Initial Angular Velocity Research Articles

A two-dimensional perspective of the rotational evolution of rapidly rotating intermediate-mass stars

Context. Recently, the first successful attempt at computing stellar structure and evolution models in two dimensions was presented with models that include centrifugal deformation and self-consistently compute the velocity field. Aims. The aim of the present study is to explore the rotational evolution of two-dimensional models of stars rotating at a significant fraction of their critical angular velocity. From the predictions of these models, we aim to improve our understanding of the formation of single Be stars. Methods. Using the ESTER code, which solves the stellar structure of a rotating star in two dimensions with time evolution, we computed evolution tracks of stars of between 4 and 10 M⊙ for initial rotation rates ranging between 60 and 90% of the critical rotation rate. Furthermore, we compute models for both a Galactic metallicity and an SMC metallicity. Results. A minimum initial rotation rate at the start of the main sequence is needed to spin up the star to critical rotation within its main sequence lifetime. This threshold depends on the stellar mass, and increases with increasing mass. The models do not predict any stars above 8 M⊙ to reach (near-)critical rotation during the main sequence. Furthermore, we find the minimum threshold of initial angular velocity is lower for SMC metallicity than for Galactic metallicity, which is in agreement with the increased fraction of observed Be stars in lower metallicity environments. The strong difference in the rotational evolution between different masses is not predicted by any one-dimensional stellar evolution models. Conclusions. Our self-consistent two-dimensional stellar evolution models provide further insight into the rotational evolution of intermediate-mass stars, and our predictions are consistent with observations of velocity distributions and the fraction of Be stars amongst B-type stars. We find that stars with a mass above 8 M⊙ do not increase their fraction of critical rotation during the main sequence. As a fraction of stars above 8 M⊙ have been observed to display the Be phenomenon, other processes or formation channels must be at play, or, alternatively, critical rotation is not required for the Be phenomenon above this mass.

Numerical–experimental study on the stability mechanism of tail slapping motion of supercavitation projectile

Tail slapping is considered to be a prominent mode for facilitating the movement of supercavitating projectiles underwater. Stability mechanism of the tail slapping and stability criterion of projectiles was numerically investigated in this paper. A numerical method was conducted to calculate the free flight of projectiles by combining the finite volume method, the mixture multiphase model, and a dynamic meshing scheme. The accuracy and applicability of the numerical calculation method are verified by experiments. Three typical stability modes of tail slapping motion, namely, stable, conditionally stable, and unstable, were identified through the free flight numerical simulations of projectiles with varying length-to-diameter ratios under different initial angular velocities. The stability criterion of projectiles was proposed, indicating that the tail slapping stability can be determined by analyzing the curve of the moment variation with the angle of attack at any velocity above 200 m/s. Furthermore, it was found that the stable projectiles possess inherent motion states that are exclusively determined by their structural features and are unaffected by the initial motion conditions.

A New Kilohertz Gravitational-wave Feature from Rapidly Rotating Core-collapse Supernovae

We present self-consistent three-dimensional core-collapse supernova simulations of a rotating 20M ⊙ progenitor model with various initial angular velocities from 0.0 to 4.0 rad s−1 using the smoothed particle hydrodynamics code SPHYNX and the grid-based hydrodynamics code FLASH. We identify two strong gravitational-wave features with peak frequencies of ∼300 Hz and ∼1.3 kHz in the first 100 ms postbounce. We demonstrate that these two features are associated with the m = 1 deformation from the proto-neutron star (PNS) modulation induced by the low-T/∣W∣ instability, regardless of the simulation code. The 300 Hz feature is present in models with an initial angular velocity between 1.0 and 4.0 rad s−1, while the 1.3 kHz feature is only present in a narrower range, from 1.5 to 3.5 rad s−1. We show that the 1.3 kHz signal originates from the high-density inner core of the PNS, and the m = 1 deformation triggers a strong asymmetric distribution of electron antineutrinos. In addition to the 300 Hz and 1.3 kHz features, we also observe one weaker but noticeable gravitational-wave feature from higher-order modes in the range between 1.5 and 3.5 rad s−1. Its initial peak frequency is around 800 Hz, and it gradually increases to 900–1000 Hz. Therefore, in addition to the gravitational bounce signal, the detection of the 300 Hz, 1.3 kHz, the higher-order mode, and even the related asymmetric emission of neutrinos could provide additional diagnostics for estimating the initial angular velocity of a collapsing core.

Blowup analysis for a quasi-exact 1D model of 3D Euler and Navier–Stokes

We study the singularity formation of a quasi-exact 1D model proposed by Hou and Li (2008 Commun. Pure Appl. Math. 61 661–97). This model is based on an approximation of the axisymmetric Navier–Stokes equations in the r direction. The solution of the 1D model can be used to construct an exact solution of the original 3D Euler and Navier–Stokes equations if the initial angular velocity, angular vorticity, and angular stream function are linear in r. This model shares many intrinsic properties similar to those of the 3D Euler and Navier–Stokes equations. It captures the competition between advection and vortex stretching as in the 1D De Gregorio (De Gregorio 1990 J. Stat. Phys. 59 1251–63; De Gregorio 1996 Math. Methods Appl. Sci. 19 1233–55) model. We show that the inviscid model with weakened advection and smooth initial data or the original 1D model with Hölder continuous data develops a self-similar blowup. We also show that the viscous model with weakened advection and smooth initial data develops a finite time blowup. To obtain sharp estimates for the nonlocal terms, we perform an exact computation for the low-frequency Fourier modes and extract damping in leading order estimates for the high-frequency modes using singularly weighted norms in the energy estimates. The analysis for the viscous case is more subtle since the viscous terms produce some instability if we just use singular weights. We establish the blowup analysis for the viscous model by carefully designing an energy norm that combines a singularly weighted energy norm and a sum of high-order Sobolev norms.

Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distribution

In many real-world settings, image observations of freely rotating 3D rigid bodies may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of classical estimation techniques to learn the dynamics. The usefulness of standard deep learning methods is also limited, because an image of a rigid body reveals nothing about the distribution of mass inside the body, which, together with initial angular velocity, is what determines how the body will rotate. We present a physics-based neural network model to estimate and predict 3D rotational dynamics from image sequences. We achieve this using a multi-stage prediction pipeline that maps individual images to a latent representation homeomorphic to SO(3), computes angular velocities from latent pairs, and predicts future latent states using the Hamiltonian equations of motion. We demonstrate the efficacy of our approach on new rotating rigid-body datasets of sequences of synthetic images of rotating objects, including cubes, prisms and satellites, with unknown uniform and non-uniform mass distributions. Our model outperforms competing baselines on our datasets, producing better qualitative predictions and reducing the error observed for the state-of-the-art Hamiltonian Generative Network by a factor of 2.

A shortening pendulum: Hoisting control for medical evacuation rescues

Strategies to vary the length of a pendular payload maneuvered by a helicopter in an aerial medical evacuation scenarios and similar situations are discussed. The aim is to rapidly stabilize the swinging payload to decrease effects of cable swing and decrease rescue time. A variable length procedure is proposed for small changes to the line length as the pendulum swings. The 2D nonlinear equation of motion of the pendulum is implemented in MATLAB, and for a proof of concept, manual intervention is used to identify values of the time interval and line parameters to achieve payload stabilization. Three time-varying line procedures are proposed. Conservation of energy is used to determine expressions for the initial angle and angular velocity that decrease the energy of the pendular payload when it swings through its highest and lowest points. Results show that the proposed stabilization strategies are able to control the swing angle due to variable length reel-in and reel-out at precise timing intervals. Further, validation of the variable length idea is demonstrated with energy calculations determined from Mathematica simulations in our prior work.

Modeling Ellipsoidal Block Impacts by an Advanced Rheological Model

In this paper, an advanced rheological model for impacts of ellipsoidal blocks on deformable ground surfaces, introducing the effects of block eccentricity and orientation at impact, is presented. This allows us to assess impact penetration and force, restitution coefficients, and block trajectories. A parametric analysis was carried out by considering different block aspect ratios, impact angles and initial block orientations at impact. The results are presented in terms of restitution coefficients, penetration and force time histories, maximum penetration depth, maximum force and rotational/total kinetic ratios. Impacts along the major block axis, versus those along minor axis, are characterized by larger penetrations (ranging from 3.3 to 50%), shorter impact durations (ca 50%) and very slightly larger vertical forces (ranging from 0.3 to 60%) according to the model parameter used. In contrast, the impact angle is shown to strongly affect maximum penetration and force values, and markedly increase rotation at impact. Analogously, normal restitution coefficient is severely dependent on impact angle, with a variation of more than two orders of magnitude. A mathematical expression for computing the energetic restitution coefficient from the normal and tangential apparent restitution coefficients and the ratio between the rotation and total kinetic energy is proposed. This overcomes the drawback of classical restitution coefficients greater than one when a change in block rotation occurs allowing us to bracket the coefficient of restitutions values to support and improve classical rock fall simulations also highlighting their intrinsic limitations. Finally, the effects of block geometry and initial angular velocity on rockfall simulations were analyzed by implementing the approach in the HyStone simulation code. The simulated frequencies of the maximum height during each ballistic trajectory follow an exponential distribution, whereas those for normal and tangential apparent restitution coefficients follow normal distributions.

Strategies for Controlling a Whole-Body Task With Uncertain Initial Conditions: Application to the Upstart on Bars.

The upstart is commonly used on bars in artistic gymnastics following a release and regrasp skill, where the gymnast will perform a flighted element before catching the bar. The variability of the flighted element leads to varying initial conditions prior to the upstart. The aim of the study was to understand how technique can be manipulated in order to ensure success at the task despite this variability. More specifically, the study aimed to quantify the ranges of initial angular velocity a gymnast could cope with in an upstart using (a)a fixed timing technique, (b)with one additional parameter to modify timings as a function of initial angular velocity, and (c)a further additional parameter to extend the range. Relationships were established, using computer simulation modeling, between the movement pattern parameters, which defined the technique, and the initial angular velocity of the upstart. A two-parameter relationship outperformed both the one-parameter relationship and the fixed timing solution in terms of the range of initial angular velocities the model could cope with. One of the two parameters governed the time by which the initiation of the shoulder extension should be reduced as a function of increased initial angular velocity, and the other parameter performed the same function for the remaining timing parameters at the hip and shoulder. The present study suggests that gymnasts, and, therefore, humans, may be able to modify movement patterns to cope with uncertain initial conditions using a relatively small number of parameters.

Heavy symmetric tops and the Hannay angle

The dynamics of a heavy symmetric top are studied in connection with the Hannay angle. When the top undergoes a steady precession due to gravity without nutation, the Hannay angle has a geometric nature such that it is identical to the solid angle subtended by the loop swept out by the symmetry axis of the top. Here, we show that the Hannay angle can also be described by the angle between two radial vectors on the disk of the top corresponding to the pure spinning motion and the coupled motion of spin and precession for one period of the precession. The geometric nature of the angle between the two radial vectors is verified by demonstrating, via parallel transport, that the magnitude of the angle is the same as that of the solid angle. In the presence of nutation, the path constructed by the symmetry axis is not closed, and the steady precession appears in the limit of infinite initial spin angular velocity. As a consequence, in an ideal situation of no friction, the Hannay angle as a pure geometric effect does not exist in the superposed motion of precession and nutation.

Three-axis high-accuracy spacecraft attitude estimation via sequential extended Kalman filtering of single-axis magnetometer measurements

Magnetometer is a highly advantageous sensor for determining a spacecraft’s attitude. This article provides a solution to the problem of spacecraft attitude estimation using magnetometer measurements only. To ensure full observability of spacecraft attitude states, it is necessary to use at least two types of sensors. Consequently, utilizing a single sensor, such as the magnetometer, poses a significant challenge for any attitude estimation algorithm, including the extended Kalman filter (EKF). Moreover, implementing the EKF algorithm, or any other attitude estimation algorithm, is computationally intensive. To address these issues, an algorithm has been developed that estimates spacecraft attitude angles and attitude rates using a sequential extended Kalman filter (SEKF). This algorithm offers numerous benefits over those found in the literature such as high accuracy, low computational resource requirements, the ability to converge even with large initial attitude and angular velocity estimation errors, and the ability to function even if two of the three measurement channels of the magnetometer are not functioning. With these benefits, the developed SEKF algorithm is capable of operating in all spacecraft operational modes, delivering accurate performance and computation time. In spite of measurements with large noise values, the high accuracy achieved by the SEKF algorithm enables the magnetometer to serve as the sole source of attitude information, even if one or two magnetometer measurement channels are not functioning.

PCB-integrated embedded planar magnetorquers for small satellites intelligent detumbling

The challenge of damping high tumbling rates after deployment of spacecraft from a rocket using PCB-integrated (printed circuit board) embedded planar coils that acts as pseudo- 2D magnetorquers is explored for higher form factor small satellites (2 U and 4 U). The magnetorquers cannot generate the torque if their axes are lined up with the local geomagnetic field and generally the reaction wheels are actuated to generate this torque component. CubeSats are small satellites that have cube units of 10 cm along each axis and they are usually detumbled using magnetorquer rods bringing norm to the point where reaction wheels take over to reduce the body rates to zero. In this paper, the task of removing the initial angular velocities is undertaken by using the embedded planar coils without relying on the secondary actuators using an intelligent projection based form of the B-Dot control. The proposed reconfigurable planar coils can effectively detumble the higher form factor small satellites using application-specific optimal coil configuration. The performance parameters for various possible combinations of the coils are thermally evaluated to sustain a stable thermal profile as the planar coils are embedded inside the multilayered PCB in the form of copper traces. Lastly, the proposed coils are compared with the performance parameters of the commercial actuators in the formal studies. It is found that the suggested embedded planar magnetorquers outperforms the competition.

Ballistic Simulation and Analysis of Turntable Rotation on the Flight Stability of Anti-aircraft Rocket

The air defense multiple launch rocket is an effective terminal air defense weapon. The rotation of its turntable has an effect on the rocket’s ballistic. In the paper, the rotation angular velocity of the turntable is combined into the initial swing angular velocity of the transverse and longitudinal axis of the projectile axis. Based on this, taking the rotation of the turntable in the direction as an example, the six-degree-of-freedom rigid body ballistic model is selected for full ballistic simulation, and the stability of the projectile flight at different rotation angular velocities is studied according to the simulation results of the rocket attitude angle.

Numerical simulation of a rockfall impacting a gravel cushion with varying initial angular velocity and particle sizes

Numerical simulation of a rockfall impacting a gravel cushion with varying initial angular velocity and particle sizes

Structural design of the fluted shaped charge liner using multi-section optimization method

Spin effect of the small diameter shaped charge results in the centrifugal stress during the jet stretching process. Consequently, the jet scatters, which deceases the jet penetration capability. In the present study, a multi-section method was proposed to design the spin-compensation liner. The spin-compensation rate (SCR) of the liner was defined as the specific angular velocity that a fluted liner can offset. Based on the plain stress theory, SPH numerical method was applied to study the converging process of the 2D fluted structure. The spin-compensation mechanism of the fluted structure was illustrated. Then, nine cross sections were chosen along the liner axis equidistantly. On each of the section, a 2D fluted structure was designed to offset a given initial angular velocity. After, the optimized fluted structures were integrated into a 3D fluted liner. Jet appearances of the normal liner and the fluted liners under different initial angular velocities were compared, which verifies the practicality of the multi-sectional method. The multi-section optimization method provides a new efficient method of designing the shaped charge liner for a specific usage.

Circumferential velocities in laminar and turbulent counter-vortex flow

Knowledge of the parameters of fluid movement is essential in the designing and operating various technological processes in various technical applications. These processes play a special role in hydro engineering, where the structures of water works are directly subjected to static and dynamic forces from the side of the water flow. The operation of hydraulic turbines, spillway and water transport systems, and other hydraulic structures is directly connected with understanding the behavior of a fluid in various regimes of movement. This report is devoted to the study of a special type of fluid and gas flow, which is called counter-vortex flow. The report compares the results of the distribution of circumferential velocities with a laminar and turbulent pattern of fluid movement. The results of the laminar flow regime were obtained using a mathematical model, and the turbulent regime on a physical model using laser technologies. Such a comparison allows one to assess two approaches in determining the kinematic structures of a complicated flow. The parameters for the viscous fluid laminar flow were determined based on the traditional system of Navier-Stokes equations by determining the dependence of the circumferential component of the total velocity at the given initial circulations and angular flow velocity. A physical model was made and equipped with a set of measuring equipment to obtain the distribution of velocities in the turbulent flow. The comparison showed that the distributions of velocities for the considered flow regimes depending on the channel radius have close coincidence. In contrast, the transformation length-wise of the active zone of the flow is significant.

Head Injuries In Rollover of Military Armoured Vehicle

Rollover crashes in vehicles are disproportionately more dangerous and posed a relatively higher risk of severe injuries and fatality rates compared to other configurations such as frontal and side crashes. To date, there is no study being conducted on injury outcomes of rollover accidents involving military armoured vehicles. This study was conducted to examine the driver’s response in rollover of SIBMAS 6X6 and with the aim to evaluate severity of head injury in the incident using finite element simulation. Hybrid III 50th percentile male dummy was incorporated to represent a driver and was thus configured to simulate a typical seated driving posture. Rollover intensity, in terms of initial kinetic energy, which capable of producing two quarter-turns of rolling with vehicle roof landing was imposed via initial angular velocity that applied to the whole vehicle. The dummy’s head was observed to make three significant impacts with hull interior structures from the initiation of rollover and until the roof landed on the ground. Head injury severity was evaluated based on resultant acceleration of head centre of gravity and also 15 ms duration Head Injury Criteria (HIC15). The maximum values of these two criteria were 531g and 9098g, respectively. Evaluation of these severity values with respect to the associated injury risks and also fatality rates as classified in Abbreviated Injury Scale (AIS) clearly indicated that the head injuries sustained by the driver were mostly fatal.

CubeSats detumbling using only embedded asymmetric magnetorquers

After deployment from a rocket, a CubeSat is detumbled using magnetorquer rods bringing the norm to the point where the reaction wheels take over to reduce the angular velocity to null. Therefore, utilizing reaction wheels for satellite detumbling at higher initial velocities is vital but they are heavy and occupy significant space on a spacecraft having challenging control. To address this challenge, this paper features a disruptive approach that conducts the control only by the PCB-integrated magnetorquers with various geometries using a diverse non-unity track width ratio. The trace widths are parametrized such that the optimal torque to power dissipation ratio is investigated. The optimizations are then simulated for various geometric distributions and validated through comprehensive measurement setups that establish a framework for selecting the best-case coil configuration according to mission requirements. The detumbling rates of multiple asymmetric coil configurations are compared with the embedded designs in published literature and state of the art. It is found that the proposed asymmetric embedded magnetorquers can detumble the vehicle at high initial angular velocities. Lastly, the simulation results of thermal analysis are validated for selecting the application-specific optimal coils configuration. At the end, the proposed system is compared with the embedded magnetorquers available in the literature and commercial attitude control systems.

Research on Fast and Precise Positioning Strategy of an Ultrasonic Motor Based on the Ultrasonic Friction Reduction Theory.

To address the problems of the large positioning error and long positioning time of the traditional positioning strategy, namely, the two-phase simultaneous power-off method (TPSPM), a new positioning strategy, called the first single-phase then two-phase power-off method (FSPTTPPM), based on the ultrasonic friction reduction theory, has been proposed in this work. This method realizes zero sliding displacement between the friction material and the stator during the torsional oscillation of the shaft by controlling the driving circle frequency and the duration of the single-phase power-off period, which reduces the deviation of the displacement reservation value. In order to verify the correctness of the driving mechanism, a test platform has been built, and two positioning strategies have been used for experimental verification. The following experimental results have been obtained: compared to TPSPM, FSPTTPPM has the advantages of higher positioning accuracy and short positioning time. In terms of the positioning accuracy, the relative errors of the displacement reservation values of FSPTTPPM and TPSPM vary with the initial angular velocity (0.24 to 1.18 rad/s) in the range of −0.4 to 0.1 and −0.8 to 0.8, respectively. In addition, the relative error of the displacement reservation value is closer to zero than that of TPSPM at the same initial angular velocity. In terms of the positioning time, when the initial angular velocity is greater than 0.7 rad/s, the positioning time of the FSPTTPPM is approximately 10 ms smaller than that of the TPSPM.

New Directions in Modeling and Computational Methods for Complex Mechanical Dynamical Systems

This paper presents a new conceptualization of complex nonlinear mechanical systems and develops new and novel computational methods for determining their response to given applied forces and torques. The new conceptualization uses the idea of including particles of zero mass to describe the dynamics of such systems. This leads to simplifications in the development of their equations of motion and engenders a straightforward new computational approach to simulate their behavior. The purpose of the paper is to develop a new analytical and computational methodology to handle complex systems and to illustrate it through the study of an old unsolved problem in classical mechanics, that of a non-uniform rigid spherical shell rolling, without slipping, under gravity on an arbitrary dimpled bowl-shaped rigid surface. The new conceptualization provides the explicit equations of motion for the system, the analytical determination of the reaction forces supplied by the surface, and a straightforward computational approach to simulate the dynamics. Detailed analytical and numerical results are provided. The computations illustrate the complexity of the dynamical behavior of the system and its high sensitivity to the initial orientation of the shell and to the presence of any initial angular velocity normal to the surface.

Exploratory scenarios for the differential nuclear and tidal evolution of TZ Fornacis

Aims. TZ Fornacis is a double-lined eclipsing binary system with similar masses (2.057 ± 0.001 and 1.958 ± 0.001 M⊙) but characterized by very different radii (8.28 ± 0.22 and 3.94 ± 0.17 R⊙). This similarity in terms of mass makes it possible to study the system’s differential stellar evolution as well as some aspects of its tidal evolution. With regard to its orbital elements, it was recently confirmed that its orbit is circular with an orbital period of 75.7 days. The less massive component rotates about 17 times faster than the primary one, which is synchronized with the mean orbital angular velocity. Our main objective in this work is to study both the nuclear and the tidal evolution of the system. Methods. To model the TZ For system, we used the MESA package, computing the grids using the exact observed masses, radii, and effective temperatures as input, and then varying the metallicity, the core overshooting amount, and the mixing-length parameter. A χ2 statistic was used to infer the optimal values of the core overshooting and the mixing-length parameters. The same procedure was used to generate rotating models with the GRANADA code. The respective errors in the average age of TZ For were less than 5%. On the other hand, the differential equations that govern the tidal evolution were integrated using the fifth-order Runge–Kutta method, ith a tolerance of 1 × 10−7. Results. We explored two scenarios regarding the initial eccentricities: a high one (0.30) and a case of an initial circular orbit. A good agreement has been found between the observational values of the eccentricity, synchronism levels, and orbital period with the values predicted by the integration of the tidal evolution equations. The influence of the friction timescale on the evolution of the orbital elements of TZ For is also studied here. The orbital elements most affected by the uncertainties in the friction timescale are the synchronism levels of the two components. On the other hand, we used the properties of the rotating models generated by the GRANADA code as the initial angular velocities instead of using trial values. In this case, comparisons between the theoretical values of the orbital elements and their observed counterparts also lead to a good interagreement.