Angular Dynamics Research Articles

Angular dynamics of small nanoparticles induced by non-vortex electron beams

In this work, we present a theoretical study of the angular dynamics of small nanoparticles induced by fast non-vortex electron beams. General expressions for the torque and the angular momentum transferred from an electron to an arbitrary—but small—nanoparticle are obtained using a full-retarded classical electrodynamics approach, within the small particle limit. We applied this methodology to study a particular case of interest: the angular dynamics of spherical nanoparticles with homogeneous and isotropic electromagnetic responses. We analytically calculate the total angular momentum transferred from a swift electron to such nanoparticles, finding that it is electric in nature and it is always in a direction determined by the electron trajectory relative to the center of the nanoparticle. We realize that it is possible to represent the angular momentum transferred as the product of two functions: the extinction cross-section of the nanoparticle and a function that only contains information about the swift electron. We present numerical results for the total angular momentum transferred from a swift electron to an aluminum and a gold nanoparticle. We also present an analysis of the temporal behavior of the torque and the electric dipole moment induced within the nanoparticle by the swift electron. We compare the angular momentum transfer calculated in this work with a previously reported case of vortex beams, finding that, for both aluminum and gold nanoparticles, our results are two orders of magnitude smaller. Finally, we consider a particular case of a frictionless gold spherical nanoparticle of radius a=5nm, obtaining that it can spin with an angular frequency up to 29.3Hz.

Synthesis of control of the aircraft angular velocities based on algorithm with a predictive model

An urgent issue is to obtain optimal control laws for nonlinear dynamic objects. The article presents a numerical algorithm to control stabilization of the angular velocities of spacecraft with various axial moments of inertia based on optimization with respect to the Krasovsky functional using the predictive model method. The simulation results are presented. The character of the curves of angular velocity dynamics and control moments obtained in the simulation corresponds to the curves of angular velocity dynamics and control moments obtained in the simulation of control using the analytical law for an axisymmetric spacecraft, which confirms the adequacy of the synthesized algorithm.

Spin and orbital angular momentum dynamics in counterpropagating vectorially structured light

It is well-known that electric spin angular momentum and electric orbital angular momentum are conserved under paraxial propagation of travelling waves in free-space. Here we study the electric and magnetic angular momentum in counter-propagating waves and show both theoretically and experimentally that neither component alone is conserved except in special cases. We attribute this non-conservation to spin-spin and orbit-orbit coupling between the electric and magnetic fields. This work generalises previous findings based on travelling waves, explains the apparent spin-orbit coupling in counter-propagating paraxial light, and broadens our understanding of angular momentum conservation in arbitrary structured light waves.

Isomeric cross section ratios data as a test for codes descriptive of nuclear reactions

Investigations of isomeric cross-section ratios of the reactions 187Re(a,n)190mgIr, 194Pt(a,n)197mgHg and 41K(a,n)44mgSc in the energy range 18 – 32 MeV are carried out using off-beam measurements of induced activity of members of the isomeric pair. Analysis of the obtained ICSR data is performed using the codes EMPIRE-3 and TALYS. The reliability of these advanced data-containing codes is analyzed. The results of the measurements of the isomeric cross section ratios are proved to be a promising test of the codes and their capability to reproduce angular momentum dynamics of the discussed and related reactions.

Acceleration tracking control for a spinning glide guided projectile with multiple disturbances

A novel acceleration tracking controller is proposed in this paper, for a Spinning Glide Guided Projectile (SGGP) subject to cross-coupling dynamics, external disturbances, and parametric uncertainties. The cross-coupled dynamics for the SGGP are formulated with mismatched and matched uncertainties, and then divided into acceleration and angular rate subsystems via the hierarchical principle. By exploiting the structural property of the SGGP, model-assisted Extended State Observers (ESOs) are designed to estimate online the lumped disturbances in the acceleration and angular rate dynamics. To achieve a rapid response and a strong robustness, integral sliding mode control laws and sigmoid-function-based tracking differentiators are integrated into the ESO-based Trajectory Linearization Control (TLC) framework. It is proven that the acceleration tracking controller can guarantee the ultimate boundedness of the signals in the closed-loop system and make the tracking errors arbitrarily small. The superiority and effectiveness of the proposed control scheme in its decoupling ability, accurate acceleration tracking performance and anti-disturbance capability are validated through comparisons and extensive simulations.

Theory of Current-Induced Angular Momentum Transfer Dynamics in Spin-Orbit Coupled Systems.

Motivated by the importance of understanding various competing mechanisms to the current-induced spin-orbit torque on magnetization in complex magnets, we develop a theory of current-induced spin-orbital coupled dynamics in magnetic heterostructures. The theory describes angular momentum transfer between different degrees of freedom in solids, e.g., the electron orbital and spin, the crystal lattice, and the magnetic order parameter. Based on the continuity equations for the spin and orbital angular momenta, we derive equations of motion that relate spin and orbital current fluxes and torques describing the transfer of angular momentum between different degrees of freedom, achieved in a steady state under an applied external electric field. We then propose a classification scheme for the mechanisms of the current-induced torque in magnetic bilayers. We evaluate the sources of torque using density functional theory, effectively capturing the impact of the electronic structure on these quantities. We apply our formalism to two different magnetic bilayers, Fe/W(110) and Ni/W(110), which are chosen such that the orbital and spin Hall effects in W have opposite sign and the resulting spin- and orbital-mediated torques can compete with each other. We find that while the spin torque arising from the spin Hall effect of W is the dominant mechanism of the current-induced torque in Fe/W(110), the dominant mechanism in Ni/W(110) is the orbital torque originating in the orbital Hall effect of the non-magnetic substrate. Thus the effective spin Hall angles for the total torque are negative and positive in the two systems. Our prediction can be experimentally identified in moderately clean samples, where intrinsic contributions dominate. This clearly demonstrates that our formalism is ideal for studying the angular momentum transfer dynamics in spin-orbit coupled systems as it goes beyond the "spin current picture" by naturally incorporating the spin and orbital degrees of freedom on an equal footing. Our calculations reveal that, in addition to the spin and orbital torque, other contributions such as the interfacial torque and self-induced anomalous torque within the ferromagnet are not negligible in both material systems.

Orbital angular momentum dynamics of Bose-Einstein condensates trapped in two stacked rings

We investigate the stability and dynamics of the orbital angular momentum modes of a repulsive Bose-Einstein condensate trapped in two tunnel-coupled rings in a stack configuration. Within mean-field theory, we derive a two-state model for the system in the case in which we populate equally both rings with a single orbital angular momentum mode and include small perturbations in other modes. Analyzing the fixed point solutions of the model and the associated classical Hamiltonian, we characterize the destabilization of the stationary states and the subsequent dynamics. By populating a single orbital angular momentum mode with an arbitrary population imbalance between the rings, we derive analytically the boundary between the regimes of Josephson oscillations and macroscopic quantum self-trapping and study numerically the stability of these solutions.

Fast finite-time backstepping for helicopters under input constraints and perturbations

This work addresses the issue of trajectory tracking of helicopters under disturbances and input constraints via the proposed fast finite-time backstepping framework. Backstepping with the property of fast finite-time convergence exhibits fast transient convergence both at a distance from and at a close range of the equilibrium. Moreover, finite-time disturbance observers based on multivariable super-twisting are employed to counteract the effect of perturbations. Aiming at the adverse effect of input saturation, a novel auxiliary system is developed to avoid the singularity by transforming auxiliary variables for three times. In addition, the framework is also applied into helicopter control problem, in which thrust magnitude and thrust direction are used as intermediate control variables, connecting external translational dynamics and internal angular dynamics. A rigorous proof of finite-time stability of the closed-loop system is derived from Lyapunov theory. Finally, the effectiveness and superiority of the proposed framework are verified by comparative simulation.

Rotation of anisotropic particles in Rayleigh–Bénard turbulence

Abstract

Jeffery orbits for an object with discrete rotational symmetry

We theoretically investigate the motions of an object immersed in a background flow at a low Reynolds number, generalizing the Jeffery equation for the angular dynamics to the case of an object with n-fold rotational symmetry (n ≥ 3). We demonstrate that when n ≥ 4, the dynamics are identical to those of a helicoidal object for which two parameters related to the shape of the object, namely, the Bretherton constant and a chirality parameter, determine the dynamics. When n = 3, however, we find that the equations require a new parameter that is related to the shape and represents the strength of triangularity. On the basis of detailed symmetry arguments, we show theoretically that microscopic objects can be categorized into a small number of classes that exhibit different dynamics in a background flow. We perform further analyses of the angular dynamics in a simple shear flow, and we find that the presence of triangularity can lead to chaotic angular dynamics, although the dynamics typically possess stable periodic orbits, as further demonstrated by an example of a triangular object. Our findings provide a comprehensive viewpoint concerning the dynamics of an object in a flow, emphasizing the notable simplification of the dynamics resulting from the symmetry of the object’s shape, and they will be useful in studies of fluid–structure interactions at a low Reynolds number.

Modelling of inter‐area angular dynamics and proactive defence strategy in deregulated power grids with large‐scale integration of renewable energy sources

Power grid restructuring together with the integration of inertia less uncertain renewable generation, has resulted in depletion of inherent primary frequency response in the grid. Characterisation of inter-area dynamics under uncertain generation and requisite reserve deployment strategies are not very well dealt with in the literature. Uncertainties in deregulated market demand proactive defence strategies to ensure stable and reliable power to consumers. This work depicts the inter-area oscillation dynamics and proposes a proactive reserve deployment strategy based on probabilistic forecast error modelling. The model of oscillatory dynamics of deregulated power grids is established based on forecast error. The developed model could deliver better insight to wide-area angular dynamics of the power grid. Reserve index developed on prior knowledge of this angular dynamics and probabilistic renewable generation serves as a key input to proposed proactive reserve deployment strategy defending the probable angular oscillations. WSCC 9-bus system and IEEE 39-bus system are adopted to analyse inter-area angular dynamics as well as validate proposed proactive defence strategies in maintaining the reliable and secure operation of a deregulated grid.

Tracking Performance of Model-Based Thruster Control of a Remotely Operated Underwater Vehicle

This article compares output feedback control strategies for an underwater thruster. There are a variety of dynamic models for thrusters, some of which can account for fluid-velocity dynamics and others that account for propeller angular velocity dynamics. Here, the contributions of both fluid and propeller velocities are modeled with three levels of complexity: simplified, hydrodynamic linear, and hydrodynamic quadratic models. Multiple methods are presented to estimate axial flow velocity, which is handled as an unmeasured state. The performance of controllers based on these models and estimators is compared for a single thruster as well as for an underwater vehicle with a nonorthogonal multithruster layout. All models, controllers, and estimators are experimentally evaluated in closed-loop experiments using a load cell to measure the tracking performance of an individual thruster. Full vehicle simulations using experimentally characterized models provide additional insights into the control and estimation strategies and their relative merits.

Robust Tuning of Geometric Attitude Controllers for Multirotor Unmanned Aerial Vehicles

In recent years there has been a significant body of literature proposing nonlinear attitude control laws for small-scale multirotor unmanned aerial vehicles (UAVs), motivated by the high maneuverability of these platforms. While tracking trajectories characterized by fast and large attitude changes makes the control problem intrinsically nonlinear, most of the works proposing nonlinear designs is concerned with establishing their stabilizing properties, often deduced by referring to simplified dynamic models, but limited attention has been devoted to performance. As a consequence, less satisfactory results than expected are typically achieved in experiments and the controller gains must be adjusted with trial-and-error procedures to obtain good performance. This paper proposes a model-based tuning method that exploits the cascade structure of the attitude dynamics and that needs only single-axis identified linear models of the angular velocity dynamics to be applied. The tuning of the controller gains is carried out on the linearized closed-loop system with structured synthesis that allows one to enforce robustness against model uncertainty in a systematic way and to achieve a desired level of performance in nominal conditions. The approach is validated by tuning the gains of a novel Proportional/Proportional Integral Derivative (P/PID)-like cascade, which has been developed in the framework of geometric control theory. A thorough analytical comparison of the proposed design with a geometric Proportional Integral (PI)-like controller borrowed from the literature is complemented with experiments conducted on a small quadrotor UAV.

Design Parameters Selection for CubeSat Nanosatellite with a Passive Stabilization System

Probabilistic study of angular motion dynamics has been performed for CubeSat nanosatellites with passive stabilization systems, including aerodynamic, aerodynamic-gravitational, gravitational, and gravitational-aerodynamic ones. Analytical functions of the maximum angle values distribution have been obtained for a nanosatellite axes deviation from required directions (orbital velocity vector or a local vertical) for uniform distribution and Rayleigh distribution of component values of the initial angular velocity vector. Formulas have been derived and nomograms have been plotted for selecting the design parameters (geometrical dimensions, static stability margin, moments of inertia) which ensure the required attitude with the specified probability in circular orbits.

Helicoidal particles and swimmers in a flow at low Reynolds number

In this paper, we consider the dynamics of a helicoidal object, which can be either a passive particle or an active swimmer, with an arbitrary shape in a linear background flow at low Reynolds number, and derive a generalized version of the Jeffery equations for the angular dynamics of the object, including a new constant from the chirality of the object as well as the Bretherton constant. The new constant appears from the inhomogeneous chirality distribution along the axis of the helicoidal symmetry, whereas the overall chirality of the object contributes to the drift velocity. Further investigations are made for an object in a simple shear flow, and it is found that the chirality effects generate non-closed trajectories of the director vector which will be stably directed parallel or anti-parallel to the background vorticity vector depending on the sign of the chirality. A bacterial swimmer is considered as an example of a helicoidal object, and we calculate the values of the constants in the generalized Jeffery equations for a typical morphology of Escherichia coli. Our results provide useful expressions for the studies of microparticles and biological fluids, and emphasize the significance of the symmetry of an object on its motion at low Reynolds number.

Whole-Body Dynamic Analysis of Challenging Slackline Jumping

Maintaining balance on a slackline is a challenging task in itself. Walking on a high line, jumping and performing twists or somersaults seems nearly impossible. Contact forces are essential to understanding how humans maintain balance in such challenging situations, but they cannot always be measured directly. Therefore, we propose a contact model for slackline balancing that includes the interaction forces and torques as well as the position of the Center of Pressure. We apply this model within an optimization framework to perform a fully dynamic motion reconstruction of a jump with a rotation of approximately 180 ° . Newton’s equations of motions are implemented as constraints to the optimization, hence the optimized motion is physically feasible. We show that a conventional kinematic analysis results in dynamic inconsistencies. The advantage of our method becomes apparent during the flight phase of the motion and when comparing the center of mass and angular momentum dynamics. With our motion reconstruction method all momentum is conserved, whereas the conventional analysis shows momentum changes of up to 30%. Furthermore, we get additional and reliable information on the interaction forces and the joint torque that allow us to further analyze slackline balancing strategies.

High-energy 2 µm pulsed vortex beam excitation from a Q-switched Tm:LuYAG laser.

We report on the first, to the best of our knowledge, direct generation of pulsed vortex beams at 2 µm from a ${ Q}$Q-switched Tm:LuYAG laser. High-energy Laguerre-Gaussian (${{\rm LG}_{0,l}}$LG0,l) pulsed laser beams with well-defined handedness are selectively excited through spatially matched pump gain distribution and asymmetric cavity loss without using any intracavity handedness-selective optical elements. Pulse energies of 1.48 mJ for the ${{\rm LG}_{0, + 1}}$LG0,+1 mode and 1.51 mJ for the ${{\rm LG}_{0, - 1}}$LG0,-1 mode, respectively, are achieved at a repetition rate of 500 Hz. The pulsed laser beams with helical wavefronts are potentially useful for studying orbital angular momentum transformation dynamics, generation of mid-IR vortex beams, and nanostructuring of organic materials.

A flatness-based predictive controller for six-degrees of freedom spacecraft rendezvous

This work presents a closed-loop guidance algorithm for six-degrees of freedom spacecraft rendezvous with a passive target flying in an eccentric orbit. The main assumption is that the chaser vehicle has an attitude control system, based on reaction wheels, providing the necessary torque to change its orientation whereas the number of thrusters is arbitrary. The goal is to design fuel optimal maneuvers while satisfying operational constraints and rejecting disturbances. The proposed method is as follows; first, the coupled translational and angular dynamics are transformed to equivalent algebraic relations using the relative translational states transition matrix and the attitude flatness property. Then, a direct transcription method, based on B-splines parameterization and discretization of time continuous constraints, is developed to obtain a tractable static program. Finally, a Model Predictive Controller, based on linearization around the previously computed solution, is considered to handle disturbances. Numerical results are shown and discussed.

Modeling the Angular Motion Dynamics of Small Spacecraft with a Magnetic Attitude Control System in a Three-Axis Stabilization Mode

The problem of modeling the attitude control modes of small spacecraft using electromagnetic systems interacting with the Earth’s magnetic field is considered. A mathematical model for the angular motion dynamics of small spacecraft has been developed. The control law for linear magnetic attitude control systems of small spacecraft is formulated. The results of our numerical modeling of the motion of a satellite with a magnetic attitude control system are presented.

Tomographic Dynamics and Scale-Dependent Viscosity in 2D Electron Systems.

Fermi gases in two dimensions display collective dynamics originating from head-on collisions, a collinear carrier scattering process that dominates angular relaxation at not-too-high temperatures T≪T_{F}. In this regime, a large family of excitations emerges, with an odd-parity angular structure of momentum distribution and exceptionally long lifetimes. This leads to "tomographic" dynamics: fast 1D spatial diffusion along the unchanging velocity direction accompanied by a slow angular dynamics that gradually randomizes velocity orientation. The tomographic regime features an unusual hierarchy of timescales and scale-dependent transport coefficients with nontrivial fractional scaling dimensions, leading to fractional-power current flow profiles and unusual conductance scaling versus sample width.