and medium rotation speed measurements.

Modeling of Differential Rotation in Rapidly Rotating Solar-type Stars

Abstract: We investigate differential rotation in rapidly rotating solar-type stars by means of an axisymmetric mean field model that was previously applied to the Sun. This allows us to calculate the latitudinal entropy gradient with a reasonable physical basis. Our conclusions are as follows. (1) Differential rotation approaches the Taylor-Proudman state when stellar rotation is faster than solar rotation. (2) Entropy gradient generated by the attached subadiabatic layer beneath the convection zone becomes relatively small with a large stellar angular velocity. (3) Turbulent viscosity and turbulent angular momentum transport determine the spatial difference of angular velocity ΔΩ. (4) The results of our mean field model can explain observations of stellar differential rotation.

Measurement of six degrees of freedom head kinematics in impact conditions employing six accelerometers and three angular rate sensors (6aω configuration).

Abstract: The ability to measure six degrees of freedom (6 DOF) head kinematics in motor vehicle crash conditions is important for assessing head-neck loads as well as brain injuries. A method for obtaining accurate 6 DOF head kinematics in short duration impact conditions is proposed and validated in this study. The proposed methodology utilizes six accelerometers and three angular rate sensors (6aω configuration) such that an algebraic equation is used to determine angular acceleration with respect to the body-fixed coordinate system, and angular velocity is measured directly rather than numerically integrating the angular acceleration. Head impact tests to validate the method were conducted using the internal nine accelerometer head of the Hybrid III dummy and the proposed 6aω scheme in both low (2.3 m/s) and high (4.0 m/s) speed impact conditions. The 6aω method was compared with a nine accelerometer array sensor package (NAP) as well as a configuration of three accelerometers and three angular rate sensors (3aω), both of which have been commonly used to measure 6 DOF kinematics of the head for assessment of brain and neck injuries. The ability of each of the three methods (6aω, 3aω, and NAP) to accurately measure 6 DOF head kinematics was quantified by calculating the normalized root mean squared deviation (NRMSD), which provides an average percent error over time. Results from the head impact tests indicate that the proposed 6aω scheme is capable of producing angular accelerations and linear accelerations transformed to a remote location that are comparable to that determined from the NAP scheme in both low and high speed impact conditions. The 3aω scheme was found to be unable to provide accurate angular accelerations or linear accelerations transformed to a remote location in the high speed head impact condition due to the required numerical differentiation. Both the 6aω and 3aω schemes were capable of measuring accurate angular displacement while the NAP instrumentation was unable to produce accurate angular displacement due to double numerical integration. The proposed 6aω scheme appears to be capable of measuring accurate 6 DOF kinematics of the head in any severity of impact conditions. Language: en

Inertial measurements Based dynamic attitude estimation and velocity-free attitude stabilization

Abstract: This paper deals with the attitude estimation and control problems for rigid bodies, using inertial vector measurements. First, we revisit the attitude estimation algorithm on SO(3) that has been recently proposed in the literature, and propose some practical extensions and new insightful unit-quaternion based proofs. Then, we propose an attitude stabilization control scheme using only inertial vector measurements. The originality of this control strategy stems from the fact that the explicit reconstruction of the attitude as well as the angular velocity measurements are not required anymore.

Steady and fluctuating inner core rotation in numerical geodynamo models

Abstract: SUMMARY We present a systematic survey of numerical geodynamo simulations where the inner core is allowed to differentially rotate in the longitudinal direction with respect to the mantle. We focus on the long-term behaviour of inner core rotation, on timescales much longer than the overturn time of the fluid outer core, including the steady component of rotation. The inner core is subject to viscous and magnetic torques exerted by the fluid outer core, and a gravitational restoring torque exerted by the mantle. We show that the rate of steady inner core rotation is limited by the differential rotation between spherical surfaces that the convective dynamics can sustain across the fluid outer core. We further show that this differential rotation is determined by a torque balance between the resistive Lorentz force and the Coriolis force on spherical surfaces within the fluid core. We derive a scaling law on the basis of this equilibrium suggesting that the ratio of the steady inner core rotation to typical angular velocity within the fluid core should be proportional to the square root of the Ekman number, in agreement with our numerical results. The addition of gravitational coupling does not alter this scaling, though it further reduces the amplitude of inner core rotation. In contrast, the long-term fluctuations in inner core rotation remain proportional to the fluid core angular velocity, with no apparent dependency on the Ekman number. If the same torque balance pertains to the Earth's core conditions, the inner core rotation then consists in a very slow super rotation of a few degrees per million years, superimposed over large fluctuations (at about a tenth of a degree per year). This suggests that the present-day seismically inferred inner core rotation is a fragment of a time-varying signal, rather than a steady super rotation. For the inner core rotation fluctuations not to cause excessive variations in the length-of-day, the strength of the gravitational coupling between the inner core and the mantle must be smaller than previously published values. We finally explore how the torque balance which we observe in our models could be altered in planetary cores, yielding possibly larger values of the steady rotation.

Nonlinear vibrations of the blade with varying rotating speed

Abstract: Nonlinear behaviors of thin-walled Euler-Bernoulli beams with varying rotating speed which are attached to a rigid hub are investigated. Centrifugal force, aerodynamic load and the perturbed angular speed due to the inconstant air velocity are considered. The nonlinear factors are involved in displacement-strain relationships. The nonlinear governing partial differential equations of high-speed rotating thin-walled beam are established by using Hamiltonian Principle. Then, the ordinary differential equations of the rotating thin-walled beam are obtained by employing Galekin's approach during which Galekin's modes satisfy corresponding boundary conditions. The four-dimensional nonlinear averaged equations are obtained by applying the method of multiple scales. In this paper, the case of 1∶1 internal resonance is only considered. The results of the numerical simulation show that there exits complicated nonlinear behaviors in thin-walled Euler-Bernoulli beams with varying rotating speed.

Rotations with Rodrigues' vector

Abstract: The rotational dynamics was studied from the point of view of Rodrigues' vector. This vector is defined here by its connection with other forms of parametrization of the rotation matrix. The rotation matrix was expressed in terms of this vector. The angular velocity was computed using the components of Rodrigues' vector as coordinates. It appears to be a fundamental matrix that is used to express the components of the angular velocity, the rotation matrix and the angular momentum vector. The Hamiltonian formalism of rotational dynamics in terms of this vector uses the same matrix. The quantization of the rotational dynamics is performed with simple rules if one uses Rodrigues' vector and similar formal expressions for the quantum operators that mimic the Hamiltonian classical dynamics.

Modeling of differential rotation in rapidly rotating solar-type stars

Abstract: We investigate differential rotation in rapidly rotating solar-type stars by means of an axisymmetric mean field model that was previously applied to the sun. This allows us to calculate the latitudinal entropy gradient with a rea- sonable physical basis. Our conclusions are as follows: (1) Differential rotation approaches the Taylor-Proudman state when stellar rotation is faster than so- lar rotation. (2) Entropy gradient generated by the attached subadiabatic layer beneath the convection zone becomes relatively small with a large stellar angu- lar velocity. (3) Turbulent viscosity and turbulent angular momentum transport determine the spatial difference of angular velocity $\Delta \Omega$. (4) The results of our mean field model can explain observations of stellar differential rotation.