Application of Synchronization to Formation Flying Spacecraft: Lagrangian Approach

The dynamics of rotations and translations in molecular crystals is derived from a microscopic Hamiltonian. The dynamical variables are the lattice displacements and their conjugate momenta for the translations and, in the case of orientationally disordered phases, the appropriate symmetry-adapted functions for the rotations. Coupled dynamical equations for the oscillatory lattice displacements and the orientational molecular relaxation are obtained. The coupling between these equations is expressed in terms of static susceptibilities which are calculated from the Hamiltonian. The coherent inelastic neutron scattering law, including interference between translations and rotations, is derived. Our results are relevant for inelastic neutron, Brillouin, and Raman scattering experiments. As a concrete example we refer to KCN.

This study proposes a finite-time tracking control system for an unmanned aerial vehicle (UAV) in the presence of dynamic payloads and external disturbances. Changes in payload result in time-varying parametric uncertainties, making traditional control strategies ineffective. A sliding mode control (SMC) scheme is designed to handle uncertainties in both translational and rotational dynamics. A finite-time SMC (FTSMC) approach is developed to handle unknown time-varying mass and external disturbances in the translational dynamics. Furthermore, differences in the payload influence the inertia characteristics of the UAV, introducing further uncertainties in the feedback control design. A finite-time sliding mode controller is also implemented for rotational dynamics to guarantee the attitude stabilization under unknown inertia parameter variations. The proposed method has the objective to attenuate the chattering effect associated with traditional SMC within a finite time frame. Theoretical stability analysis with rigorous mathematical proofs is presented to confirm the effectiveness of the control scheme. Numerical simulations are provided to validate its performance under dynamic operating conditions.

Dynamics of freely falling perforated disks

While conventional Single Particle Tracking (SPT) techniques acquire 2D or 3D trajectories of particle probes, we have developed Single Particle Orientation and Rotational Tracking (SPORT) techniques to extract orientation and rotational information. Combined with DIC microscopy, the SPORT technique has been applied in biophysical studies, including membrane diffusion and intracellular transport. The rotational dynamics of nanoparticle vectors on live cell membranes was recorded and its influence on the fate of these nanoparticle vectors was elucidated. The rotational motions of gold nanorods with various surface modifiers were tracked continuously at a temporal resolution of 5 ms under a DIC microscope. We found that the rotational behaviors of gold nanorod vectors are strongly related to their surface charge, specific surface functional groups, and the availability of receptors on cell membranes. The study of rotational Brownian motion of nanoparticles on cell membranes will lead to a better understanding of the mechanisms of drug delivery and provide guidance in designing surface modification strategies for drug delivery vectors under various circumstances. To characterize the rotation mode of surface functionalized gold nanorods on cell membranes, the SPORT technique is combined with the correlation analysis of the bright and dark DIC intensities. The unique capabilities of visualizing and understanding rotational motions of functionalized nanoparticles on live cell membranes allow us to correlate rotational and translational dynamics in unprecedented detail and provide new insights for complex membrane processes, including electrostatic interactions, ligand-receptor binding, and lateral (confined and hopping) diffusion of membrane receptors. Surface-functionalized nanoparticles interact with the membrane in fundamentally different ways and exhibit distinct rotational modes. The early events of particle-membrane approach and attachment are directly visualized for the first time. The rotational dynamics of cargos in both active directional transport and pausing stages of axonal transport was also visualized using high-speed SPORT with a temporal resolution of 2 ms. Both long and short pauses are imaged, and the correlations between the pause duration, the rotational behaviour of the cargo at the pause, and the moving direction after the pause are established. Furthermore, the rotational dynamics leading to switching tracks are visualized in detail. These first-time observations of cargo's rotational dynamics provide new insights on how kinesin and dynein motors take the cargo through the alternating stages of active directional transport and pause. To improve the localization precision of the SPT technique with DIC microscopy, a precise three-dimensional (3D) localization method of spherical gold nanoparticle probes using model-based correlation coefficient mapping was introduced. To accomplish this, a stack of sample images at different z-positions are acquired, and a 3D intensity profile of the probe serving as the model is used to map out the positions of nanoparticles in the sample. By using this model-based correlation imaging method, precise localization can be achieved in imaging techniques with complicated point spread functions (PSF) such as differential interference contrast (DIC) microscopy. The 3D superlocalization method was applied to tracking gold nanospheres during live endocytosis events. Finally, a novel dual-modality imaging technique has been developed to super-localize a single gold nanorod while providing its orientation and rotational information. The super-localization of the gold nanorod can be accomplished by curve fitting the modified bright-field images generated by one of the two beams laterally shifted by the first Nomarski prism in a DIC microscope. The orientation and rotational information is derived from the DIC images of gold nanorods. The new imaging setup has been applied to study the steric hindrance induced by relatively large cargos in the microtubule gliding assay and to track nanocargos in the crowded cellular environment.

This paper deals with the problem of designing a controller for a thrust-propelled vehicle which steers the vehicle to track a 3D spatial path, while effective compensation for both time-varying disturbances and uncertainties is achieved as well. Taking advantage of extraction algorithm, we separate the design for the translational and rotational dynamics. A back-stepping-based controller and a sliding mode controller are, respectively, designed for the translational and rotational dynamics in succession. The stability of the control framework is established through Lyapunov analysis. A numerical simulation is also included in the paper to render the effectiveness of the proposed control scheme.

SummaryIn this paper, we present an extended state observer–based robust dynamic surface trajectory tracking controller for a quadrotor unmanned aerial vehicle subject to parametric uncertainties and external disturbances. First, the original cascaded dynamics of a quadrotor unmanned aerial vehicle is formulated in a strict form with lumped disturbances to facilitate the backstepping design. Second, based on the separate outer‐ and inner‐loop control methodologies, the extended state observers are constructed to online estimate the unmeasurable velocity states and lumped disturbances existed in translational and rotational dynamics, respectively. Third, to overcome the problem of “explosion of complexity” inherent in backstepping control, the technique of dynamic surface control is utilized for trajectory tracking and attitude stabilization, and with the velocity and disturbance estimates incorporated into the dynamic surface control, a robust dynamic surface flight controller that guarantees asymptotic tracking in the presence of lumped disturbances is synthesized. In addition, the stability analysis is given, showing that the present robust controller can ensure the ultimate boundedness of all signals in the closed‐loop system and make the tracking errors arbitrarily small. Finally, comparisons and extensive simulations under different flight scenarios are performed to validate the effectiveness and superiority of the proposed scheme in accurate tracking performance and enhanced antidisturbance capability.

A multi-rate hierarchical fault-tolerant adaptive model predictive control framework: Theory and design for quadrotors

Straw biomass particles, characterized by their complex non-spherical geometries, exhibit intricate motion and coupling mechanisms with combustion processes in gas flow fields, which remain largely unexplored. Current models, predominantly based on spherical particle assumptions, fail to accurately describe the dynamic behavior of biomass particles with high aspect ratios (Ar) and complex shapes, particularly when translational and rotational dynamics are coupled. This study focuses on the Motion characteristics of non-spherical, cylindrical straw biomass particles. By integrating visualization experiments and computational fluid dynamics-discrete element method numerical simulations, a novel non-spherical motion model applicable to particles with varying aspect ratios was developed and validated, building upon the findings from our previous Particle-resolved Direct numerical simulations research. The study systematically analyzed the translational and rotational behavior of particles with aspect ratios of 6, 10, and 15 in upward gas flows with a particular focus on the dynamic variations in drag coefficients (CD), lift coefficients (CL), and torque coefficients (CT) and their influence on particle motion. Experimental results demonstrate that the developed model effectively predicts the trajectories of particles with different aspect ratios. The prediction errors for vertical and lateral positions were both below 5%, while errors for incident angles and angular velocities remained within 8% under different aspect ratio geometries, indicating the model's high accuracy and applicability. Beyond its ability to accurately simulate the detailed motion of particles, the model also addresses the coupling of translational and rotational dynamics in non-spherical particles. In the future, this model can serve as a theoretical and optimization tool for studying the transportation and combustion of biomass particles in coal-fired boilers. Moreover, it lays a solid foundation for further research on the dynamics of complex-shaped particles and their applications in intricate flow fields and industrial environments.

Accurate navigation of Mars entry vehicles suggests that estimators should couple translational and rotational dynamics while accommodating time-varying atmospheric and aerodynamic uncertainty. This paper proposes a first step towards a generalized framework with nonlinear state and parameter (i.e., aerodynamic and atmospheric) estimation that is applicable to most entry vehicle design configurations. The framework described in this paper fuses inertial-measurement unit (IMU) measurements with distributed surface-pressure data to estimate coupled translational and rotational dynamics. Atmospheric density and pressure are included as parameters in augmented state vector, enabling the filter to decouple aerodynamic from environmental uncertainty. Presented results demonstrate that it is promising to identify aerodynamic coefficients in real-time via direct calculation based on the estimated states and IMU measurements. The resulting framework could support further research on aerodynamic parameter identification, observability studies, and closed-loop adaptive estimation.

Dynamics of confined molecules within porous materials is equally important as local structural order, and it is necessary to quantify it and to reveal the microscopic mechanisms ruling it for better control of adsorption applications. In this study, molecular dynamics simulations were carried out to investigate the translational and the rotational dynamics of methanol trapped into the flexible NH2-MIL-53(Al) metal-organics framework (MOF). Indeed, atomistic simulation is nowadays a relevant tool to explore matter at the nanoscale. Very recently it has been shown that the NH2-MIL-53(Al) MOF material was capable to undergo a reversible structural transition (breathing phenomenon) by combining adsorption and thermal stimuli. This flexibility can drastically affect the dynamics of confined molecules and therefore the successful conduct of adsorption applications such as gas storage and separation. Rotational and translational dynamics of confined methanol through nanoporous flexible NH2-MIL-53(Al) MOF were then deeply investigated by exploring a broad range of dynamical properties to extract the molecular mechanisms ruling them. This study allowed us to shed light on the interplay of dynamics of confined fluids and flexibility of porous material and to highlight the physical insights in diffusion mechanisms of confined molecules. Anomalous translational diffusion was evidenced due to a dynamical heterogeneity caused by a combination of a localized dynamics at the subnanometric scale and translational jumps between nanodomains in a zigzag scheme between the hydroxide group of the NH2-MIL-53(Al). Actually, the non-Fickian dynamics of methanol is the result of the specific host-guest interactions and the MOF flexibility involving the pore opening. Eventually, decoupling between both rotational and translational dynamics related to breaking in the Stokes-Einstein relation was highlighted.

This manuscript presents a universal control law for a class of complex dynamic systems, such as mobile robots. The trajectory tracking problem is among the major problems in the field of robotics. The proposed universal control law solves the trajectory tracking problem of mobile robots. Despite a large body of research on developing robot's control laws conducted in the literature, the dynamic effects of robots are often not taken into consideration while deriving control laws that define their trajectories. In most cases, the robot's trajectory tracking and/or stabilization problems are addressed based on its kinematic model due to simplicity. Therefore, the need for a universal control law based on the robot's dynamic and/or kinematic model is significant. Even though the feedback control theory is well-established in the field of robotics, the control laws for dynamic systems are typically more complex than system models themselves. Furthermore, control laws are required to be adapted depending on models of different mobile robot systems. Here, the development of universal control law is underscored, i.e., the paper is aimed at developing universal dynamic tracking control law that solves the trajectory tracking problem of a class of mobile robots. The controller is tested through a set of computer simulations using a differential drive mobile robot operating in an indoor planar environment.

Exploring the water mobility in gelatin based soft candies by means of Fast Field Cycling (FFC) Nuclear Magnetic Resonance relaxometry

The translational, rotational, and phonon dynamics of water in ZrO2 /water nanofluid

Translation and Rotation Dynamics in a Magnetic-Label Biosensor

A multi-view reflector microscope visualizes six-dimensional single-molecule translational and rotational dynamics with isotropic nanoscale resolution.