Angular Dynamics Research Articles

Internal Model‐Based Anti‐Disturbances Low‐Level Control for Drones Considering Actuator Dynamics

ABSTRACTLow‐level control plays a critical role in the overall flight performance of drones. Despite some progress, existing methods do not adequately consider the complex electromechanical characteristics of actuators and aerodynamic disturbances of propellers, which deteriorates low‐level control performance. To tackle these issues, we propose a new nonlinear low‐level controller for higher precision control. First, a high‐precision low‐level model that integrates the actuator dynamics and angular velocity dynamics is presented. Based on this model, a dynamic compensator is designed using the internal model method to handle aerodynamic disturbances. Next, a high‐gain observer is designed to estimate the actuator states without adding new sensors, and an observer‐based low‐level controller is proposed through a recursive design process. Finally, the local asymptotic stability of the closed‐loop system is analyzed. The effectiveness and superiority of the proposed method are validated through simulations and physical experiments.

Angular dynamics of molecular bodies

Angular dynamics of molecular bodies

Exploring waveforms with non-GR deviations for extreme mass-ratio inspirals

The fundamental process of detecting and examining the polarization modes of gravitational waves plays a pivotal role in enhancing our grasp on the precise mechanisms behind their generation. A thorough investigation is essential for delving deeper into the essence of gravitational waves and rigorously evaluating and validating the range of modified gravity theories. In this line of interest, a general description of black holes in theories beyond general relativity can serve a meaningful purpose where distinct deviation parameters can be mapped to solutions representing distinct theories. Employing a refined version of the deformed Kerr geometry, which is free from pathological behaviours such as unphysical divergences in the metric, we explore an extreme mass-ratio inspiral system, wherein a stellar-mass object perturbs a supermassive black hole. We compute the effects of deformation parameters on the rate of change of orbital energy and angular momentum, orbital evolution and phase dynamics with leading order post-Newtonian corrections. With the waveform analysis, we assess the plausibility of detecting deviations from general relativity through observations facilitated by the Laser Interferometer Space Antenna (LISA), simultaneously constraining the extent of these deviations. Therefore, this analysis provides an understanding while highlighting the essential role of observations in advancing gravitational phenomena beyond general relativity.

Exploring run-and-tumble movement in confined settings through simulation.

Motion in bounded domains is a fundamental concept in various fields, including billiard dynamics and random walks on finite lattices, and has important applications in physics, ecology, and biology. An important universal property related to the average return time to the boundary, the Mean Path Length Theorem (MPLT), has been proposed theoretically and experimentally confirmed in various contexts. We investigated a wide range of mechanisms that lead to deviations from this universal behavior, such as boundary effects, reorientation, and memory processes. This study investigates the dynamics of run-and-tumble particles within a confined two-dimensional circular domain. Through a combination of theoretical approaches and numerical simulations, we validate the MPLT under uniform and isotropic particle inflow conditions. This research demonstrates that although the MPLT is generally applicable for different step length distributions, deviations occur for non-uniform angular distributions, non-elastic boundary conditions, or memory processes. These results underline the crucial influence of boundary interactions and angular dynamics on the behavior of particles in confined spaces. Our results provide new insights into the geometry and dynamics of motion in confined spaces and contribute to a better understanding of a broad spectrum of phenomena ranging from the motion of bacteria to neutron transport. This type of analysis is crucial in situations where inhomogeneity occurs, such as multiple real-world scenarios within a limited domain.

Self-aligning active agents with inertia and active torque.

We extend the study of the inertial effects on the two-dimensional dynamics of active agents to the case where self-alignment is present. In contrast with the most common models of active particles, we find that self-alignment, which couples the rotational dynamics to the translational one, produces unexpected and nontrivial dynamics, already at the deterministic level. Examining first the motion of a free particle, we contrast the role of inertia depending on the sign of the self-aligning torque. When positive, inertia does not alter the steady-state linear motion of an a-chiral self-propelled particle. On the contrary, for a negative self-aligning torque, inertia leads to the destabilization of the linear motion into a spontaneously broken chiral symmetry orbiting dynamics. Adding an active torque, or bias, to the angular dynamics, the bifurcation becomes imperfect in favor of the chiral orientation selected by the bias. In the case of a positive self-alignment, the interplay of the active torque and inertia leads to the emergence, out of a saddle-node bifurcation, of solutions which coexist with the simply biased linear motion. In the context of a free particle, the rotational inertia leaves unchanged the families of steady-state solutions but sets their stability properties. The situation is radically different when considering the case of a collision with a wall, where a very singular oscillating dynamics takes place which can only be captured if both translational and rotational inertia are present.

Effect of slip-induced fluid inertial torque on the angular dynamics of spheroids in a linear shear flow

The angular dynamics of tiny spheroidal particles in shear flows have been widely investigated, but most of the studies mainly focus on the effect of strong shear, while the combined effect of both shear and slip velocity at the center of the particle has been less considered. Actually, the fluid inertial torque induced by the slip velocity between particle and fluid plays a significant role in spheroid angular dynamics. However, it is difficult to investigate these dynamics theoretically until the analytical expression of the fluid inertial torque at a small Reynolds number was derived by Dabade et al. [J. Fluid Mech. 778, 133–188 (2015)]. In this study, the effect of the fluid inertial torque on the particle rotations is considered in a linear shear flow with a small streamwise slip velocity at the center of the particle. We find that as the fluid inertial torque dominates, the prolate spheroids tend to logroll while oblate ones have a tendency to tumble or align to a direction with a relative angle to the streamwise direction. These results are opposite to the earlier results in the absence of the fluid inertial torque. Different ultimate rotation modes of spheroids are dependent on the relative importance between the fluid inertial torque and the particle inertia, as well as the initial orientations. This reflects a non-trivial effect of fluid inertial torque on the angular dynamics of inertial spheroidal particles.

Ultrafast Chiral Precession of Spin and Orbital Angular Momentum Induced by Circularly Polarized Laser Pulse in Elementary Ferromagnets.

Despite spin (SAM) and orbital (OAM) angular momentum dynamics being well-studied in demagnetization processes, their components receive less focus. Here, we utilize real-time time-dependent density functional theory (rt-TDDFT) to unveil significant x and y components of SAM and OAM induced by circularly left (σ+) and right (σ-) polarized laser pulses in ferromagnetic Fe, Co, and Ni. Our results show that the magnitude of the OAM is an order of magnitude larger than that of the SAM, highlighting a stronger optical response from the orbital degrees of freedom of electrons. Intriguingly, σ+ and σ- pulses induce chirality in the precession of SAM and OAM, respectively, with clear associations with laser frequency and duration. Finally, we demonstrate the time scale of the OAM and SAM precession occurs even earlier than that of the demagnetization process and the OISTR effect. Our results provide detailed insight into the dynamics of SAM and OAM during and shortly after a polarized laser pulse.

Confined chaos and the chaotic angular motion of Atlas, a Saturn’s inner satellite

ABSTRACT The dynamics of the Solar system exhibit inherent chaos and instability. Mathematical tools, such as the maximum Lyapunov characteristic exponent (LCE) and Lyapunov time (TL), play a crucial role in providing a qualitative understanding of chaos within celestial objects, such as asteroids and moonlets. Celestial bodies with relatively small Lyapunov times have garnered significant research interest due to their stable orbits, a phenomenon referred to as stable or confined chaos. Notable examples include Saturn’s satellites: Atlas, with a Lyapunov time on the order of 10 yr, Prometheus, and Pandora. This work aims to study the chaotic behaviour of the Atlas satellite and its relatively small TL. We present a three-dimensional model approach designed to isolate the radial contribution from the LCE and assess its influence within the LCE. Our investigation focuses on the Saturn system, comprising Saturn itself, along with its satellites Atlas, Prometheus, Pandora, and Mimas. To estimate the radial contribution of the LCE, we find the projection of the radial vector of a ghost Atlas (a slightly displaced Atlas) onto the Atlas radial vector, which allows us to calculate the difference between the radial vectors. This methodology enables us to estimate the radial contribution of the LCE and calculate the Lyapunov time. Remarkably, our results demonstrate that orbits remain confined even for integration times exceeding TL. Furthermore, we investigate the temporal behaviour of Atlas’ angular position in its orbit, potentially shedding light on chaotic angular dynamics.

Generalised Jeffery's equations for rapidly spinning particles. Part 2. Helicoidal objects with chirality

In this two-part study, we investigate the motion of rigid, active objects in shear Stokes flow, focusing on bodies that induce rapid rotation as part of their activity. In Part 2, we derive and analyse governing equations for rapidly spinning complex-shaped particles – general helicoidal objects with chirality. Using the multiscale framework that we develop in Part 1 (Dalwadi et al., J. Fluid Mech., vol. 979, 2024, A1), we systematically derive emergent equations of motion for the angular and translational dynamics of these chiral spinning objects. We show that the emergent dynamics due to rapid rotation can be described by effective generalised Jeffery's equations, which differ from the classic versions via the inclusion of additional terms that account for chirality and other asymmetries. Furthermore, we use our analytic results to characterise and quantify the explicit effect of rotation on the effective hydrodynamic shape of the chiral objects, expanding significantly the scope of Jeffery's seminal study.

Dynamics of freely falling perforated disks

The dynamics of free-falling perforated disks within the moderate Reynolds number Rem regime (700<Rem<1400) are experimentally investigated in this paper, including translation and rotation dynamics. Four falling styles are analyzed, including spiral motion, Hula-Hoop motion, helical precession motion and spiral irregular motion. In contrast to spiral irregular motion, we group the other three motions as regular motions. The relative contribution of different dynamical effects (impulsive effect, Magnus effect and viscous effect respectively) is quantitatively determined. The contribution of impulsive effect is commonly ignorable during the descent, and Magnus effect plays a crucial role in horizontal oscillations. Vortex loads always dominate this dynamical process, and balance the gravity along the vertical direction. In the Frenet–Serret coordinate system, the contribution resulting from Magnus effect is relatively small to that of vorticity-induced fluid force. Hence, an alternative way to model this involved system is presented, which is based on the extended Kelvin-Kirchhoff equations. A Fast Fourier Transform (FFT) is performed on total hydrodynamics forces FHx and FHy. For regular motions with the dimensionless inertia ratio I∗≤1×10−3, sub-harmonic force components are identified in the frequency domain. However, the frequency ratio of high-frequency components and the dominant peak is no longer integer in spiral irregular motion. The azimuth distribution of angular velocity is counted in the Frenet–Serret coordinate system. For spiral irregular motion with the dimensionless inertia ratio I∗>1×10−3, no preferential alignment is observed and its distribution scatters, while those of regular motions are rather concentrated. The probability density functions (PDFs) of angular velocity components in spiral and Hula-Hoop motions share similar distributions, which indicates angular dynamics may decouple from translation dynamics in high Reynolds number regime under certain circumstances.

Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems

Geometric singular perturbation theory provides a powerful mathematical framework for the analysis of ‘stationary’ multiple time-scale systems which possess a critical manifold, i.e. a smooth manifold of steady states for the limiting fast subsystem, particularly when combined with a method of desingularisation known as blow-up. The theory for ‘oscillatory’ multiple time-scale systems which possess a limit cycle manifold instead of (or in addition to) a critical manifold is less developed, particularly in the non-normally hyperbolic regime. We use the blow-up method to analyse the global oscillatory transition near a regular folded limit cycle manifold in a class of three time-scale ‘semi-oscillatory’ systems with two small parameters. The systems considered behave like oscillatory systems as the smallest perturbation parameter tends to zero, and stationary systems as both perturbation parameters tend to zero. The additional time-scale structure is crucial for the applicability of the blow-up method, which cannot be applied directly to the two time-scale oscillatory counterpart of the problem. Our methods allow us to describe the asymptotics and strong contractivity of all solutions which traverse a neighbourhood of the global singularity. Our main results cover a range of different cases with respect to the relative time-scale of the angular dynamics and the parameter drift. We demonstrate the applicability of our results for systems with periodic forcing in the slow equation, in particular for a class of Liénard equations. Finally, we consider a toy model used to study tipping phenomena in climate systems with periodic forcing in the fast equation, which violates the conditions of our main results, in order to demonstrate the applicability of classical (two time-scale) theory for problems of this kind.

Regimes of Angular Dynamics and Spin Formation of the C59Fe Molecule

Regimes of Angular Dynamics and Spin Formation of the C59Fe Molecule

DEVELOPMENT OF A METHOD FOR CALCULATING LOADS ON IMPLANTS AND PROSTHESES USED FOR THE HUMAN SKELETON

The study proposes a novel computational approach for customizing sustainable knee disarticulation prostheses, aimed at improving the quality of life for users. A specialized calculation technique for assessing the loads and moments on the prosthesis was formulated, leveraging MATLAB for solving kinematic equations, Solidworks for motion analysis, and ANSYS Workbench for material and static analysis. The integration of these tools enabled the validation of the design and analytical outcomes. The kinematic solutions accounted for individual and prosthesis weights, analyzing linear and angular dynamics over a motion range pertinent to the prosthetic leg's function. Static analysis was executed to determine maximum force impact on the prosthesis. The study's results were conducive to identifying the most suitable prosthesis characteristics for individuals aged 20 to 80, with a height of 160-190 cm and a weight of 80-120 kg. The prosthetic design promoted ease of movement in activities requiring a range of motion, such as running and jumping. The prosthesis adapted swiftly to body movements, achieving readiness in approximately three seconds. The research underscores the importance of interdisciplinary collaboration between engineers and medical professionals to optimize the anatomical and kinematic aspects of prosthesis design.

Robust gain-scheduled missile autopilot design based on multifrequency extended state observers

This paper describes the design and implementation of a three-axis acceleration control autopilot for an asymmetric tail-controlled, skid-to-turn tactical missile. In an earlier flight test, degraded autopilot performance was attributed to multiple disturbances and uncertainties and the presence of hidden coupling terms, giving rise to a miss distance of greater than 20 m. To address these issues, the missile dynamics are decomposed into the angular rate dynamics as fast and the acceleration dynamics as slow subsystem using the singular perturbation theory to analyze a multi-time-scale property. Multifrequency extended state observers are then incorporated into the gain scheduling technique to attenuate disturbances, thus enhancing the control performance significantly. In the proposed engineering/practical design framework for missile autopilot, simple, conventional, and explicit tuning rules are provided. And the proposed control scheme can achieve input-to-state stability across the entire flight envelope under unknown but bounded disturbances. The advantages of the method over existing benchmark approaches are shown through nonlinear numerical simulations. This is supported by evidence from a new flight test result with a miss distance of only 2 m.

Spin current driven by ultrafast magnetization of FeRh

Laser-induced ultrafast demagnetization is an important phenomenon that probes arguably the ultimate limits of the angular momentum dynamics in solid. Unfortunately, many aspects of the dynamics remain unclear except that the demagnetization transfers the angular momentum eventually to the lattice. In particular, the role and origin of electron-carried spin currents in the demagnetization process are debated. Here we experimentally probe the spin current in the opposite phenomenon, i.e., laser-induced ultrafast magnetization of FeRh, where the laser pump pulse initiates the angular momentum build-up rather than its dissipation. Using the time-resolved magneto-optical Kerr effect, we directly measure the ultrafast-magnetization-driven spin current in a FeRh/Cu heterostructure. A strong correlation between the spin current and the magnetization dynamics of FeRh is found even though the spin filter effect is negligible in this opposite process. This result implies that the angular momentum build-up is achieved by an angular momentum transfer from the electron bath (supplier) to the magnon bath (receiver) and followed by the spatial transport of angular momentum (spin current) and dissipation of angular momentum to the phonon bath (spin relaxation).

Low-level control with actuator dynamics for multirotor UAVs

PurposeA low-level controller is critical to the overall performance of multirotor unmanned aerial vehicles. The purpose of this paper is to propose a nonlinear low-level angular velocity controller for multirotor unmanned aerial vehicles in various operating conditions (e.g. different speed and different mode).Design/methodology/approachTo tackle the above challenge, the authors have designed a nonlinear low-level controller taking the actuator dynamics into account. The authors first build the actuator subsystem by combining the actuator dynamics with the angular velocity dynamics model. Then, a recursive low-level controller is developed by designing a high-gain observer to estimate unmeasurable states. Furthermore, a detailed stability analysis is given with the Lyapunov theory.FindingsSimulation tests and real-world flying experiments are provided to validate the proposed approach. In particular, we illustrate the performance of the proposed controller using violent random command test, attitude mode flight and high-speed flight of up to 18.7 m/s in real world. Compared with the classical method used in PX4 autopilot and the estimation-based incremental nonlinear dynamic inversion method, experimental results show that the proposed method can further reduce the control error.Research limitations/implicationsLow-level control of multirotor UAVs is challenging due to the complex dynamic characteristics of UAVs and the diversity of tasks. Although some progress has been made, the performance of existing methods will deteriorate as operating conditions change due to the disregard for the electromechanical characteristics of the actuator.Originality/valueTo solve the low-level angular velocity control problem in various operating conditions of multirotor UAVs, this paper proposes a nonlinear low-level angular velocity controller which takes the actuator dynamics into account.

Competition between fusion and quasifission in the angular momentum dependent dynamics of heavy element synthesis reactions

Background: Mass and angle distribution measurements have illuminated many aspects of the physical variables controlling quasifission. However, mapping from detection angle to reaction time is clouded by the wide range of contributing angular momenta $L\ensuremath{\hbar}$, ranging from $0\ensuremath{\hbar}$ to the maximum of the reaction ($⪆100\ensuremath{\hbar}$), which complicates the mapping, and thus limits our understanding of the reaction dynamics.Purpose: To investigate the angular momentum dependence of the reaction dynamics in quasifission and determine the fission fragment mass evolutions in the reaction.Method: The mass and angular distributions of products of the reactions $^{52}\mathrm{Cr}+^{198}\mathrm{Pt}$ and $^{54}\mathrm{Cr}+^{196}\mathrm{Pt}$ were measured. The distributions were compared with quasifission simulation results.Results: Mass angle distributions are reproduced by utilizing a new quasifission mass evolution model, and including a mass-symmetric component associated with low $L$. The latter increases in yield at higher beam energy.Conclusions: The symmetric component represents the total of slow quasifission and fusion-fission. The increase in contribution with energy above the Coulomb barrier suggests that an extra-push energy is required to achieve fusion.

Observation of SLAMS‐Like Structures Close to Martian Aphelion by MAVEN

AbstractAccording to various orientation of the interplanetary magnetic field (IMF), the planetary shock can be either quasi‐parallel or quasi‐perpendicular. Under quasi‐parallel conditions a significant number of solar wind suprathermal particles are reflected from the shock and drift along IMF, forming an extended and highly turbulent region called the foreshock where various nonlinear plasma phenomena are observed. In this research, a case study of the structures in the foreshock region at Mars as observed by Mars Atmosphere and Volatile Evolution is performed close to Martian aphelion, when the foreshock wave activity is usually low. Data from plasma analyzer STATIC and magnetometer MAG is used to analyze ion beams angular spectrum and magnetic field dynamics. It is shown that the observed structures are consistent with Short Large‐Amplitude Magnetic Structures (SLAMS), commonly detected in foreshock regions of magnetized and unmagnetized bodies throughout the Solar system. Finally, the Alfven Mach number is calculated to analyze characteristics of the observed foreshock structures. The analysis shows that the observed SLAMS‐like structures at Mars are steepened waves formed by the ion cyclotron resonance between plasma waves propagating along the IMF and the back‐streaming scattered solar wind H+ and exospheric O+ and O2+ ions, with the dominant impact of O+ ions. The steepening process is accompanied with observation of gradients in the diffuse ion density near the bowshock, like it has been previously reported near the Earth (e.g., Scholer, 1993, https://doi.org/10.1029/92JA01875; Tsubouchi &amp; Lembege, 2004, https://doi.org/10.1029/2003JA010014).

Orbital torque originating from orbital Hall effect in Zr

We investigate current-induced torques generated by Zr. We show that the generation efficiency of the current-induced torque increases with increasing the thickness of the Zr layer in ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}/\mathrm{Zr}$ and Ni/Zr bilayers, which indicates that the observed current-induced torque originates from the bulk of the Zr layer. We find that the sign of the current-induced torques is opposite to that expected from the spin Hall effect but is consistent with that expected from the orbital Hall effect in the Zr layer. Furthermore, we find that the torque efficiency increases with increasing the thickness of the ferromagnetic layer, which is consistent with the prediction of long-range orbital transport in ferromagnets. These observations demonstrate that the orbital Hall effect in the Zr layer is the main source of the current-induced torque. This finding highlights the important role of orbital transport in generating current-induced torques, advancing the understanding of angular momentum dynamics in solid-state devices with $4d$ transition metals.

Filtering‐based concurrent learning adaptive attitude tracking control of rigid spacecraft with inertia parameter identification

SummaryThis paper investigates the attitude tracking control problem of rigid spacecraft with inertia parameter identification. Based on the relative attitude and angular velocity error dynamics, a basic adaptive backstepping based attitude tracking control scheme is firstly designed such that asymptotic attitude tracking can be achieved. However, the parameter identification error cannot decay to zero if the persistent excitation (PE) condition is not satisfied. To solve this issue, a filtering‐based concurrent learning adaptive backstepping control scheme is then proposed, by incorporating torque filtering technique with concurrent learning technique. A more mild rank condition, which consists of some collectable historical data, is provided to guarantee the convergence of parameter identification error. In addition, a valid data collection algorithm is given. It should be mentioned that a distinctive feature of the proposed filtering‐based concurrent learning adaptive control scheme is that the convergence rate of attitude tracking errors can be improved from asymptotical to exponential. Finally, simulation results are provided to illustrate the effectiveness of the proposed control schemes.