Showing papers on "Angular velocity published in 2015"
TL;DR: The proposed angular displacement and angular velocity sensors based on coplanar waveguide transmission lines and S-shaped split ring resonators are presented and it is shown that the angular velocity can be accurately determined from the time-domain response of a carrier time-harmonic signal tuned at the S-SRR resonance frequency.
Abstract: In this paper, angular displacement and angular velocity sensors based on coplanar waveguide (CPW) transmission lines and S-shaped split ring resonators (S-SRRs) are presented. The sensor consists of two parts, namely a CPW and an S-SRR, both lying on parallel planes. By this means, line-to-resonator magnetic coupling arises, the coupling level being dependent on the line-to-resonator relative angular orientation. The line-to-resonator coupling level is the key parameter responsible for modulating the amplitude of the frequency response seen between the CPW ports in the vicinity of the S-SRR fundamental resonance frequency. Specifically, an amplitude notch that can be visualized in the transmission coefficient is changed by the coupling strength, and it is characterized as the sensing variable. Thus, the relative angular orientation between the two parts is measured, when the S-SRR is attached to a rotating object. It follows that the rotation angle and speed can be inferred either by measuring the frequency response of the S-SRR-loaded line, or the response amplitude at a fixed frequency in the vicinity of resonance. It is in addition shown that the angular velocity can be accurately determined from the time-domain response of a carrier time-harmonic signal tuned at the S-SRR resonance frequency. The main advantage of the proposed device is its small size directly related to the small electrical size of the S-SRR, which allows for the design of compact angular displacement and velocity sensors at low frequencies. Despite the small size of the fabricated proof-of-concept prototype (electrically small structures do not usually reject signals efficiently), it exhibits good linearity (on a logarithmic scale), sensitivity and dynamic range.
122 citations
TL;DR: In this article, a self-powered, sliding electrification based quasi-static triboelectric sensor (QS-TES) for detecting angle from rotating motion is reported, which can read and remember the absolute angular position, angular velocity, and acceleration regardless being continuously monitored or segmented monitored.
Abstract: A self-powered, sliding electrification based quasi-static triboelectric sensor (QS-TES) for detecting angle from rotating motion is reported. This innovative, cost-effective, simply-designed QS-TES has a two-dimensional planar structure, which consists of a rotator coated with four channel coded Cu foil material and a stator with a fluorinated ethylenepropylene film. On the basis of coupling effect between triboelectrification and electrostatic induction, the sensor generates electric output signals in response to mechanical rotating motion of an object mounted with the sensor. The sensor can read and remember the absolute angular position, angular velocity, and acceleration regardless being continuously monitored or segmented monitored. Under the rotation speed of 100 r min−1, the output voltage of the sensor reaches as high as 60 V. Given a relatively low threshold voltage of ±0.5 V for data processing, the robustness of the device is guaranteed. The resolution of the sensor is 22.5° and can be further improved by increasing the number of channels. Triggered by the output voltage signal, the rotating characteristics of the steering wheel can be real-time monitored and mapped by being mounted to QS-TES. This work not only demonstrates a new principle in the field of angular measurement but also greatly expands the applicability of triboelectric nanogenerator as self-powered sensors.
111 citations
TL;DR: In this paper, the rotation of neutrally buoyant axisymmetric particles suspended in isotropic turbulence is investigated using laboratory experiments as well as numerical and analytical calculations, and it is shown that shape strongly affects orientational trajectories, but that it has negligible effect on the variance of the particle angular velocity.
Abstract: We consider the rotation of neutrally buoyant axisymmetric particles suspended in isotropic turbulence. Using laboratory experiments as well as numerical and analytical calculations, we explore how particle rotation depends upon particle shape. We find that shape strongly affects orientational trajectories, but that it has negligible effect on the variance of the particle angular velocity. Previous work has shown that shape significantly affects the variance of the tumbling rate of axisymmetric particles. It follows that shape affects the spinning rate in a way that is, on average, complementary to the shape-dependence of the tumbling rate. We confirm this relationship using direct numerical simulations, showing how tumbling rate and spinning rate variances show complementary trends for rod-shaped and disk-shaped particles. We also consider a random but non-turbulent flow. This allows us to explore which of the features observed for rotation in turbulent flow are due to the effects of particle alignment in vortex tubes.
95 citations
TL;DR: A fault-tolerant control approach without rate sensors is presented for the attitude stabilization of a satellite being developed and it is proven that reconstruction with zero observer error is achieved in finite time.
Abstract: A fault-tolerant control approach without rate sensors is presented for the attitude stabilization of a satellite being developed. External disturbances, reaction wheel faults, actuator saturation, and unavailable angular velocity are addressed. A sliding-mode observer is proposed by using attitude feedback only, and the unavailable angular velocity is estimated by this observer in finite time. Using the attitude and the estimated velocity, another sliding-mode observer is proposed to reconstruct actuator faults and disturbances. It is proven that reconstruction with zero observer error is achieved in finite time. With the reconstructed value, a velocity-free controller is then developed to asymptotically stabilize the attitude. Simulation results are also provided to verify the effectiveness of the proposed approach.
86 citations
TL;DR: A dynamic-model-based control scheme for the balancing and velocity control of a unicycle robot using a sliding-mode control and a nonzero set-point linear quadratic regulator (LQR) to achieve real-time speed control.
Abstract: This paper presents a dynamic-model-based control scheme for the balancing and velocity control of a unicycle robot. Unicycle robot motion consists of a pitch that is controlled by an in-wheel motor and a roll that is controlled by a reaction wheel pendulum. The unicycle robot lacks an actuator for yaw-axis control, which makes the derivation of the dynamics relatively simple although it may limit the motion control. The Euler-Lagrange equation is applied to derive the dynamic equations of the unicycle robot to implement dynamic speed control. To achieve real-time speed control, a sliding-mode control and a nonzero set-point linear quadratic regulator (LQR) are utilized to guarantee stability while maintaining the desired speed-tracking performance. In the roll controller, a sigmoid-function-based sliding-mode controller has been adopted to minimize switching-function chattering. An LQR controller has been implemented for pitch control to drive the unicycle robot to follow the desired velocity trajectory in real time using the state variables of pitch angle, angular velocity, wheel angle, and angular velocity. The control performance of the two control systems using a single dynamic model has been experimentally demonstrated.
66 citations
TL;DR: In this paper, a rotating electro-osmotic flow (EOF) of an incompressible third grade fluid between micro-parallel plates is considered and the analysis is based upon the modified Navier-Stokes (N-S) equation for a transport electrolyte in a rotating frame of reference.
65 citations
Patent•
28 Apr 2015TL;DR: In this article, an angular velocity sensor including a drive extension mode is presented, where at least one actuator drives the masses in an extension mode, such that in the extension mode the masses move in the plane simultaneously away or simultaneously towards the center of mass.
Abstract: An angular velocity sensor including a drive extension mode. In one aspect, an angular rate sensor includes a base and at least three masses disposed substantially in a plane parallel to the base, the masses having a center of mass. At least one actuator drives the masses in an extension mode, such that in the extension mode the masses move in the plane simultaneously away or simultaneously towards the center of mass. At least one transducer senses at least one Coriolis force resulting from motion of the masses and angular velocity about at least one input axis of the sensor. Additional embodiments can include a linkage that constrains the masses to move in the extension mode.
60 citations
TL;DR: An anharmonic propagation of two-dimensional beams in a harmonic potential is investigated, finding the "center of mass" and the orbital angular momentum of a beam exhibit harmonic motion, but the motion of the beam intensity distribution in detail is subject to external and internal torques and forces, causing it to be an Harmonic.
Abstract: We analytically and numerically investigate an anharmonic propagation of two-dimensional beams in a harmonic potential. We pick noncentrosymmetric beams of common interest that carry orbital angular momentum. The examples studied include superposed Bessel–Gauss (BG), Laguerre–Gauss (LG), and circular Airy (CA) beams. For the BG beams, periodic inversion, phase transition, and rotation with periodic angular velocity are demonstrated during propagation. For the LG and CA beams, periodic inversion and variable rotation are still there but not the phase transition. On the whole, the “center of mass” and the orbital angular momentum of a beam exhibit harmonic motion, but the motion of the beam intensity distribution in detail is subject to external and internal torques and forces, causing it to be anharmonic. Our results are applicable to other superpositions of finite circularly asymmetric beams.
55 citations
TL;DR: This article compares three different algorithms used to compute Euler angles from data obtained by the angular rate sensor—the algorithms based on a rotational matrix, on transforming angular velocity to time derivations of the Euler angle, and on unit quaternion expressing rotation.
Abstract: This article compares three different algorithms used to compute Euler angles from data obtained by the angular rate sensor (e.g., MEMS gyroscope)—the algorithms based on a rotational matrix, on transforming angular velocity to time derivations of the Euler angles and on unit quaternion expressing rotation. Algorithms are compared by their computational efficiency and accuracy of Euler angles estimation. If attitude of the object is computed only from data obtained by the gyroscope, the quaternion-based algorithm seems to be most suitable (having similar accuracy as the matrix-based algorithm, but taking approx. 30% less clock cycles on the 8-bit microcomputer). Integration of the Euler angles’ time derivations has a singularity, therefore is not accurate at full range of object’s attitude. Since the error in every real gyroscope system tends to increase with time due to its offset and thermal drift, we also propose some measures based on compensation by additional sensors (a magnetic compass and accelerometer). Vector data of mentioned secondary sensors has to be transformed into the inertial frame of reference. While transformation of the vector by the matrix is slightly faster than doing the same by quaternion, the compensated sensor system utilizing a matrix-based algorithm can be approximately 10% faster than the system utilizing quaternions (depending on implementation and hardware).
52 citations
TL;DR: In this paper, a smooth angular velocity observer is proposed for the attitude tracking control of a rigid body in the absence of angular velocity measurements, which ensures asymptotic convergence of estimation errors irrespective of the control torque or the initial attitude state of the spacecraft.
Abstract: A smooth angular velocity observer is proposed for the attitude tracking control of a rigid body in the absence of angular velocity measurements. The observer design ensures asymptotic convergence of angular velocity state estimation errors irrespective of the control torque or the initial attitude state of the spacecraft. Unlike existing rate observer formulations that attain estimation error convergence by imposing certain switching conditions or hybrid logic, the proposed observer has a smooth structure that ensures C∞ continuity of all estimated states. Furthermore, the combined implementation of the proposed observer with a proportional-derivative type of attitude control law leads to an important “separation property.” In particular, an independently designed proportional-derivative control law driven by angular velocity estimates generated from the smooth observer results in (almost) global asymptotic stability of the overall closed-loop tracking error dynamics. The main feature of this key technic...
51 citations
TL;DR: In this paper, a finite-time attitude coordinated control for spacecraft formation flying (SFF) subjected to input saturation is investigated, where a bounded finitetime state feedback control law is first developed with the assumption that both attitude and angular velocity signals can be measured and transmitted between formation members.
Abstract: In this paper, finite-time attitude coordinated control for spacecraft formation flying (SFF) subjected to input saturation is investigated. More specifically, a bounded finitetime state feedback control law is first developed with the assumption that both attitude and angular velocity signals can be measured and transmitted between formation members. Then, a bounded finite-time output feedback controller is designed with the addition of a filter, which removes the requirement of the angular velocity measurements. In both cases, actuator saturation is explicitly taken into account, and the homogeneous system method is employed to demonstrate the finite-time stability of the closed-loop system. Numerical simulation results are presented to illustrate the efficiency of the proposed control schemes. [DOI: 10.1115/1.4029467]
TL;DR: A new approach for solving the simultaneous localization and mapping problem for inspecting an unknown and uncooperative object that is spinning about an arbitrary axis in space, which probabilistically models the six degree-of-freedom rigid-body dynamics in a factor graph formulation.
Abstract: This paper presents a new approach for solving the simultaneous localization and mapping problem for inspecting an unknown and uncooperative object that is spinning about an arbitrary axis in space. This approach probabilistically models the six degree-of-freedom rigid-body dynamics in a factor graph formulation. Using the incremental smoothing and mapping system, this method estimates a feature-based map of the target object, as well as this object's position, orientation, linear velocity, angular velocity, center of mass, principal axes, and ratios of inertia. This solves an important problem for spacecraft proximity operations. Additionally, it provides a generic framework for incorporating rigid-body dynamics that may be applied to a number of other terrestrial-based applications. To evaluate this approach, the Synchronized Position Hold Engage Reorient Experimental Satellites SPHERES were used as a testbed within the microgravity environment of the International Space Station. The SPHERES satellites, using body-mounted stereo cameras, captured a dataset of a target object that was spinning at ten rotations per minute about its unstable, intermediate axis. This dataset was used to experimentally evaluate the approach described in this paper, and it showed that it was able to estimate a geometric map and the position, orientation, linear and angular velocities, center of mass, and ratios of inertia of the target object.
TL;DR: The aim of this study is to assess how the orientation estimation accuracy is affected by each of these disturbances, and whether it is influenced by the angular velocity magnitude and 3D distribution across the gyroscope axes.
Abstract: In human movement analysis, 3D body segment orientation can be obtained through the numerical integration of gyroscope signals. These signals, however, are affected by errors that, for the case of micro-electro-mechanical systems, are mainly due to: constant bias, scale factor, white noise, and bias instability. The aim of this study is to assess how the orientation estimation accuracy is affected by each of these disturbances, and whether it is influenced by the angular velocity magnitude and 3D distribution across the gyroscope axes. Reference angular velocity signals, either constant or representative of human walking, were corrupted with each of the four noise types within a simulation framework. The magnitude of the angular velocity affected the error in the orientation estimation due to each noise type, except for the white noise. Additionally, the error caused by the constant bias was also influenced by the angular velocity 3D distribution. As the orientation error depends not only on the noise itself but also on the signal it is applied to, different sensor placements could enhance or mitigate the error due to each disturbance, and special attention must be paid in providing and interpreting measures of accuracy for orientation estimation algorithms.
TL;DR: In this paper, a finite element model has been developed and validated to calculate the acoustic radiation torque on a microfiber and the influence of different parameters such as the frequency, fiber size and position in the acoustic field is evaluated.
Abstract: This study is aimed at the theoretical analysis of the acoustic radiation torque and the experimental realization of a controlled rotation of non-spherical particles by ultrasound. A finite element model has been developed and validated to calculate the acoustic radiation torque on a microfiber. The influence of different parameters such as the frequency, fiber size and position in the acoustic field are evaluated. The rotational motion of a non-spherical particle and the resulting drag torque are analyzed as well. This allows for the calculation of the angular velocity of a fiber. Various rotation methods for non-spherical particles with the acoustic radiation torque have been developed, tested experimentally with a microdevice at frequencies in the MHz range and compared to each other. The first method relies on successive change of the wave propagation direction in discrete steps. Three additional rotation methods have been developed which allow for a continuous rotation and alignment at defined orientations. The methods are characterized by the modulation of one single parameter (amplitude, phase or frequency) over time.
TL;DR: In this article, a design for small vibrotactors called the Dual Excenter is presented, which makes it possible to produce vibrations with independently adjustable frequency and amplitude, using two coaxially aligned eccentric rotors driven by DC motors independently.
TL;DR: In this paper, an algorithm for setting the dynamic parameters of the classic main mechanism of the internal combustion engines is presented, which can be applied separately for two distinct situations: when the engine is working on a compressor and into the motor system.
Abstract: This paper presents an algorithm for setting the dynamic parameters of the classic main mechanism of the internal combustion engines. One presents the dynamic, original, machine motion equations. The equation of motion of the machine that generates angular speed of the shaft (which varies with position and rotation speed) is deduced by conservation kinetic energy of the machine. An additional variation of angular speed is added by multiplying by the coefficient dynamic (generated by the forces out of mechanism). Kinetic energy conservation shows angular speed variation (from the main shaft) with inertial masses, while the dynamic coefficient introduces the variation of ω with forces acting in the mechanism. Deriving the first equation of motion of the machine it obtains the second equation of motion dynamics. From the second equation of motion of the machine one determines the angular acceleration of the motor shaft. It shows the distribution of the forces (on the main mechanism of the engine) to the internal combustion heat engines. Dynamic, the velocities can be distributed in the same way as forces. Practically, in the dynamic regimes, the velocities have the same timing as the forces. The method is applied separately for two distinct situations: When the engine is working on a compressor and into the motor system. For the two separate cases, two independent formulas are obtained for the engine dynamic cinematic (forces speeds). Calculations should be made for an engine with a single cylinder.
TL;DR: In this article, a mixed convection of a lid driven cavity in the presence of two rotating cylinders was numerically investigated by using the finite element method and the results revealed that cylinder angular velocities, ratio of the angular velocity and diameter ratios have profound effect on heat transfer enhancement within the cavity.
TL;DR: The results indicated that the angular velocity in the frontal axis, which is the sequence of the plantar/dorsiflexion movements, can also be used to identify different locomotion.
TL;DR: A dynamic model for an LMA actuation unit was developed by extending the theory proposed for coaxial magnetic gears for closed-loop control, and two alternative strategies-using either the angular velocity at the motor or at the load as feedback parameter-were compared.
Abstract: We propose local magnetic actuation (LMA) as an approach to robotic actuation for surgical instruments. An LMA actuation unit consists of a pair of diametrically magnetized single-dipole cylindrical magnets, working as magnetic gears across the abdominal wall. In this study, we developed a dynamic model for an LMA actuation unit by extending the theory proposed for coaxial magnetic gears. The dynamic model was used for closed-loop control, and two alternative strategies—using either the angular velocity at the motor or at the load as feedback parameter—were compared. The amount of mechanical power that can be transferred across the abdominal wall at different intermagnetic distances was also investigated. The proposed dynamic model presented a relative error below 7.5% in estimating the load torque from the system parameters. Both the strategies proposed for closed-loop control were effective in regulating the load speed with a relative error below 2% of the desired steady-state value. However, the load-side closed-loop control approach was more precise and allowed the system to transmit larger values of torque, showing, at the same time, less dependence from the angular velocity. In particular, an average value of 1.5 mN $\cdot$ m can be transferred at 7 cm, increasing up to 13.5 mN $\cdot$ m as the separation distance is reduced down to 2 cm. Given the constraints in diameter and volume for a surgical instrument, the proposed approach allows for transferring a larger amount of mechanical power than what would be possible to achieve by embedding commercial dc motors.
TL;DR: Investigation of magnetohydrodynamic free convective flow of micropolar fluid over a moving flat plate using the Lie group transformations and numerical methods revealed that the dimensionless velocity and angular velocity decrease whilst the dimensioned temperature increases with the velocity slip parameter.
Abstract: In this paper, we investigate magnetohydrodynamic free convective flow of micropolar fluid over a moving flat plate using the Lie group transformations and numerical methods. Instead of using conventional no-slip boundary conditions, we used both the velocity and thermal slip boundary conditions to achieve physically realistic and practically useful results. The governing boundary layer equations are non-dimensionalized and transformed into a set of coupled ordinary differential equations (ODEs) using similarity transformations generated by the Lie group, before being solved numerically using Matlab stiff ODE solver ode15s and Matlab trust-region-reflective algorithm lsqnonlin. The effects of governing parameters on the dimensionless velocity, angular velocity, temperature, skin friction and heat transfer rate are investigated. Our analysis revealed that the dimensionless velocity and angular velocity decrease whilst the dimensionless temperature increases with the velocity slip parameter. Thermal slip reduces the dimensionless velocity and temperature but raises the dimensionless angular velocity. Magnetic field suppresses the velocity but elevates the temperature and angular velocity. Results reported in this paper are in good agreement with the ones reported by the previous authors.
TL;DR: In this paper, the elasto-plastic oblique impact of a rod with a flat has been analyzed experimentally and theoretically in terms of the linear and the angular motion, the contact force during the impact, and the permanent deformation.
TL;DR: In this paper, the authors investigated the non-linear dynamic pull-in instability of a double-sided nano-bridge incorporating the effects of angular velocity and rarefied gas damping.
Abstract: Double-sided electromechanical nano-bridges can potentially be used as angular speed sensors and accelerometers in rotary systems such as turbine blades and vacuum pumps. In such applications, the influences of the centrifugal force and rarefied flow should be considered in the analysis. In the present study, the non-linear dynamic pull-in instability of a double-sided nano-bridge is investigated incorporating the effects of angular velocity and rarefied gas damping. The non-linear governing equation of the nanostructure is derived using Euler-beam model and Hamilton׳s principle including the dispersion forces. The strain gradient elasticity theory is used for modeling the size-dependent behavior of the system. The reduced order method is also implemented to discretize and solve the partial differential equation of motion. The influences of damping, centrifugal force, length scale parameters, van der Waals force and Casimir attraction on the dynamic pull-in voltage are studied. It is found that the dispersion and centrifugal forces decrease the pull-in voltage of a nano-bridge. Dynamic response of the nano-bridge is investigated by plotting time history and phase portrait of the system. The validity of the proposed method is confirmed by comparing the results from the present study with the experimental and numerical results reported in the literature.
TL;DR: Distributed control strategies for the attitude synchronization and set-point tracking control of multiple heterogeneous spacecraft (SC) in a formation flying mission are proposed and developed.
Abstract: Distributed control strategies for the attitude synchronization and set-point tracking control of multiple heterogeneous spacecraft (SC) in a formation flying mission are proposed in this work The first scheme requires feedback and exchange of angular velocity measurements among the SC in the formation However, the second scheme does not require measurement and exchange of angular velocities (or their estimates) among the SC in the formation We have employed unit-quaternion, which is a singularity free attitude representation, to describe the SC attitude so that large attitude maneuvers can be executed We have also developed two constrained control schemes for attitude synchronization and set-point tracking control for (i) a single SC with and without angular velocity feedback, and (ii) SC formation flying with and without angular velocity feedback A number of simulation case studies are provided to demonstrate the advantages and benefits of our proposed algorithms as compared to the available results in the literature
TL;DR: In this paper, the stability of multibody drill-strings with stick-slip oscillations is studied from the point of view of underactuated system and three sliding-mode controllers are studied for the drill-string with estimated physical parameters.
Abstract: Stabilisation of multibody drill-strings which exhibit stick-slip oscillations is studied in this paper from the point of view of underactuated system. The model has one control torque input acting on the rotary table from the land surface and multi-degree-of-freedom downhole parts to be controlled. Three motion regimes of the model including bit sticking, stick-slip oscillation and rotating at a constant speed are identified and their equilibria are analysed accordingly. The control objective of the system is to avoid the undesired bit sticking and stick-slip oscillation while tracking a desired angular velocity. Three sliding-mode controllers are studied for the drill-string with estimated physical parameters. The stabilities of the proposed controllers are proved by using the Lyapunov direct method ensuring that any trajectory of the system can reach and stays thereafter on the pre-designed sliding surface where the desired equilibrium is asymptotically stable. Extensive simulation results are given to demonstrate the effectiveness of the proposed controllers and their robustness to parametric uncertainties.
TL;DR: In this article, the von Zeipel theorem was extended to the magnetohydrodynamic regime, under the assumption of an infinitely conductive fluid, both in the Newtonian and in the relativistic framework.
Abstract: We analyze a class of physical properties, forming the content of the so-called von Zeipel theorem, which characterizes stationary, axisymmetric, non-selfgravitating perfect fluids in circular motion in the gravitational field of a compact object. We consider the extension of the theorem to the magnetohydrodynamic regime, under the assumption of an infinitely conductive fluid, both in the Newtonian and in the relativistic framework. When the magnetic field is toroidal, the conditions required by the theorem are equivalent to integrability conditions, as it is the case for purely hydrodynamic flows. When the magnetic field is poloidal, the analysis for the relativistic regime is substantially different with respect to the Newtonian case and additional constraints, in the form of PDEs, must be imposed on the magnetic field in order to guarantee that the angular velocity \(\varOmega \) depends only on the specific angular momentum \(\ell \). In order to deduce such physical constraints, it is crucial to adopt special coordinates, which are adapted to the \(\varOmega =\mathrm{const}\) surfaces. The physical significance of these results is briefly discussed.
TL;DR: In this paper, the second-order phase coefficients of the range echoes are a linear polynomial of the rotating angular velocity and range geometry, and the least square error method is used to estimate the rotation angular velocity of the targets with dominant scatters.
Abstract: The cross-range scaling of inverse synthetic aperture radar image depends on both the radar wavelength and the rotating angle of the target relative to the radar line-of-sight. After compensating the translational motion, the second-order phase coefficients of the range echoes are a linear polynomial of the rotating angular velocity and range geometry. In this study, a novel method for estimating the rotating angular velocity of the targets with dominant scatters is proposed. The range cells where the amplitudes have smaller normalised variances are selected, and then frequency domain windowing is applied to extract echoes of dominant scatters. Based on the discrete polynomial-phase transform, the second-order phase coefficients of the strong scatter echoes are estimated, and thus the rotating angular velocity can be obtained through the least-square-error method. Simulated and real-data results have shown the effectiveness and robustness of this method.
TL;DR: In this paper, the free vibration of rotating tapered cantilever beams with rotary inertia was studied and the effects of the rotary momentum, angular velocity, taper ratio and hub radius were analyzed and presented in tables and graphs.
TL;DR: In this article, it was shown that the Sagnac effect can be obtained in the absence of rotation, when there is relative motion (be it inertial or not) between the source/receiver of light and the interferometer.
Abstract: The Sagnac effect is usually deemed to be a special-relativistic effect produced in an interferometer when the device is rotating. Two light beams traveling around the interferometer in opposite directions require different times of flight to complete their closed path, giving rise to a phase shift proportional to the angular velocity of the apparatus. Here, we show that the same result can be obtained in the absence of rotation, when there is relative motion (be it inertial or not) between the source/receiver of light and the interferometer. Our argument will use both a simple algebraic analysis and a plain geometric approach in flat spacetime. We present an explicit example to illustrate our point and briefly discuss other apparently correct interpretations of the Sagnac effect, including an analogy to the Aharonov-Bohm effect. Finally, we sketch a possible application of the non-rotational Sagnac effect.
TL;DR: In this article, the internal rotation of post-main sequence stars is investigated, in response to the convective pumping of angular momentum toward the stellar core, combined with a tight magnetic coupling between core and envelope.
Abstract: The internal rotation of post-main sequence stars is investigated, in response to the convective pumping of angular momentum toward the stellar core, combined with a tight magnetic coupling between core and envelope. The spin evolution is calculated using model stars of initial mass 1, 1.5, and , taking into account mass loss on the giant branches. We also include the deposition of orbital angular momentum from a sub-stellar companion, as influenced by tidal drag along with the excitation of orbital eccentricity by a fluctuating gravitational quadrupole moment. A range of angular velocity profiles is considered in the envelope, extending from solid rotation to constant specific angular momentum. We focus on the backreaction of the Coriolis force, and the threshold for dynamo action in the inner envelope. Quantitative agreement with measurements of core rotation in subgiants and post-He core flash stars by Kepler is obtained with a two-layer angular velocity profile: uniform specific angular momentum where the Coriolis parameter (here is the convective time), and where . The inner profile is interpreted in terms of a balance between the Coriolis force and angular pressure gradients driven by radially extended convective plumes. Inward angular momentum pumping reduces the surface rotation of subgiants, and the need for a rejuvenated magnetic wind torque. The co-evolution of internal magnetic fields and rotation is considered in Kissin & Thompson, along with the breaking of the rotational coupling between core and envelope due to heavy mass loss.
01 Jan 2015
TL;DR: In this paper, the rotational analogue to translational momentum, rotational momentum or angular momentum, and the rotation analogue to force: torque, are introduced and compared to Newton's second law for rotational motion.
Abstract: You know how to describe the rotation of a wheel around a fixed or moving axis, using the angle, the angular velocity, and the angular acceleration of the wheel. And you know how to find the kinetic energy of a rotating rigid body. But what causes changes in rotational motion? For translational motion we can use Newton’s second law to determine the change in the translational state, in the translational momentum, from the external forces acting on a body. We use this both to find the acceleration of a body, and from the acceleration we can calculate the motion, and to find conservation laws for the translational momentum. Can we find a similar law for rotational motion? In this chapter we will introduce the rotational analogue to translational momentum: rotational momentum or angular momentum; the rotational analogue to force: torque; and the rotational analogue to Newton’s second law: Newton’s second law for rotational motion. Armed with these tools you will see that you are ready to solve any problem of moving and rotating rigid bodies, such as figuring out what causes a ball to spin or how you jump-spin on skates.