Search Results (3,862)

Despite the growing use of acceleration–speed (AS) profiling in elite football, the number and composition of sessions required to generate stable in situ profiles remain unclear. AS profiling provides estimates of maximal theoretical acceleration (A0) and maximal theoretical velocity (S0), which may offer practically relevant information for monitoring player sprint-related qualities. This study examined the influence of profiling-window length and match exposure on in situ AS profile outcomes in 19 professional football players competing in the 2023–2024 English Football League Championship. Profiles were generated using two non-overlapping conditions comprising five consecutive sessions (5SS) and ten consecutive sessions (10SS). Mean A0 values were 6.91 ± 0.36 m/s² for 5SS and 7.12 ± 0.40 m/s² for 10SS, while mean S0 values were 9.52 ± 0.29 m/s and 9.89 ± 0.28 m/s, respectively. Reliability was assessed using intraclass correlation coefficients (ICCs), standard error of measurement (SEM), and smallest worthwhile change (SWC). The match count within each profiling window was associated with A0 and S0 outcomes in both 5SS and 10SS conditions (all p ≤ 0.004). However, ICC values were low, particularly for S0, and SEM exceeded SWC across conditions, indicating limited sensitivity for detecting small meaningful changes. These findings suggest that longer profiling windows may provide slightly more stable A0 estimates, whereas S0 appears more sensitive to match exposure and contextual variability. The results highlight the importance of interpreting AS profiles at an individual level and accounting for match exposure when comparing profile outcomes across monitoring windows. Full article

Background/Objectives: Force platforms and optoelectronic motion capture systems are considered gold standards for postural sway assessment, although their use is confined to dedicated laboratory settings. Wearable inertial systems represent a practical alternative; however, their validity compared with reference systems within a shared physical domain (i.e., displacement domain) remains insufficiently investigated. This methodological requirement, frequently overlooked in the existing literature, is here adopted as an explicit inclusion criterion for the first time to ensure an appropriate metrological comparison. This review critically examines the validity of inertial systems for postural sway assessment, only including studies in which sway parameters derived from inertial measurement units (IMUs) were expressed in the same physical domain as the corresponding reference measurements. Methods: A systematic search of the Scopus database was conducted to identify English-language studies published up to January 2026 that compared IMU-derived sway parameters with those obtained from gold-standard systems, using parameters expressed in consistent measurement units. Sensor placement, postural tasks, signal processing techniques, extracted sway parameters, and statistical validation methods were analyzed as key methodological aspects. Results: Eight studies published between 2015 and 2022 met the inclusion criteria. The predominant configuration consisted of a single lumbar-mounted IMU, and quiet bipedal standing was the most frequently investigated postural task. Velocity-based parameters, particularly mean sway velocity, demonstrated moderate to high agreement with reference systems. In contrast, spatial dispersion measures, including the 95% confidence ellipse area and root mean square displacement, showed greater variability and, in some cases, systematic bias in Bland–Altman analyses. Conclusions: Wearable inertial systems demonstrated strong potential for estimating global and velocity-related sway parameters during quiet standing, supporting their clinical applicability. However, spatial metrics and dynamic postural tasks remain more challenging for IMU-based assessment. Methodological standardization of validation protocols and signal processing pipelines is essential to improve comparability and reproducibility across studies. Full article

In this paper, we apply the double Fourier transform method to the two-dimensional Vlasov equations for a charged particle subjected to white noise, exponentially correlated Gaussian forces, trap forces and thermal and active noises in a magnetic field. By deriving the corresponding Fokker–Planck equation, analytical solutions for the joint probability density are obtained in different time domains. The mean squared displacement and velocity of a charged particle driven by white noise exhibits a super-diffusive behavior, scaling as ∼t² in the short-time regime, while it grows linearly with time (~t) in the long-time regime, in agreement with numerical simulations of the mean squared displacement. When thermal noise is included together with harmonic trap and viscous forces, the characteristic time scale increases as ~t^2h+1 in the corresponding time domains, whereas the mean squared velocity scales as ~t^2h+3. The moments of the joint probability density under thermal noise scale as ~t^2h+5. Furthermore, when the persistent Hurst exponent h→1/2, the entropy of the joint probability density associated with thermal noise coincides with that obtained for active noise in both the short-time (t ≪ τ) and long-time (t ≫ τ) limits. Full article

The distributed electric propulsion (DEP) system offers significant potential for enhancing aerodynamic efficiency, reducing emissions, and enabling innovative aerodynamic configurations. However, the strong coupling between propeller slipstream effects and wing structural dynamics presents new challenges for aeroelastic analysis. To address this issue, this paper proposes an aeroelastic modeling approach tailored for DEP systems that systematically accounts for the effects induced by propeller slipstreams. Specifically, the induced velocity generated by the propeller slipstreams is computed using a slipstream tube model and incorporated into the unsteady aerodynamic modeling via the unsteady vortex lattice method. Under appropriate assumptions, a state-space formulation of the unsteady aerodynamic forces is derived, while the wing structural dynamics are represented using the finite element method. After establishing the subsystem models, a complete aeroelastic model of the DEP system is assembled based on the input–output relationships among the subsystems. Nonlinear simulations are conducted using this integrated model. The results demonstrate the potential of distributed propellers for suppressing wing vibrations and alleviating structural loads. Full article

This work presents a nonlinear dynamic model and an energy-based control strategy for a coaxial vertical take-off and landing Unmanned Aerial Vehicle (UAV) equipped with independently tilting propulsion units. The proposed model captures the full six-degree-of-freedom motion of the vehicle and explicitly incorporates the forces and moments produced by the coaxial thrust-vectoring propulsion system, as well as the additional force components induced by the two-degree-of-freedom thrust vectoring mechanism. To regulate the vehicle during hover, cruise, and transition maneuvers, a passivity-based control framework formulated in terms of unit quaternions is developed. The control law simultaneously stabilizes the translational and rotational subsystems without relying on model linearization. In order to map the virtual control forces and torques into physically realizable actuator commands, a nonlinear control allocation procedure is introduced. This allocation scheme enables independent angular positioning of the propulsion units while computing the corresponding motor angular velocities. The effectiveness of the proposed modeling and control framework is assessed through three-dimensional dynamic simulations and numerical experiments, demonstrating accurate trajectory tracking, autonomous UAV landing capabilities, and smooth transitions between flight regimes for thrust-vectored UAV platforms. Full article

Severe longitudinal vibrations and abnormal tension fluctuations in hoisting ropes pose significant threats to the safe and stable operation of mine hoisting systems. To address these issues, this paper proposes a semi-active vibration-suppression strategy combining a magnetorheological damper (MRD) with output-feedback adaptive sliding-mode control (ASMC). A dynamic model of the MRD-equipped hoisting system is developed using Hamilton’s principle. The nonlinear hysteresis of the MRD is described by a simplified extended hyperbolic tangent function model (SEHTFM), and an inverse model converts the desired control force into a feasible real-time current command. Using only displacement and velocity measurements at the conveyance–rope connection, the ASMC compensates for matched uncertainties, including boundary excitation, modeling and truncation errors, and force-realization errors. Numerical simulations compare an optimized passive viscous damper benchmark, SMC–MRD, and ASMC–MRD responses under varying payloads, accelerations, and hoisting speeds. During constant-speed operation, ASMC–MRD achieves peak reduction rates of 82.8% in dynamic displacement and 77.6% in dynamic tension relative to the optimized passive benchmark. The results demonstrate accurate force realization with small bounded tracking errors and improved robustness under variable operating conditions. Full article

Initial value problems of the third order featuring explicit dependence on velocity, denoted as $y^{‴}=f(x,y,y^{\prime })$, emerge regularly across applications such as electromechanical networks, structural mechanics, and robotic trajectory control. Despite their practical prevalence, these differential equations remain insufficiently addressed by standard numerical integration techniques. Orthodox Runge–Kutta–Nyström (RKN) schemes are fundamentally formulated for differential equations lacking the first derivative, specifically $y^{‴}=f(x,y)$. Due to this algorithmic constraint, researchers frequently resort to computationally demanding first-order system reductions or rely upon standard Runge–Kutta methods. The present study resolves this methodological gap by defining an explicit s-stage integration architecture that natively incorporates the first derivative within the internal stage evaluations. Such structural modifications require the deployment of a supplementary coefficient matrix, denoted as D, to formulate the corresponding order theory. The complete set of algebraic order conditions is systematically established up to the seventh order, accompanied by a generic mathematical framework for generating schemes of arbitrary order. Based on this analytical foundation, an embedded $6(4)$ method is constructed. This specific pair achieves strict error tolerances utilizing merely six function evaluations per integration step, representing a substantial operational reduction compared to the eight computations strictly required by equivalent Runge–Kutta pairs. Direct numerical integration of the native third-order system prevents the dimensionality increase from reducing to first-order systems. Performance validation of the numerical solver involves two representative physical benchmarks: a coupled robotic appendage subjected to platform excitation and an electromechanical actuator array regulated by transient control inputs. Both dynamical systems exhibit severe velocity-dependent dissipation mechanisms and nonlinear external forcing. Quantitative numerical evaluations confirm that the constructed 6(4) pair yields higher precision and demands less computational expenditure than prevailing RK and RKN integrators. The analytical and empirical findings establish that derivative-capable Nyström integration algorithms furnish mathematically rigorous and computationally efficient numerical solutions for velocity-coupled third-order dynamics. Full article

Explicit expressions for bubbly Taylor–Couette flow fields are rarely available in the literature. The present work aims to derive explicit expressions for bubble velocity fields in laminar gas–liquid Taylor–Couette flow between two rotating coaxial cylinders with the buoyancy effect on gas bubbles. It is assumed that the angular velocity of the rotating cylinder(s) is moderately low and the bubble radius is relatively small so that the Stokes number of bubbles is small enough and, consequently, the radial bubble migration is ignorable and the bubble volume fraction can be treated as being constant in a limited period of time. Explicit leading-order solutions are derived for the spiral rising bubble velocity field in the dilute limit. Unlike the heavy particles dominated by the Stokes drag, the added mass and lift forces are shown to be relevant for the bubbly flows. The radial bubble velocity field is discussed in detail for several cases of major interest under the condition that the added mass coefficient is equal to the lift force coefficient, as assumed by some authors in the literature. Our results show that the radial-to-azimuthal velocity ratio of bubbles is linearly proportional to the Stokes number of bubbles and can be controlled by the angular velocity of the rotating cylinder(s) and the bubble radius so that the assumption of ignorable radial bubble migration can be reasonably justified within a limited period of time (for example, in the first few tens of revolutions of the rotating cylinder(s)). Full article

Starting from the circular aperture diffraction experiment, this paper decomposes the intrinsic interactions underlying wave–particle duality and proposes a specific interaction force: the velocity-perpendicular interaction force. We derive the characterization formula of this force and show that it can induce the phenomenon of circular aperture diffraction of light, with the theoretical results being highly consistent with those calculated by the Huygens–Fresnel principle. The direction of this force is perpendicular to the relative velocity, originating from the coupling effect between the wave nature of light and the particle nature of the circular aperture structure, and it satisfies a modified inverse square law of distance related to the relative velocity. When photons pass through different positions of the circular aperture, the symmetry effect generates a net interaction time. The product of the main component of this force, the net interaction time, and the radius of the circular aperture constitutes a modulation quantity (a ratio of the Planck’s constant), which exerts an on–off modulation effect on the interaction force, thereby inducing the emergence of annular diffraction fringes. This study provides a novel physical interpretation for the circular aperture diffraction of light from the perspective of interaction forces and clarifies the possible existence form of wave–matter interaction forces. This force formula is expected to effectively describe the behavior of microscopic particles, just like the Schrödinger equation, while providing a brand-new perspective on interactions. It holds great application prospects in fields such as single-photon manipulation and quantum precision measurement. Full article

The belt velocity is not strictly constant but exhibits periodic oscillations in certain industrial applications. A lumped mass model of a two-dimensional nonlinear friction-induced slider moving on an oscillating belt is established in this paper. Tangential stick-slip motion and normal separation–re-contact behavior are both considered under a symmetrically and uniformly distributed interface force. The analytical expression of the static friction force is deduced in terms of dynamic equations and stick-slip-separate state transition boundaries of the slider. The sliding friction force is modelled by a dynamic model that accounts for relative velocity. The Runge–Kutta algorithm combining the bisection method to capture the transition point between stick and slip motions is adopted to compute the vibration responses of the slider. The numerical results indicate that the belt’s oscillatory angular vibration frequency, the vertical preload, and the nonlinear stiffness have great effects on the dynamic characteristics of the slider, and the slider can experience $\mathrm{p}$-periodic ($\mathrm{p}=1,2,3,4,\mathrm{ect}.$) and chaotic vibration due to the non-smooth behavior at the contact interface. Full article

Macroevolutionary analysis evaluating structural monophyly as descent with modification allows recasting of taxa in terms of physics as evolutionary mechanics. There are four natural ranks, as generalized taxa: the species, genus, lineage, and metalineage, each with distinctive evolutionary processes. The species is the smallest group of organisms whose traits exclude two-sigma of uncertainty and otherwise are active in processes at the genus level. The genus is a complex engine using the Rule of Four and the Pareto Fractal Dimension to fashion and control changes over time in minimally monophyletic groups. Immediate descendant species are limited to four per genus. The lineage is modeled as a caulogram, a stem-taxon tree of present-day species and genera arranged in a timelike sequence. The metalineage is an informationally structured n-tuple set of caulograms for one lineage as calculated at successive times in the past following a morphological clock. Metalineages reveal sustained similar numbers of species across ca. 100 million years, or four or five ticks of a Nemesis extinction clock. Force values associated with evolutionary processes are calculated and compared for two bryophyte lineages at species, genus, and lineage levels. These comparisons include Efficiency Ratio and Evolutionary Force, as well as analogues of classical mechanics: evolutionary distance, velocity, acceleration, force, work, and kinetic energy. A geometric explanation is offered for the Rule of Four constraining the size of minimally monophyletic groups. Full article

Accurate onboard velocity updating is essential for UAV strapdown inertial navigation, especially under GNSS-degraded and high-dynamic conditions. Instead of relying only on local Taylor-series cancellation as λ → 0 or directly transferring coning compensation coefficients, the proposed method redesigns velocity-specific sculling coefficients over the finite dimensionless interval λ = ΩΔT ∈ [⁰,¹]. A two-stage strategy is developed. Stage I constructs a low-cost proxy error model from the analytical expansion and applies a minimax criterion to generate robust candidate coefficients. Stage II further refines them by minimizing a multi-condition time-domain RMS sculling error. Attitude-transfer coefficients are also tested to assess the transferability of optimized coning coefficients to velocity sculling compensation. Under a stringent single-frequency sculling protocol, the velocity-specific Stage-II coefficients reduce the global RMS and worst-case errors by 12.57% and 14.20%, respectively, compared with the classical six-sample coefficients. Under constant specific-force bias, constant angular-rate bias, and double-frequency sculling, the reductions remain 10.62–12.44% and 12.29–16.17%. Ablation and reproducibility checks show that the main gain comes from Stage-II time-domain RMS refinement and remains stable under grid, reference-integration, and base-index variations. Full article

Four-wheel-independent-drive electric vehicles are gaining increasing research attention due to their comprehensive dynamic performance. Real-time tire–road friction coefficient information contributes to the development of adaptive control algorithms and active safety control systems for such vehicles. However, traditional tire models widely adopted in existing estimation methods may fail to match practical tire characteristics accurately. Furthermore, lateral velocity serves as a critical state variable for tire–road friction coefficient estimation, whereas existing lateral velocity observers using low-cost inertial measurement unit sensors suffer from degraded estimation performance under complex driving maneuvers. To address the above challenges, this paper proposes a three-stage friction coefficient estimation framework. Firstly, vehicle lateral velocities are estimated via a piecewise gain-scheduled observer using inertial measurement unit measurements. Secondly, tire slip ratios are calculated based on the observed lateral velocities; meanwhile, the longitudinal, lateral and vertical forces of each tire are reconstructed. Lastly, tire force and slip information under combined slip conditions are acquired, and a multilayer perceptron neural network is established to achieve individual tire–road friction coefficient estimation. The simulation results verify the numerical feasibility and preliminary effectiveness of the proposed estimation method under ideal simulation conditions. Full article

Background: Evidence on powered wearable exoskeleton gait training in patients with chronic hypoxic-ischemic encephalopathy (HIE) is virtually absent, and existing studies have focused on macroscopic functional outcomes while neglecting joint-level neuromuscular force-generation characteristics such as rate of force development (RFD). Objective: To examine the effects of a six-week powered exoskeleton gait training program on isometric hip strength and RFD, sit-to-stand (STS) performance, frontal-plane hip strength, and center-of-pressure (CoP) dynamics in a patient with chronic HIE-induced quadriparesis. Methods: A case report with pre- and post-intervention evaluation was conducted. A 47-year-old male with chronic HIE-induced quadriparesis (onset 2017) completed 18 sessions (three per week, six weeks) of powered lower-limb exoskeleton gait training. Outcomes included isometric hip peak force and RFD (DynaMo, Vald Performance), STS peak force and body mass-normalized RFD (ForceDecks, Vald Performance), frontal-plane hip strength (ForceFrame, Vald Performance), and CoP path length and mean velocity. Results: Hip extension peak force increased by 247–256% bilaterally, and hip extension RFD increased by 174–188%, whereas hip flexion peak force showed minimal change (+3.3–5.2%). Body mass-normalized STS RFD increased by 250% (10 to 35 N·s⁻¹·kg⁻¹), representing the largest relative gain. Hip abduction strength increased by 27.1–36.8% with improved bilateral symmetry; hip adduction imbalance reversed from right to left dominance. CoP path length and mean velocity each decreased by 3.7%. Conclusions: Six weeks of powered exoskeleton gait training selectively enhanced time-dependent neuromuscular output—particularly RFD—beyond maximal strength gains, with meaningful improvements in functional weight acceptance during STS. These findings support exoskeleton-based training as a promising rehabilitation strategy for patients with chronic CNS injury. Full article

The optimized design of key components in harvesting equipment is significantly impeded by the significant grain loss from the header and high energy consumption during stalk cutting that result from the lack of physical and mechanical parameters regarding the plant-flower head system during the mechanized harvesting of edible sunflowers. To furnish the design of mechanized harvesting equipment for palatable sunflowers with theoretical support and foundational data, physical parameters measured included geometrical properties, critical bending angle, coefficient of static friction, moisture content, and head seed collision loss rate. Mechanical parameters—radial elastic modulus, shear modulus, and shear strength—were obtained from stalk compression and shear tests using a universal testing machine. Stem-head detachment force was quantified with a universal testing machine fitted with bespoke fixtures, and orthogonal experiments were conducted with tensile speed, head-picking plate spacing, and tensile angle as factors to establish the significance hierarchy and optimal configuration. Considerable heterogeneity was observed: mean plant height, head diameter, and head thickness were (1733 ± 153) mm, (275 ± 28) mm, and (93 ± 19) mm, respectively. The critical bending angle decreased with height, whereas stalk moisture content increased from base to apex. Mean stalk and head moisture contents were 65% and 61.4%. The coefficient of static friction varied from 0.24 to 0.63 depending on contact material. A critical impact velocity of 2–3 m/s induced mechanical damage and seed cracking. The stalk radial elastic modulus was (1.12 ± 0.27) MPa; shear modulus and shear strength increased with decreasing sampling height, with basal stalks exhibiting a mean shear modulus of 2.47 MPa and shear strength of 1.87 MPa. Sampling position significantly influenced shear modulus (p < 0.05). The factor significance for stem-head detachment force was head-picking plate spacing > tensile angle > tensile speed. The optimal combination (tensile speed 500 mm/min, head-picking plate spacing 50 mm, tensile angle 10°) yielded a detachment force of (202.3 ± 9.5) N, with a relative error below 5% compared to prior detachment force measurements, confirming the reliability of the optimised results. These data provide essential foundations for developing stalk cutting, head inserting, and combine harvesting equipment. Full article