Angular Velocity Components Research Articles

Relation Between Lift Force and Ball Spin for Different Baseball Pitches.

Although the lift force (F(L)) on a spinning baseball has been analyzed in previous studies, no study has analyzed such forces over a wide variety of spins. The purpose of this study was to describe the relationship between F(L) and spin for different types of pitches thrown by collegiate pitchers. Four high-speed video cameras were used to record flight trajectory and spin for 7 types of pitches. A total of 75 pitches were analyzed. The linear kinematics of the ball was determined at 0.008-s intervals during the flight, and the resultant fluid force acting on the ball was calculated with an inverse dynamics approach. The initial angular velocity of the ball was determined using a custom-made apparatus. Equations were derived to estimate the F(L) using the effective spin parameter (ESp), which is a spin parameter calculated using a component of angular velocity of the ball with the exception of the gyro-component. The results indicate that F(L) could be accurately explained from ESp and also that seam orientation (4-seam or 2-seam) did not produce a uniform effect on estimating F(L) from ESp.

Retraction Note to: Exact solutions for the incompressible viscous magnetohydrodynamic fluid of a rotating disk flow

The main interest of the present paper is to generate exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow motion due to a disk rotating with a constant angular speed. In place of the traditional von Karman’s axisymmetric evolution of the flow, the rotational non-axisymmetric stationary conducting flow is taken into consideration here. As a consequence, for an external uniform magnetic field applied perpendicular to the plane of the disk, the governing equations allow an exact solution to develop, which is influenced by a fixed point on the disk and also is bounded everywhere in the normal direction to the wall. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions, which differ from those of corresponding to the classical von Karman’s conducting flow. Making use of this solution, analytical formulas for the angular velocity components as well as for the wall shear stresses are extracted. The critical peripheral locations at which extrema of the local skin friction occur are also determined. It is proved from the analytical results that for the specific flow the properly defined thicknesses decay as the magnetic field strength increases in magnitude. Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. According to the Fourier’s heat law, a constant heat transfer from the disk to the fluid occurs, though decreases for small magnetic fields because of the dominance of Joule heating, it eventually increases for growing magnetic field parameters.

Validation of Inter-Subject Training for Hidden Markov Models Applied to Gait Phase Detection in Children with Cerebral Palsy.

Gait-phase recognition is a necessary functionality to drive robotic rehabilitation devices for lower limbs. Hidden Markov Models (HMMs) represent a viable solution, but they need subject-specific training, making data processing very time-consuming. Here, we validated an inter-subject procedure to avoid the intra-subject one in two, four and six gait-phase models in pediatric subjects. The inter-subject procedure consists in the identification of a standardized parameter set to adapt the model to measurements. We tested the inter-subject procedure both on scalar and distributed classifiers. Ten healthy children and ten hemiplegic children, each equipped with two Inertial Measurement Units placed on shank and foot, were recruited. The sagittal component of angular velocity was recorded by gyroscopes while subjects performed four walking trials on a treadmill. The goodness of classifiers was evaluated with the Receiver Operating Characteristic. The results provided a goodness from good to optimum for all examined classifiers (0 < G < 0.6), with the best performance for the distributed classifier in two-phase recognition (G = 0.02). Differences were found among gait partitioning models, while no differences were found between training procedures with the exception of the shank classifier. Our results raise the possibility of avoiding subject-specific training in HMM for gait-phase recognition and its implementation to control exoskeletons for the pediatric population.

An activity recognition model using inertial sensor nodes in a wireless sensor network for frozen shoulder rehabilitation exercises.

This paper proposes a model for recognizing motions performed during rehabilitation exercises for frozen shoulder conditions. The model consists of wearable wireless sensor network (WSN) inertial sensor nodes, which were developed for this study, and enables the ubiquitous measurement of bodily motions. The model employs the back propagation neural network (BPNN) algorithm to compute motion data that are formed in the WSN packets; herein, six types of rehabilitation exercises were recognized. The packets sent by each node are converted into six components of acceleration and angular velocity according to three axes. Motor features such as basic acceleration, angular velocity, and derivative tilt angle were input into the training procedure of the BPNN algorithm. In measurements of thirteen volunteers, the accelerations and included angles of nodes were adopted from possible features to demonstrate the procedure. Five exercises involving simple swinging and stretching movements were recognized with an accuracy of 85%–95%; however, the accuracy with which exercises entailing spiral rotations were recognized approximately 60%. Thus, a characteristic space and enveloped spectrum improving derivative features were suggested to enable identifying customized parameters. Finally, a real-time monitoring interface was developed for practical implementation. The proposed model can be applied in ubiquitous healthcare self-management to recognize rehabilitation exercises.

Optimal Selection of Supersonic Separators Inlet Velocity Components via Maximization of Swirl Strength and Centrifugal Acceleration

Revolutionary supersonic separator (3S) technology has been used extensively in natural gas dehydration. Static vanes angle of 3S plenum chamber controls various velocity components of rotating fluid and swirl strength. To provide highest swirl numbers and centrifugal accelerations, optimal values of axial, angular, and radial velocity components of entering fluid are found 20 m/s, 70 rps, and 60 m/s, respectively. Various definitions are employed to compute the swirl number. Furthermore, both swirl number and centrifugal acceleration are decreased with increasing of pressure and temperature. Maximum obtained centrifugal acceleration of 606294×g is achieved which enables the 3S unit to separate submicron droplets.

Vanishing Shear Viscosity and Boundary Layer for the Navier–Stokes Equations with Cylindrical Symmetry

Both the global well-posedness for large data and the vanishing shear viscosity limit with a boundary layer to the compressible Navier–Stokes system with cylindrical symmetry are studied under a general condition on the heat conductivity coefficient that, in particular, includes the constant coefficient. The thickness of the boundary layer is proved to be almost optimal. Moreover, the optimal L1 convergence rate in terms of shear viscosity is obtained for the angular and axial velocity components.

Attitude control with active actuator saturation prevention

Spacecraft attitude control in the presence of actuator saturation is considered. The attitude controller developed has two components: a proportional component and an angular velocity component. The proportional control has a special form that depends on the attitude parameterization. The angular velocity control is realized by a strictly positive real system with its own input nonlinearity. The strictly positive real system can filter noise in the angular velocity measurement. With this control architecture the torques applied to the body are guaranteed to be below a predetermined value, thus preventing saturation of the actuators. The closed-loop equilibrium point corresponding to the desired attitude is shown to be asymptotically stable. Additionally, the control law does not require specific knowledge of the body׳s inertia properties, and is therefore robust to such modelling errors.

Temperature Error Compensation in Two-Component Microelectromechanical Gyroscope

This paper presents the design and simulation of a microelectromechanical gyroscope that simultaneously determines two components of angular velocity. In this device, the silicon sensor is started by an electrostatic actuator to perform a linear harmonic motion at a controlled speed. The movable masses of the sensor move in two directions, orthogonal to the primary vibrations of the sensor under the action of Coriolis forces. This paper considers how temperature influences eigenfrequencies and informative vibrational magnitudes of the micromechanical angular velocity sensor. The parameters that have the greatest impact on the sensor output behavior are determined by a finite-element analysis method. Techniques to stabilize vibration eigenfrequencies of the sensing element are suggested.

Integrated structure for a resonant micro-gyroscope and accelerometer

This paper presents the study of the mechanical behavior of a microstructure designed to detect acceleration and angular velocity simultaneously. The new resonant micro-sensor proposed, fabricated by the ThELMA© surface-micromachining technique, bases detection of two components of external acceleration (one in-plane component and one out-of plane component) and two components of angular velocity (roll and yaw) on the variation of frequency of several elements set in resonance. The device, despite its small dimensions, provides a differential decoupled detection of four external quantities thanks to the presence of four slender beams resonating in bending and four torsional resonators.

English

This paper evaluates the impact that helical motion of fluid products of combustion within the combustion chamber of a rocket can have on the attitude dynamics of rocket systems. By developing the study presented by Sookgaew (2004), we determined the configuration of the Coriolis moment components, which catch the impact of the combustion product's whirling motion, for the radial and centripetal propellant burn pattern specific to S-5M and S-5K solid rocket motors. We continue the investigation of the effects of internal whirling motion of fluid products of combustion on the attitude behavior of variable mass systems of the rocket type by examining the spin motion and transverse attitude motion of such systems. The results obtained show that internal fluid whirling motion can cause appreciable deviations in spin rate predictions, and also affects the frequencies of the transverse angular velocity components.

Consistent shallow-water equations on the rotating sphere with complete Coriolis force and topography

AbstractConsistent shallow-water equations are derived on the rotating sphere with topography retaining the Coriolis force due to the horizontal component of the planetary angular velocity. Unlike the traditional approximation, this ‘non-traditional’ approximation captures the increase with height of the solid-body velocity due to planetary rotation. The conservation of energy, angular momentum and potential vorticity are ensured in the system. The caveats in extending the standard shallow-water wisdom to the case of the rotating sphere are exposed. Different derivations of the model are possible, being based, respectively, on (i) Hamilton’s principle for primitive equations with a complete Coriolis force, under the hypothesis of columnar motion, (ii) straightforward vertical averaging of the ‘non-traditional’ primitive equations, and (iii) a time-dependent change of independent variables in the primitive equations written in the curl (‘vector-invariant’) form, with subsequent application of the columnar motion hypothesis. An intrinsic, coordinate-independent form of the non-traditional equations on the sphere is then given, and used to derive hyperbolicity criteria and Rankine–Hugoniot conditions for weak solutions. The relevance of the model for the Earth’s atmosphere and oceans, as well as other planets, is discussed.

A dynamic model of an underwater quadruped walking robot using Kane’s method

In this paper, the kinematics and dynamics of an underwater quadruped walking robot were derived based on Kane dynamic equations. This methodology allows construction of the dynamic model simply and incrementally. The velocity and angular velocity components of an underwater quadruped walking robot were served as the generalized velocities. The forces which contribute to dynamics of an underwater quadruped walking robot were determined by Kane’s approach. The equations of hydrodynamic forces of an underwater quadruped walking robot were deduced. Hydrodynamic coefficients were determined by experiments. The dynamic model was established by obtaining the generalized active forces and the generalized inertia forces. Numerical simulations of the walking behavior on underwater flat ground were implemented to verify the dynamic model of an underwater quadruped walking robot. Simulation results show that the dynamic model is correct.

Satellite Attitude Control Using Analytical Solutions to Approximations of the Hamilton-Jacobi Equation

The solution to the Hamilton-Jacobi equation associated with the nonlinear ℋ∞ control problem is approximated using a Taylor series expansion. A recently developed analytical solution method is used for the second-, third-, and fourth-order terms. The proposed controller synthesis method is applied to the problem of satellite attitude control with attitude parameterization accomplished using the modified Rodrigues parameters and their associated shadow set. This leads to kinematical relations that are polynomial in the modified Rodrigues parameters and the angular velocity components. The proposed control method is compared with existing methods from the literature through numerical simulations. Disturbance rejection properties are compared by including the gravity-gradient and geomagnetic disturbance torques. Controller robustness is also compared by including unmodeled first- and second-order actuator dynamics, as well as actuation time delays in the simulation model. Moreover, the gap metric distance induced by the unmodeled actuator dynamics is calculated for the linearized system. The results indicated that a linear controller performs almost as well as those obtained using higher-order solutions for the Hamilton-Jacobi equation and the controller dynamics.

A novel high precision inertial measurement scheme and its optimization method for high-speed rotating ammunition

A novel inertial measurement unit scheme with five accelerometers and two gyros (5A2G) is proposed in this paper to achieve high precision measurement in high dynamic environment. The three channels are decoupled during the angular velocity calculation procedure to ensure the precision and efficiency. The yawing and pitching angular velocities are directly measured by gyros, while only the rolling angular velocity is inferred indirectly from the rolling angular information vector composed of rolling angular acceleration and quadratic component of rolling angular velocity. Based on the proposed scheme, the configuration ascertainment problem for acquiring the required installation parameters of accelerometers is transformed into a constraint optimization problem with the objective of minimizing the error of rolling angular information vector. A single channel rolling angular velocity calculation model is then established on the basis of the optimal configuration and the extended Kalman filter algorithm is utilized for state estimation. Simulations are implemented and results indicate that the optimal 5A2G scheme is feasible for high-speed rotating ammunition.

Analytical Solution for MHD Flow of a Magnetic Fluid within a Thick Porous Annulus

The steady-state problem of a magnetic fluid filling a porous annulus between two cylindrical walls under the influence of a nonuniform radially outward magnetic field has been investigated. The cylindrical walls are either electrically perfectly insulated or electrically perfectly conducting. The permeability of the porous annulus increases with its radial location. The governing partial differential equations were derived carefully and closed form solutions for the profiles of the velocity component and the induced magnetic component were obtained. The effect of the strength of the externally applied magnetic field, the permeability of the porous annulus, and the conductivity of the cylindrical walls were examined through the angular velocity components, as well as the induced magnetic field.

Molecular dynamic simulations of the elastic and inelastic surface scattering of nanoparticles

Molecular dynamics calculations have been undertaken to simulate the collision of a solid, rotating nanoparticle with a planar, two-dimensional surface at thermal velocities (linear and rotational) equivalent to 500 K. During the course of a collision, mechanisms have been introduced into the simulation process that allows for the dissipation of kinetic energy and for components of linear and angular velocity to couple. Although previous studies of particle-particle collisions have used a similar energy dissipation procedure, in these first calculations on particle-surface collisions, it is found that the mechanism actually facilitates the movement of particles across a surface. It is also shown that the direction of travel of particles on a surface is strongly influenced by their rotational motion.

Determination of the maximum values of the spatial angle of attack of a nanosatellite in motion on lowcircular orbits

Spatial motion of an uncontrolled nanosatellite around its center of mass on low circular orbits is considered. The aerodynamic characteristics of nanosatellites CubeSat-2U and CubeSat-3U are determined. The distribution functions of the maximum angle of attack of nanosatellites for various flight altitudes depending on the dispersion of the components of the initial angular velocity are obtained.

New exact solution of Euler’s equations (rigid body dynamics) in the case of rotation over the fixed point

A new exact solution of Euler’s equations (rigid body dynamics) is presented here. All the components of angular velocity of rigid body for such a solution differ from both the cases of symmetric rigid rotor (which has two equal moments of inertia: Lagrange’s or Kovalevskaya’s case), and from the Euler’s case when all the applied torques are zero, or from other well-known particular cases. The key features are the next: the center of mass of rigid body is assumed to be located at meridional plane along the main principal axis of inertia of rigid body, besides, the principal moments of inertia are assumed to satisfy to a simple algebraic equality. Also, there is a restriction at choosing of initial conditions. Such a solution is also proved to satisfy to Euler–Poinsot equations, including invariants of motion and additional Euler’s invariant (square of the vector of angular momentum is a constant). So, such a solution is a generalization of Euler’s case.

Satellite Angular Velocity Estimation Based on Star Images and Optical Flow Techniques

An optical flow-based technique is proposed to estimate spacecraft angular velocity based on sequences of star-field images. It does not require star identification and can be thus used to also deliver angular rate information when attitude determination is not possible, as during platform de tumbling or slewing. Region-based optical flow calculation is carried out on successive star images preprocessed to remove background. Sensor calibration parameters, Poisson equation, and a least-squares method are then used to estimate the angular velocity vector components in the sensor rotating frame. A theoretical error budget is developed to estimate the expected angular rate accuracy as a function of camera parameters and star distribution in the field of view. The effectiveness of the proposed technique is tested by using star field scenes generated by a hardware-in-the-loop testing facility and acquired by a commercial-off-the shelf camera sensor. Simulated cases comprise rotations at different rates. Experimental results are presented which are consistent with theoretical estimates. In particular, very accurate angular velocity estimates are generated at lower slew rates, while in all cases the achievable accuracy in the estimation of the angular velocity component along boresight is about one order of magnitude worse than the other two components.

Effects of gait speed on stability of walking revealed by simulated response to tripping perturbation

The objective of this work was to study stability of walking over a range of gait speeds by means of muscle-driven simulations. Fast walking has previously been related to high likelihood of falling due to tripping. Various measures of stability have shown different relationships between walking speed and stability. These measures may not be associated with tripping, so it is unclear whether the increase in likelihood of falling is explicable by an increase in instability. Here, stability with respect to a constant tripping perturbation was quantified as the immediate passive response of torso to the perturbation. Subject-specific muscle-driven simulations of eight young healthy subjects walking at four speeds, created by combining a generic musculoskeletal model with gait data, were analyzed. In the simulations, short perturbations were performed several times throughout the swing-phase by applying a constant backward force to the swing-foot of the model. Maxima of changes in the torso (angular) velocity components during the swing-phase were studied. These changes in the velocity components correlated with the walking speed as follows: anterior-posterior r=0.37 (p<0.05), vertical r=0.41 (p<0.05), and medio-lateral r=−0.40 (p<0.05). Of the angular velocity components, only the vertical component correlated statistically significantly with speed, r=0.52 (p<0.01). The weak and varying speed effects suggest that fast walking is not necessarily more unstable than slow walking, in the sense of response to a constant perturbation.