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Showing papers on "Angular velocity published in 2021"


Journal ArticleDOI
TL;DR: A fault-tolerant control scheme is proposed for the rigid spacecraft attitude control system subject to external disturbances, multiple system uncertainties, and actuator faults and it is shown that the attitude orientations converge to the desired values exponentially.
Abstract: In this paper, a fault-tolerant control scheme is proposed for the rigid spacecraft attitude control system subject to external disturbances, multiple system uncertainties, and actuator faults. The angular velocity measurement is unavailable, which increases the complexity of the problem. An observer is first designed based on the super-twisting sliding mode method, which can provide accurate estimates of the angular velocity in finite time. Then, an adaptive fault-tolerant controller is proposed based on neural networks using the information from the observer. It is shown that the attitude orientations converge to the desired values exponentially. Finally, a simulation example is utilized to verify the effectiveness of the proposed scheme.

64 citations


Journal ArticleDOI
TL;DR: The radial symmetry properties of stationary and uniformly rotating solutions of the 2D Euler and gSQG equations, both in the smooth setting and the patch setting, were studied in this paper.
Abstract: We study the radial symmetry properties of stationary and uniformly rotating solutions of the 2D Euler and gSQG equations, both in the smooth setting and the patch setting. For the 2D Euler equation, we show that any smooth stationary solution with compactly supported and nonnegative vorticity must be radial, without any assumptions on the connectedness of the support or the level sets. For the 2D Euler equation in the patch setting, we show that every uniformly rotating patch D with angular velocity Ω≤0 or Ω≥1 2 must be radial, where both bounds are sharp. For the gSQG equation, we obtain a similar symmetry result for Ω≤0 or Ω≥Ωα (with the bounds being sharp), under the additional assumption that the patch is simply connected. These results settle several open questions posed by Hmidi, de la Hoz, Hassainia, and Mateu on uniformly rotating patches. Along the way, we close a question by Choksi, Neumayer, and Topaloglu on overdetermined problems for the fractional Laplacian, which may be of independent interest. The main new ideas come from a calculus-of-variations point of view.

40 citations


Journal ArticleDOI
TL;DR: In this article, the system of equations governing the thermoelastic behavior of a rotating viscoelastic microbeam has been derived based on the non-Fourier heat conduction model.

38 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of rapid rotation on the phase diagram of hadronic matter was discussed, and it was shown that rotation decreases the deconfinement temperature, which suggests that rotation should lower the critical temperature of chiral restoration.

35 citations


Journal ArticleDOI
TL;DR: In this article, the authors used vectorially structured light with spatially variant polarization to determine both the magnitude of velocity and motion direction of a moving particle, and the instantaneous position of the moving particle is also tracked under the conditions of knowing its starting position and continuous tracking.
Abstract: The Doppler effect is a universal wave phenomenon that has spurred a myriad of applications. In early manifestations, it was implemented by interference with a reference wave to infer linear velocities along the direction of motion, and more recently lateral and angular velocities using scalar phase structured light. A consequence of the scalar wave approach is that it is technically challenging to directly deduce the motion direction of moving targets. Here we overcome this challenge using vectorially structured light with spatially variant polarization, allowing the velocity and motion direction of a moving particle to be fully determined. Using what we call a vectorial Doppler effect, we conduct a proof of principle experiment and successfully measure the rotational velocity (magnitude and direction) of a moving isotropic particle. The instantaneous position of the moving particle is also tracked under the conditions of knowing its starting position and continuous tracking. Additionally, we discuss its applicability to anisotropic particle detection, and show its potential to distinguish the rotation and spin of the anisotropic particle and measure its rotational velocity and spin speed (magnitude and direction). Our demonstration opens the path to vectorial Doppler metrology for detection of universal motion vectors with vectorially structured light. The Doppler effect is a wave phenomenon that can find the magnitude of velocity of moving targets with scalar waves. Here, the authors use vectorially structured light with spatially variant polarization to fully determine both the magnitude of velocity and motion direction of a moving particle.

31 citations


Journal ArticleDOI
TL;DR: In this article, the authors study stable circular orbits in spherically symmetric AdS black holes in various dimensions and their limiting innermost stable circular orbit (ISCOs) and provide analytic expressions for their size, angular velocity and angular momentum.
Abstract: We study stable circular orbits in spherically symmetric AdS black holes in various dimensions and their limiting innermost stable circular orbits (ISCOs). We provide analytic expressions for their size, angular velocity and angular momentum in a large black hole mass regime. The dual interpretation is in terms of meta-stable states not thermalising in typical thermal scales and whose existence is due to non-perturbative effects on the spatial curvature. Our calculations reproduce the binding energy known in the literature, but also include a binding energy in the radial fluctuations corresponding to near circular trajectories. We also describe how particles are placed on these orbits from integrated operators on the boundary: they tunnel inside in a way that can be computed from both complex geodesics in the black hole background and from the WKB approximation of the wave equation. We explain how these two computations are related.

25 citations


Journal ArticleDOI
TL;DR: This paper investigates the robust tracking control problem for spacecraft attitude maneuvering with prescribed performance by studying a control scheme based on a quasi-sliding-mode approach which can simultaneously restrict the convergence speed and the steady-state error of both Euler angle and relative angular velocity.

25 citations


Journal ArticleDOI
TL;DR: In this article, the authors introduced directional Fermi-Walker transportation along with the vortex lines of nonvanishing vector fields in the ordinary three-dimensional space and investigated the geometric phase and angular velocity vector (Darboux vector) of vortex lines.
Abstract: In this study, we introduce directional Fermi–Walker transportation along with the vortex lines of nonvanishing vector fields in the ordinary three-dimensional space. Moreover, we investigate the geometric phase and angular velocity vector (Darboux vector) of vortex lines. Then, we define directional magnetic and electric vortex lines by considering the Lorentz force law and electromagnetic force equation. Finally, we prove a significant relation between directional magnetic and electric vortex lines and angular velocity vector of vortex lines.

24 citations


Journal ArticleDOI
TL;DR: In this article, the objective for a group of nonholonomic agents is to achieve multicircular circumnavigation with any desired angular spacing around a nonstationary target and a cooperative protocol is proposed to achieve this objective.
Abstract: In this article, the objective for a group of nonholonomic agents is to achieve multicircular circumnavigation with any desired angular spacing around a nonstationary target. A cooperative protocol is proposed to achieve this objective and, additionally, generalizes the circumnavigation problem of unicycle vehicles around a target (moving and stationary). Due to the nonholonomic constraints, existing protocols cannot be extended directly to achieve this objective. Thus, the proposed algorithm is worked out from the desired geometry to achieve the objective. A fixed-time consensus estimator is designed under a cyclic digraph to arrive at the desired interagent angular separation in the target-centric frame. The target information and desired formation parameters are assumed to be known to only one agent partially. Due to uncertainty in the target’s motion, it is assumed that the target’s acceleration and angular velocity are unknown. Fixed-time estimators under a digraph address the lack of information. The tracking controller drives the agents to the desired position around the target, thus making the errors go to zero instead of any finite bounds. The controller guarantees the bounded control effort irrespective of the error magnitude. The numerical examples are presented to show the effectiveness of the algorithm.

23 citations


Journal ArticleDOI
TL;DR: In this paper, the influence of angular momentum on quantum complexity for CFT states dual to rotating BTZ was studied using the holographic complexity=action (CA) and complexity=volume (CV) proposals, and it was shown that the CA and CV complexity of formation are linear in the temperature and diverge with the same structure in the speed of light angular velocity limit.
Abstract: We study the influence of angular momentum on quantum complexity for CFT states holographically dual to rotating black holes. Using the holographic complexity=action (CA) and complexity=volume (CV) proposals, we study the full time dependence of complexity and the complexity of formation for two dimensional states dual to rotating BTZ. The obtained results and their dependence on angular momentum turn out to be analogous to those of charged states dual to Reissner-Nordstrom AdS black holes. For CA, our computation carefully accounts for the counterterm in the gravity action, which was not included in previous analysis in the literature. This affects the complexity early time dependence and its effect becomes negligible close to extremality. In the grand canonical ensemble, the CA and CV complexity of formation are linear in the temperature, and diverge with the same structure in the speed of light angular velocity limit. For CA the inclusion of the counterterm is crucial for both effects. We also address the problem of studying holographic complexity for higher dimensional rotating black holes, focusing on the four dimensional Kerr-AdS case. Carefully taking into account all ingredients, we show that the late time limit of the CA growth rate saturates the expected bound, and find the CV complexity of formation of large black holes diverges in the critical angular velocity limit. Our holographic analysis is complemented by the study of circuit complexity in a two dimensional free scalar model for a thermofield double (TFD) state with angular momentum. We show how this can be given a description in terms of non-rotating TFD states introducing mode-by-mode effective temperatures and times. We comment on the similarities and differences of the holographic and QFT complexity results.

23 citations


Journal ArticleDOI
TL;DR: An active disturbance rejection control is designed to improve the position tracking performance of an electro-hydraulic actuation system in the presence of parametric uncertainties, non-parametric uncertainty, and external disturbances as well.
Abstract: In this paper, an active disturbance rejection control is designed to improve the position tracking performance of an electro-hydraulic actuation system in the presence of parametric uncertainties, non-parametric uncertainties, and external disturbances as well. The disturbance observers (Dos) are proposed to estimate not only the matched lumped uncertainties but also mismatched disturbance. Without the velocity measurement, the unmeasurable angular velocity is robustly calculated based on the high-order Levant’s exact differentiator. These disturbances and angular velocity are integrated into the control design system based on the backstepping framework which guarantees high-accuracy tracking performance. The system stability analysis is analyzed by using the Lyapunov theory. Simulations based on an electro-hydraulic rotary actuator are conducted to verify the effectiveness of the proposed control method.

Journal ArticleDOI
01 Jan 2021
TL;DR: In this paper, the role of angular acceleration, angular velocity, and angular jerk on the brain tissue strain and strain rates was investigated, and the results showed that both angular acceleration and angular velocity have a significant effect on the peak tissue strain rates.
Abstract: Given the complex nature of traumatic brain injury (TBI), assessment of injury risk directly from kinematic measures of head motion remains a challenge. Despite this challenge, kinematic-based measures of injury continue to be widely used to guide the design of protective equipment. In an effort to provide more insight into the relationship between rotational head kinematics and injury risk, we have conducted a large scale parametric finite element analysis (FEA) to investigate the role of angular acceleration, angular velocity, and angular jerk on the brain tissue strains and strain rates. The peak strains and strain rates resulting from rotational head accelerations were obtained for peak angular accelerations ranging from 0.5 - 25 krad/s 2 and peak angular velocities ranging from 10 - 100 rad/s. The results of this study show that both angular acceleration and angular velocity have a significant effect on the peak tissue strains and strain rates, reinforcing the importance of accounting for both of these kinematic measures when evaluating injury risk. For a given magnitude of peak angular acceleration and angular velocity, increases in angular jerk are shown to have minimal effect on the peak tissue strains but can lead to an increase in the peak tissue strain rates. This advancement in our understanding of the relationship between angular head kinematics, tissue strain, and tissue strain rate is an important step toward developing improved kinematic-based measures of injury. Statement of Significance To reduce the risk of traumatic brain injury, we must first fully understand the relationship between impact-induced head motions and the brain deformation response. Large deformations of the brain have been shown to cause damage to neural cells and can result in long-term neurocognitive deficits. This study investigates the role of angular acceleration, angular velocity, and angular jerk on the tissue strains and strain rates that develop in the brain. By providing further insight into how each of these kinematic parameters affect the brain deformation response, we can begin to identify the types of head motions that are the most injurious and develop new targeted approaches to reduce the risk of injury.

Journal ArticleDOI
TL;DR: In this article, a rotator capable of self-excited movement is proposed, which consists of a liquid crystal elastomer (LCE) bar and a regular bar with an axle.
Abstract: Self-excited motions have the advantages of directly harvesting energy from the environment, autonomy, and portability of the equipment, and consequently, the development of a wealth of new self-excited motion modes can greatly expand the application of active machines. In this paper, a rotator capable of self-excited movement is proposed, which consists of a liquid crystal elastomer (LCE) bar and a regular bar with an axle. Based on the dynamic LCE model, through theoretical modeling and numerical calculation, it is found that the LCE rotator has three motion modes, namely static mode, oscillation mode and rotation mode. The detailed dynamical process reveals the mechanism of self-excited oscillation and rotation. In this paper, the effects of parameters such as light intensity, damping coefficient, dimensionless gravitational acceleration, length ratio, illumination region and initial angular velocity on the self-excited oscillation and rotation are further studied systematically, and the corresponding limit cycles are given by various cases. The results show that the light intensity, damping coefficient and length ratio have important influence on the motion mode, while the initial angular velocity does not affect the motion mode. The influence of various parameters including light intensity and illumination region on the amplitude and frequency of self-excited oscillation is also studied. It is found that the amplitude mainly depends on light intensity and damping. This study can deepen people's understanding of non-equilibrium self-excited motions and provide promising applications in the fields of energy harvest, power generation, monitoring, soft robotics, medical devices and micro–nano-devices.

Journal ArticleDOI
TL;DR: This article investigates the attitude control problem of a rigid body subject to attitude and angular rate constraints (double-level state constraints), and inertia uncertainties, and proposes a data-driven immersion and invariance (I&I) adaptive control scheme to tackle this technically challenging problem.
Abstract: This article investigates the attitude control problem of a rigid body subject to attitude and angular rate constraints (double-level state constraints), and inertia uncertainties. A data-driven immersion and invariance (I&I) adaptive control scheme is proposed to tackle this technically challenging problem. As a stepping stone, a novel dynamically scaled I&I adaptive controller is designed to bypass the realizability condition that may not hold in the Lyapunov sense when considering angular rate constraints. Lyapunov stability analysis shows that this controller can enable the attitude errors and angular rates to converge asymptotically to zero for most initial conditions in the accessible space, while strictly obeying double-level state constraints with the help of two judiciously constructed potential functions. After that, to further relax the dependence of parameter convergence on the persistent excitation (PE) condition, the I&I adaptive law is extended to a data-driven counterpart through adding a learning term that is acquired by adopting the regressor filtering in conjunction with the dynamic regressor extension and mixing (DREM) procedure. The extended adaptive controller can not only preserve all the results obtained by the earlier proposed I&I adaptive controller, but also ensure asymptotic parameter convergence under a finite excitation condition much weaker than PE. In addition, benefiting from the DREM method and some special designs, the parameter convergence rates across all the parameter vector components can be flexibly tuned in an explicit way, and moreover, they are independent of the excitation level. Finally, simulation results are given to show the effectiveness of the proposed method.

Journal ArticleDOI
TL;DR: In this article, the authors show the relevance of penetrative convection for the depletion of light elements in the radiative interior of solar-type stars, in particular Li, and the evolution of their rotation rates.
Abstract: Transport processes occurring in the radiative interior of solar-type stars are evidenced by the surface variation of light elements, in particular Li, and the evolution of their rotation rates. For the Sun, inversions of helioseismic data indicate that the radial profile of angular velocity in its radiative zone is nearly uniform, which implies the existence of angular momentum transport mechanisms. While there are many independent transport models for angular momentum and chemical species, there is a lack of self-consistent theories that permit stellar evolution models to simultaneously match the present-day observations of solar lithium abundances and radial rotation profiles. We explore how additional transport processes can improve the agreement between evolutionary models of rotating stars and observations. We constrain the resulting models by simultaneously using the evolution of the surface rotation rate and Li abundance in the solar-type stars of open clusters, and the solar surface and internal rotation profile as inverted from helioseismology. We show the relevance of penetrative convection for the depletion of Li. The rotational dependence of the depth of penetrative convection yields an anti-correlation between the initial rotation rate and Li depletion in our models of solar-type stars that is in agreement with the observed trend. Simultaneously, the addition of an ad hoc vertical viscosity leads to efficient transport of angular momentum between the core and the envelope. We also self-consistently compute for the first time the thickness of the tachocline and find that it is compatible with helioseismic estimations. However, the main sequence depletion of Li in solar-type stars is only reproduced when adding a parametric turbulent mixing below the convective envelope. The need for additional transport processes in stellar evolution models is confirmed.

Journal ArticleDOI
TL;DR: In this paper, the authors simulated mixed convection in a lid-driven square cavity with different walls temperature in the existence of four rotating cylinders having harmonic motion for various parameters such as the solid volume fraction, Richardson number, and type of motion for each cylinder.
Abstract: Mixed convection in a lid-driven square cavity with different walls temperature in the existence of four rotating cylinders having harmonic motion is simulated numerically for various parameters such as the solid volume fraction (0 ≤ ϕ ≤ 0.03), Richardson number (0.1 ≤ Ri ≤ 10) and type of motion for each cylinder. Cu–water nanofluids are considered as fluid inside the enclosure. A comparison of full rotation and harmonic rotation in steady and transient cases was made to get a better understanding of the effect of harmonic rotation. The consequences of this study are obtainable in terms of average and local Nusselt numbers, isotherm contours, streamlines contours, velocity profiles, PEC, and entropy generation profiles. Obtained results show that the heat transfer is dependent on the angular velocity of the cylinder, type of rotation, and the nanoparticle concentration. Adding nanoparticles causes to improve the heat transfer rate. However, the effect of the nanofluids on geometry has decreased for the PEC, except for Ri = 1 and a few particular cases. Also, according to the Nusselt number graphs, we can tell that the harmonic motion in this study did not have a considerable effect on the heat transfer rate.

Journal ArticleDOI
14 Jun 2021
TL;DR: In this article, the rotational position and velocity estimation method using an event camera is proposed to maximize the contrast of an image of events in a single temporal window and also maximizes the contrast image observed over time.
Abstract: Contrast maximization is an event camera application that can estimate angular velocity, depth, and optical-flow using a subset of events observed in a temporal window. In the estimation of rotational motion, we can compute the angular position by integrating the angular velocity. However, the accumulation of drift error degrades the accuracy of motion estimation. If the contrast maximization framework utilizes events measured before the temporal window, the performance of the framework will be improved, including the alleviation of drift error in motion estimation. In this work, we utilize the globally aligned event data and propose the rotational position and velocity estimation method using an event camera only. The proposed algorithm not only maximizes contrast of an image of events in a single temporal window but also maximizes the contrast image of events observed over time. Our algorithm works in real-time by reducing additional computations of the existing contrast maximization. We confirm the real-time operation with a single-core CPU on a laptop and show that the maximum error is within 3 degrees on public data sets and acquired real-world data sets. To contribute to the community, we provide the source code and the real-world data sets to the public.

Journal ArticleDOI
TL;DR: This paper addresses the trajectory tracking problem for robotic manipulators without angular velocity measurements in the presence of parameter perturbation and torque disturbance with a novel fast terminal sliding mode surface developed to ensure global strong robustness and fast error convergence.
Abstract: This paper addresses the trajectory tracking problem for robotic manipulators without angular velocity measurements in the presence of parameter perturbation and torque disturbance. A novel fast terminal sliding mode surface is developed to ensure global strong robustness and fast error convergence. Then, a high-order sliding mode observer (HOSMO) is constructed to estimate unknown joints’ angular velocities and the system lumped disturbance in a finite time. Chattering avoidance can be realized via the continuous control strategy based on super-twisting method. The finite-time arrival of sliding mode surface and fast-exponential convergence of the tracking error are strictly proved based on the Lyapunov stability theory. Finally, an example of a two-link robotic manipulator is provided. From the comparison with other control strategies, the advantages of proposed method are fully demonstrated.

Journal ArticleDOI
TL;DR: In this article, the existence of corotating and counter-rotating unequal-sized pairs of simply connected patches for Euler equations has been studied, and it has been shown that the asymptotic behavior for the angular velocity and the translating speed close to the point vortex pairs can be characterized.
Abstract: In this paper, we study the existence of co-rotating and counter-rotating unequal-sized pairs of simply connected patches for Euler equations. In particular, we prove the existence of curves of steadily co-rotating and counter-rotating asymmetric vortex pairs passing through a point vortex pairs with unequal circulations. We also provide a careful study of the asymptotic behavior for the angular velocity and the translating speed close to the point vortex pairs.

Journal ArticleDOI
TL;DR: In this paper, a frequency simulation and critical angular velocity of a size-dependent laminated rotary microsystem using modified couple stress theory (MCST) as the higher-order elasticity model is undertaken.
Abstract: In this study, frequency simulation and critical angular velocity of a size-dependent laminated rotary microsystem using modified couple stress theory (MCST) as the higher-order elasticity model is undertaken. The centrifugal and Coriolis impacts due to the spinning are taken into account. The size-dependent thick annular microsystem's computational formulation, non-classical governing equations, and corresponding boundary conditions are obtained by using the higher-order stress tensors and symmetric rotation gradient to the strain energy. By using a single material length scale factor, the most recent non-classical approach captures the size-dependency in the annular laminated microsystem. Furthermore, by ignoring the length scale element of the material, an annular microsystem’s mathematical formulation based on the classical model can be retrieved from the current model. Ultimately, the governing equations, which are non-classic, have been solved for various boundary conditions (BCs) using the two-dimensional generalized differential quadrature (2D-GDQ) approach. The effects of Young's modulus ratio the, rotating speed, radius ratio, laminated layers’ number, length scale element, and laminated types on the critical rotating speed and frequency responses of the laminated spinning microdisk are then investigated using MCST. The outcomes reveal that the negative influence from spinning velocity on the system’s dynamics is more significant than the negative influence from radius ratio, and the mentioned problem is more considerable for the vertical laminated pattern. Finally, the critical radius ratio and rotating speed increase by changing the laminated pattern from vertical to longitudinal.

Journal ArticleDOI
TL;DR: In this paper, the authors employed deep learning to estimate the frequency performance of the rotating multi-layer nanodisks and determined the optimum values of the parameters involved in the mechanism of the fully connected neural network through the momentum-based optimizer.
Abstract: This article is the first attempt to employ deep learning to estimate the frequency performance of the rotating multi-layer nanodisks. The optimum values of the parameters involved in the mechanism of the fully connected neural network are determined through the momentum-based optimizer. The strength of the method applied in this survey comes from the high accuracy besides lower epochs needed to train the multi-layered network. It should be mentioned that the current nanostructure is modeled as a nanodisk on the viscoelastic substrate. Due to rotation, the centrifugal and Coriolis effects are considered. Hamilton’s principle and generalized differential quadrature method (GDQM) are presented for obtaining and solving the governing equations of the high-speed rotating nanodisk on a viscoelastic substrate. The outcomes show that the number of layers viscoelastic foundation, angular velocity speed, angle of ply, nonlocal, and length-scale parameters have a considerable impact on the amplitude and vibration behavior of a laminated rotating cantilevered nanodisk. As an applicable result in related industries, in the initial value of radius ratio, damping of the foundation does not have any effect on the dynamics of the system, but when the outer radius is bigger enough, the effect of damping parameter on the frequency of the laminated nanostructure will be bold sharply.

Journal ArticleDOI
TL;DR: The EOF of two layers consisting of Newtonian fluid and fractional second-order fluid in a rotating frame in parallel microchannel is investigated and two interesting phenomena can be found.

Journal ArticleDOI
TL;DR: In this article, a rotating multi-hybrid nanocomposite reinforced (MHCR) cylindrical microshell covered with a piezoelectric layer as sensor and actuator (PLSA) is presented.
Abstract: In this article, critical angular velocity, critical velocity of fluid flow and vibration control analysis of a rotating multi-hybrid nanocomposite reinforced (MHCR) cylindrical microshell covered with a piezoelectric layer as sensor and actuator (PLSA) are presented. The current non-classical model is capable of capturing the size dependency in the microshells using only one material length scale parameter; moreover, the mathematical formulation of microshells based on the classical model can be recovered from the present model by neglecting the material length scale parameter. This structure is under conveying viscous fluid, and the related force is calculated by the modified formulation of Navier–Stokes. In addition, the current structure rotates around its axial direction. The Coriolis and centrifugal effects due to the rotation are considered. For semi-numerical method, the strains and stresses can be determined through via the first-order shear deformable theory (FSDT). For accessing to various mass densities, thermal expansion as well as Poisson ratio, the rule of mixture is applied, although a modified Halpin–Tsai theory is used for obtaining the module of elasticity. The external voltage is applied to the sensor layer, while a Proportional-Derivative (PD) controller has been utilized for controlling output of sensors. The boundary conditions are derived through governing equations of the MHCR cylindrical microshell using energy method known as Hamilton’s principle and finally are solved using generalized differential quadrature method (GDQM). The outcomes show that the angular velocity, velocity of fluid flow, external force, PD controller, external voltage and MHC’s weight fraction have a considerable impact on the amplitude, and vibration behavior of a spinning MHCR cylindrical shell conveying fluid flow.

Journal ArticleDOI
TL;DR: In this paper, the nonlinear dynamical motion of an unstretched two degrees of freedom double pendulum in which its pivot point follows an elliptic route with steady angular velocity was studied.
Abstract: This work looks at the nonlinear dynamical motion of an unstretched two degrees of freedom double pendulum in which its pivot point follows an elliptic route with steady angular velocity. These pendulums have different lengths and are attached with different masses. Lagrange’s equations are employed to derive the governing kinematic system of motion. The multiple scales technique is utilized to find the desired approximate solutions up to the third order of approximation. Resonance cases have been classified, and modulation equations are formulated. Solvability requirements for the steady-state solutions are specified. The obtained solutions and resonance curves are represented graphically. The nonlinear stability approach is used to check the impact of the various parameters on the dynamical motion. The comparison between the attained analytic solutions and the numerical ones reveals a high degree of consistency between them and reflects an excellent accuracy of the used approach. The importance of the mentioned model points to its applications in a wide range of fields such as ships motion, swaying buildings, transportation devices and rotor dynamics.

Journal ArticleDOI
TL;DR: Liutex was proposed as a vector indicator of vortex in this article, where the direction of Liutex represents the swirling axis and the magnitude of L 2 is defined as twice the angular speed of rotation.

Journal ArticleDOI
W.S. Amer1
TL;DR: In this article, the rotational motion of a symmetric gyrostat around a fixed point under the effectiveness of both a magnetic field and a Newtonian one besides the action of a gyrostatic moment around the principal inertia's axes is analyzed.
Abstract: This article sheds light on the rotatory motion of a symmetric gyrostat around a fixed point under the effectiveness of both a magnetic field and a Newtonian one besides the action of a gyrostatic moment around the principal inertia’s axes. The gyrostat is assumed to have initially high angular velocity around the principal axis of dynamic symmetry. The controlling system of motion and its first integrals are significantly decreased to a new autonomous system and only one first integral. Poincare’s method of a small parameter is utilized to achieve the asymptotic solutions of the controlling system. Euler’s angles are evaluated to perceive the motion at every blink. The achieved solutions are graphically portrayed through certain plots for various values of the charge causing the magnetic field and gyrostatic projection's values to estimate the output of these values on the gyrostatic motion. Moreover, the graphs of phase planes for these solutions are sketched to provide a complete explanation of the stability of considered motion. Many applications such as submarines, aircraft, and satellites, are of great interest to the topic concerned.

Journal ArticleDOI
TL;DR: In this article, the photonic vortical effect, i.e., the difference of the flows of left and right-handed photons along the vector of angular velocity in rotating photonic medium, is considered.
Abstract: We consider the photonic vortical effect, i.e., the difference of the flows of left- and right-handed photons along the vector of angular velocity in rotating photonic medium. Two alternative frameworks to evaluate the effect are considered, both of which have already been tried in the literature: first, the standard thermal field theory and, alternatively, Hawking-radiation-type derivation. In our earlier attempt to compare the two approaches, we found a crucial factor of 2 difference. Here, we revisit the problem, paying more attention to details of infrared regularizations. We find out that introduction of an infinitesimal mass of the vector field brings the two ways of evaluating the chiral vortical effect into agreement with each other. Some implications, on both the theoretical and phenomenological sides, are mentioned.

Journal ArticleDOI
TL;DR: In this article, the authors explored the general rotatory 3D motion of a magnetic heavy solid body around one fixed point under the impact of a gyrostatic moment when the body awarded initially high angular velocity about one of its inertia principal axes.
Abstract: This paper attempts to explore the general rotatory 3D motion of a magnetic heavy solid body around one fixed point under the impact of a gyrostatic moment when the body awarded initially high angular velocity about one of its inertia principal axes. The asymptotic technique of Krylov-Bogoliubov-Mitropolski and its adjustment are applied to achieve new asymptotic periodic solutions of the controlling equations of motion. Discussion of these solutions is presented taking into consideration their graphs representations. The graphical depictions of such solutions and their corresponding phase planes are plotted to give an induction about its behaviour during the interval time of motion and to reveal the good effect of the different applied forces and moments on the body's motion. The application of the achieved results of the present work can be widely found in gyroscopic devices especially that used inertia reference systems like in satellites, airplanes, and missiles. Moreover, for devices that are responsible for the stability of motion for these applications.

Journal ArticleDOI
TL;DR: A nonlinear model predictive control law accounting for nonlinear dynamics and system constraints is proposed to achieve this control goal by actively regulating the changing rate of the bounded tether current.

Journal ArticleDOI
TL;DR: In this paper, a complex dynamic model of cylindrical roller bearings with consideration of surface texture is developed and verified by simulations and experiments about the relationship between wave numbers and vibration responses.