Rotation Vector Research Articles

Numerical-analytical optimization of orientation algorithms on a spherical model of angular motion of a rigid body

The problem of numerical-analytical optimization of three algorithms for determining orientation quaternions due to refinement of coefficients in the structure of algorithms is considered. Of them, two algorithms use the orientation vector as an "intermediate parameter". The coefficients are refined on the basis of computer modeling and the minimization of the error of the accumulated computational drift using the analytical reference model of the spherical motion of a rigid body as a model rotational motion in a sequence of Krylov angles that change over time according to a linear law. For this, the test motion model is supplemented by modeling ideal information from the outputs of the angular velocity sensors in the form of quasi-coordinates using analytical formulas for the apparent rotation vector. It is shown that the accumulated error of computational drift on the proposed reference model of rotary motion has a linear law of growth with time for all algorithms under consideration. As a result of the numerical experiment, new values ​​of the coefficients in the structures of the algorithms were obtained, which minimize the error of the accumulated drift and improve the characteristics of the trend of this error. The carried out optimization leads to a decrease by an order of magnitude of the maximum error value and a change in the linearly growing nature of the dependence of the calculation drift error on time to an oscillatory one. The results of the computational experiment are given.

Anisotropic Thermal Conductivity Oscillations in Relation to the Putative Kitaev Spin Liquid Phase of α-RuCl_{3}.

In the presence of an external magnetic field, the Kitaev model could host either gapped topological anyons or gapless Majorana fermions. In α-RuCl_{3}, the gapped and gapless cases are only separated by a 30° rotation of the in-plane magnetic field vector. The presence or absence of the spectral gap is key for understanding the thermal transport behavior in α-RuCl_{3}. Here, we study the anisotropy of the oscillatory features of thermal conductivity in α-RuCl_{3}. We examine the oscillatory features of thermal conductivities (κ//a, κ//b) with fixed external fields and find distinct behavior for the gapped (B//a) and gapless (B//b) scenarios. Furthermore, we track the evolution of thermal resistivity (λ_{a}) and its oscillatory features with the rotation of in-plane magnetic fields from B//b to B//a. The thermal resistivity λ(B,ϕ) displays distinct rotational symmetries before and after the emergence of the field-induced Kitaev spin liquid phase. These results suggest that oscillatory features of thermal conductivity in α-RuCl_{3} are closely linked to the putative Kitaev spin liquid phase and its excitations.

Methodology For Extracting Poplar Planted Fields From Very High-Resolution Imagery Using Object-Based Image Analysis and Feature Selection Strategy

Abstract. Poplars (Populus sp.), a tree that grows rapidly species, are significant as industrial forest products. The delineation and monitoring of poplar cultivated areas are invaluable for decision-making processes. With the remote sensing technology, accurate detection of poplar planted areas could be determined much faster, more economically, and with minimum labor requirements. The objective of this research is to create a map of poplar plantations in the Sakarya region of Turkey utilizing Worldview-3 satellite imagery. Object-based image analysis (OBIA) through the application of the multi-resolution segmentation method (MRS) was employed to generate image segments, and then three prevailing machine learning algorithms, namely Support Vector Machine (SVM), Random Forest (RF) and Rotation Forest (RotFor) were implemented to produce LULC maps of the study area including 11 landscape features. The most effective and contributing object features that assure high separability between landscape features were determined using a filter-based Chi-square algorithm for the prediction models constructed with SVM, RF, and RotFor classifiers. Results revealed that the SVM classifier achieved the highest overall accuracy (91.73%) with 38 features out of 88 features, about 3% improvement compared to the other algorithms. According to the SHAP analysis, the IHS feature was the most effective one in the constructed RF model, followed by the CI (red edge), NDVI-1 and NDVI-2 vegetation indices.

A Novel Recognition Method for Complex Power Quality Disturbances Based on Rotation Vector and Fuzzy Transfer Field

A Novel Recognition Method for Complex Power Quality Disturbances Based on Rotation Vector and Fuzzy Transfer Field

Orientation of inertialess spheroidal particles in turbulent channel flow with spanwise rotation

The orientation dynamics of inertialess prolate and oblate spheroidal particles in a directly simulated spanwise-rotating turbulent channel flow has been investigated by means of an Eulerian–Lagrangian point-particle approach. The channel rotation and the particle shape were parameterized using a rotation number Ro and the aspect ratio λ, respectively. Eleven particle shapes 0.05 ≤ λ ≤ 20 and four rotation rates 0 ≤ Ro ≤ 10 have been examined. The spheroidal particles retained their almost isotropic orientation in the core region of the channel, despite the significant mean shear rate set up by the Coriolis force. Irrespective of channel rotation rate Ro, rod-like spheroids tend to align in the streamwise direction, while disk-like particles are oriented in the wall-normal direction. These trends were accentuated with increasing departure from sphericity λ = 1. The changeover from the isotropic orientation mode in the centre to the highly anisotropic near-wall orientation mode commenced further away from the suction-side wall with increasing Ro, whereas the particle orientations on the pressure side of the rotating channel remained essentially unaffected by Ro. We observed that the alignments of the fluid rotation vector with the Lagrangian stretching direction were similarly unaffected by the imposed system rotation, except that the de-alignment set in deeper into the core at high Ro. This contrasts with the well-known substantial impact of system rotation on the velocity and vorticity fields. Similarly, slender rods and flatter disks were aligned with the Lagrangian stretching and compression directions, respectively, for all Ro considered, except in the vicinity of the walls. The typical near-wall de-alignment extended considerably further away from the suction-side wall at high Ro. We conjecture that this phenomenon reflects a change in the relative importance of mean shear and small-scale turbulence caused by the Coriolis force. Preferential particle alignment with Lagrangian stretching and compression directions are known from isotropic and anisotropic turbulence in inertial reference systems. The present results demonstrate the validity of this principle also in a non-inertial system.

A Low-Computational-Complexity Digital Predistortion Model for Wideband Power Amplifier.

This paper proposes a Composition Piecewise Memory Polynomial (CPMP) digital predistortion model based on a Vector Switched (VS) behavioral model to address the challenges of severe nonlinearity and strong memory effects in wideband power amplifiers (PAs). To tackle this issue, two thresholds are calculated and used to segment the envelope values of the input signal according to the nonlinear distortion characteristics of the PA. In this approach, a Generalized Memory Polynomial (GMP) model is employed for the lower segment, a Memory Polynomial (MP) model is employed for the middle segment, and a higher-order GMP model is employed for the upper segment. By sharing the fundamental MP among the proposed segmented models and leveraging a design methodology that configures different cross terms, memory depths, and polynomial orders for each segment, this model achieves superior linearization performance while simultaneously reducing the computational complexity associated with model extraction. The experimental results demonstrate that the adjacent channel power ratio (ACPR) of the predistorted PA output signal using the proposed model improves from -36 dBc to -54 dBc, matching the performance of the GMP model. Furthermore, this performance is 0.5 dBc better than the Piecewise Dynamic Deviation Reduction (PDDR) and Decomposed Vector Rotation (DVR) models. Notably, the complexity of the proposed parameter extraction process is 28.8% of the DVR model, 21.79% of the GMP model, and 12.83% of the PDDR model.

Shape and stability of rotation sets for incompressible flows on the torus

AbstractIn this paper we introduce the concept of rotation cones, determined by rotation sets, and use these to describe the stability of rotation sets of incompressible and fixed-point free continuous flows on the torus $$\mathbb{T}^{d}$$ T d , d ⩾ 2. The previous concept is equivalent and extends the stability of rotation numbers (and rotation vectors) in the special case of fixed-point free continuous flows on $$\mathbb{T}^{2}$$ T 2 . We prove that incompressible Lipschitz vector fields with stable rotation sets have convex rotation cones with non-empty interior, and that all extremal edges are collinear with vectors in ℤd. If, in addition, the rotation cones are proper, then these are polyhedral with finitely many edges. Finally we prove that the set of vector fields with stable rotation sets is C0-open and dense among those having proper rotation cones.

A Generalization of the Finsler–Hadwiger Theorem

Summary We give a new generalization of the Finsler–Hadwiger theorem along with a proof using the rotation of vectors.

Analysis of the degradation in transmission accuracy of RV reducers considering the wear clearance between cycloidal wheels and pinwheels

To accurately determine the transmission accuracy degradation pattern of Rotate Vector (RV) reducers due to wear, a predictive method is proposed that simultaneously considers the initial clearance and wear clearance between the cycloid wheel and the pinwheel. The initial clearance is derived from a comprehensive gear system analysis, considering assembly errors, manufacturing errors and modifications. Building on this, the wear depth of the cycloid wheel tooth profile is numerically simulated using Archard's wear theory, revealing the wear distribution pattern under various operating conditions. A Gaussian regression model is used to predict the maximum wear amount for different operational durations. Based on the predicted wear amount, a multi-body dynamic simulation model incorporating wear clearance was established to analyze the transmission error under varying clearance conditions. Results indicate that the wear depth along the tooth profile initially increases and then decreases. The depth and region of wear along the tooth profile gradually increase with load and output speed, with the impact of load on the wear region being greater than that of output speed. Under the initial clearance condition, the maximum transmission error is 22.91″. As the wear clearance increases, transmission accuracy declines sharply. When the cumulative wear clearance reaches 0.2 mm, the transmission error exceeds the allowable backlash limit. This study provides a theoretical reference for predicting accuracy degradation and guides the manufacturing design of RV reducers.

An accurate and locking-free geometric exact beam formulation on the special orthogonal group SO(3)

An accurate and locking-free geometric exact beam formulation (GEBF) on the special orthogonal group SO(3) is developed for slender beams with large deformations and large rotations. Due to the nonlinear nature of the spatial rotations, the classical GEBFs usually have a non-constant mass matrix and complex expressions of inertia forces; meanwhile, the singularity and locking issues are also key matters of concern. Aiming at resolving these drawbacks, two main contributions are achieved in the present work. First, the angular velocity is independently interpolated, resulting in a constant mass matrix and explicitly representable inertial forces, which can offer significant advantages for efficient dynamic simulations. Second, inspired by the assumed natural strain method in shell theory, the stretch-shear strain is interpolated to obtain simplified and locking-free elastic forces, which is a new attempt to alleviate the locking problems for the GEBFs. In addition, the special orthogonal group SO(3) is utilized for updating incremental rotation vectors to eliminate singularities, and objective strain measurement is achieved by employing relative rotation vector interpolation. The effectiveness and superiority of the developed low-order and high-order elements are demonstrated through numerical simulations of standard benchmark examples. The present work contributes to the advancement of accurate and reliable formulation for slender beams; the constant mass matrix, the locking-free characteristics, and the elegant form of the formulation make it particularly suitable for multibody dynamic analysis.

Eulerian rates of elastic incompatibilities applied to size-dependent hardening in finite torsion

Measures of rates of elastic incompatibilities are developed within an Eulerian framework for finite-deformation response of anisotropic elastic–inelastic materials. Such framework relies on the evolution of microstructural vectors. It is emphasized that the rates of incompatibilities, here denoted as Rij, depend on the constitutive equation for the rate of inelasticity. For small strains and rotations, Rij are equal to the negative of the components of the rate of Nye-Kröner’s dislocation density tensor. In contrast to these small strain components, each Rij is invariant under superposed rigid body motions such that it can be used independently in the constitutive equations to describe the material behavior. Specifically, in this work, Rij provide a size-dependent enhancement to hardening that can increase or decrease during loading history, modeling the generation and annihilation of densities of geometrically necessary dislocations in metal plasticity. The application to the finite-deformation cyclic torsion of thin wires demonstrates the potential of this approach and the importance of the constitutive equation for the plastic spin rate both on the rotations of the microstructural vectors and on the predicted size-effect.

Shear-driven magnetic buoyancy in the solar tachocline: Dependence of the mean electromotive force on diffusivity and latitude

Abstract The details of the dynamo process that is responsible for driving the solar magnetic activity cycle are still not fully understood. In particular, whilst differential rotation provides a plausible mechanism for the regeneration of the toroidal (azimuthal) component of the large-scale magnetic field, there is ongoing debate regarding the process that is responsible for regenerating the Sun’s large-scale poloidal field. Our aim is to demonstrate that magnetic buoyancy, in the presence of rotation, is capable of producing the necessary regenerative effect. Building upon our previous work, we carry out numerical simulations of a local Cartesian model of the tachocline, consisting of a rotating, fully compressible, electrically conducting fluid with a forced shear flow. An initially weak, vertical magnetic field is sheared into a strong, horizontal magnetic layer that becomes subject to magnetic buoyancy instability. By increasing the Prandtl number we lessen the back reaction of the Lorentz force onto the shear flow, maintaining stronger shear and a more intense magnetic layer. This in turn leads to a more vigorous instability and a much stronger mean electromotive force, which has the potential to significantly influence the evolution of the mean magnetic field. These results are only weakly dependent upon the inclination of the rotation vector, i.e. the latitude of the local Cartesian model. Although further work is needed to confirm this, these results suggest that magnetic buoyancy in the tachocline is a viable poloidal field regeneration mechanism for the solar dynamo.

A Calculation Method of Bearing Balls Rotational Vectors Based on Binocular Vision Three-Dimensional Coordinates Measurement

The rotational speed vectors of the bearing balls affect their service life and running performance. Observing the actual rotational speed of the ball is a prerequisite for revealing its true motion law and conducting sliding behavior simulation analysis. To address the need for accuracy and real-time measurement of spin angular velocity, which is also under high-frequency and high-speed ball motion conditions, a new measurement method of ball rotation vectors based on a binocular vision system is proposed. Firstly, marker points are laid on the balls, and their three-dimensional (3D) coordinates in the camera coordinate system are calculated in real time using the triangulation principle. Secondly, based on the 3D coordinates before and after the movement of the marker point and the trajectory of the ball, the mathematical model of the spin motion of the ball was established. Finally, based on the ball spin motion model, the three-dimensional vision measurement technology was first applied to the measurement of the bearing ball rotation vector through formula derivation, achieving the analysis of bearing ball rolling and sliding characteristics. Experimental results demonstrate that the visual measurement system with the frame rate of 100 FPS (frames per second) yields a measurement error within ±0.2% over a speed range from 5 to 50 RPM (revolutions per minute), and the maximum measurement errors of spin angular velocity and linear velocity are 0.25°/s and 0.028 mm/s, respectively. The experimental results show that this method has good accuracy and stability in measuring the rotation vector of the ball, providing a reference for bearing balls' rotational speed monitoring and the analysis of the sliding behavior of bearing balls.

Numerical study of dispersion characteristics of cylindrical spiral lines and periodic gratings based on them

Numerical studies of the dispersion characteristics of cylindrical spiral lines have been carried out. One-dimensional and two-dimensional periodic lattices formed by such lines are also considered. The eigenvalue method was used in combination with periodic boundary conditions. The dispersion characteristics are calculated in the range of parameters for which the conditions of applicability of the known approximate numerical-analytical methods for analyzing spiral lines are not met. The dispersion characteristics of the first two eigen-waves in one-dimensional and two-dimensional periodic lattices of spirals are obtained for different values of phase shifts between lattice periods. It is shown that the main type of wave in them is a wave slowed down relative to the axes of the lines with the direction of rotation of the field vector determined by the direction of winding of the spiral.

Lifespan Evaluation for a Standard RV Reducer based on Fatigue Strength Theory

Rotate vector (RV) reducers are the two-stage deceleration device comprising involute and cycloid-pin gear transmission mechanisms. As the typical deceleration elements, they are widely applied in industrial robots, digitally controlled machine tools and automation fields due to their compact structure and high precision. However, a reducer may lose precision after a long-term operation. Moreover, pitting and metal peeling of internal components may also occur, leading to a fatigue failure. Therefore, it is necessary to conduct investigations on lifespan evaluation for RV reducers. In this study, the CRV-80E reducer is taken as the research object. Firstly, according to its transmission characteristics, the lifespan evaluation model for a standard RV reducer is established based on fatigue strength theory and Palmgren-Miner linear cumulative damage law, with the internal crankshaft bearing is considered as the key component. Then, the simulations are carried out on crankshaft bearing by the ANSYS Workbench and SKF SimPro. The contact stress, deformation on bearing rollers, and the rated lifespan of the reducer are simulated. Finally, the accelerated life test is conducted on an RV reducer by increasing the external load with the positioning precision as an output and criterion. After the test, the reducer is disassembled, and metal peeling failure is observed on the crankshaft bearing while other parts are relatively intact. The test results validate the feasibility and accuracy of the service life evaluation model and simulation analysis. This study provides a new research approach for researchers and manufacturers and a design reference for engineers to improve the lifespan of RV reducers by optimizing crankshaft bearings, which have a certain academic value.

A new variational integrator for constrained mechanical system dynamics

A new variational integrator is proposed to solve constrained mechanical systems. The main distinguishing feature of the present integrator comes from the distinct discretization of Lagrangians based on the Hamilton's principle in its most general form. Specifically, Hermite interpolation is used for discrete positions, which provides at least C1 continuity for generalized coordinates. The velocities and momentums are interpolated using quadratic polynomials for the consistency, such that the kinematic relation between velocities and positions can be exactly satisfied. Meanwhile, the Gauss-Legendre quadrature rule is employed to guarantee the accuracy of discrete Lagrange equations. To tackle constrained mechanical systems, a coordinate partition approach is used to eliminate the constraint equations. The local incremental rotation vector is exploited to get rid of rotation singularities in spatial problems. Moreover, an adaptive stepsize strategy is implemented to improve the efficiency. The strengths of the new integrator lie in the accessible large step sizes in the simulation and its global second-order accuracy for positions as well as velocities. Several examples are performed and analyzed to validate its accuracy and capabilities.

Deep Learning-Based Obesity Identification System for Young Adults Using Smartphone Inertial Measurements.

Obesity recognition in adolescents is a growing concern. This study presents a deep learning-based obesity identification framework that integrates smartphone inertial measurements with deep learning models to address this issue. Utilizing data from accelerometers, gyroscopes, and rotation vectors collected via a mobile health application, we analyzed gait patterns for obesity indicators. Our framework employs three deep learning models: convolutional neural networks (CNNs), long-short-term memory network (LSTM), and a hybrid CNN-LSTM model. Trained on data from 138 subjects, including both normal and obese individuals, and tested on an additional 35 subjects, the hybrid model achieved the highest accuracy of 97%, followed by the LSTM model at 96.31% and the CNN model at 95.81%. Despite the promising outcomes, the study has limitations, such as a small sample and the exclusion of individuals with distorted gait. In future work, we aim to develop more generalized models that accommodate a broader range of gait patterns, including those with medical conditions.

Behavior of the Position and Ellipticity Angles at Polarization Mode Transitions in Pulsar Radio Emission

Polarization observations of radio pulsars show that abrupt transitions in the polarization vector’s position angle can be accompanied by large excursions in the vector’s ellipticity angle, suggesting the vector passes near the right or left circular pole of the Poincaré sphere. The behavior of the angles can be explained by a transition in dominance of the orthogonal polarization modes or a vector rotation caused by a change in the phase difference between the modes. Four polarization models are examined to quantify and understand the behavior of the angles at a mode transition: coherent polarization modes, partially coherent modes, incoherent modes with nonorthogonal polarization vectors, and incoherent orthogonal modes with an elliptically polarized emission component. In all four models, the trajectory of the mode transition on the Poincaré sphere follows the geodesic that connects the orientations of the mode polarization vectors. The results from the models can be similar, indicating that the interpretation of an observed transition within the context of a particular model is not necessarily unique. The polarization fraction of the emission and the average ellipticity angle depend upon the statistical character of the mode intensity fluctuations. The polarization fraction increases as the fluctuations increase. The excursion in ellipticity angle can be large when the mode intensities are quasi-stable and is suppressed when the intensity fluctuations are large.

X-ray Polarization of Blazars and Radio Galaxies Measured by the Imaging X-ray Polarimetry Explorer

X-ray polarization, which now can be measured by the Imaging X-ray Polarimetry Explorer (IXPE), is a new probe of jets in the supermassive black hole systems of active galactic nuclei (AGNs). Here, we summarize IXPE observations of radio-loud AGNs that have been published thus far. Blazars with synchrotron spectral energy distributions (SEDs) that peak at X-ray energies are routinely detected. The degree of X-ray polarization is considerably higher than at longer wavelengths. This is readily explained by energy stratification of the emission regions when electrons lose energy via radiation as they propagate away from the sites of particle acceleration as predicted in shock models. However, the 2–8 keV polarization electric vector is not always aligned with the jet direction as one would expect unless the shock is oblique. Magnetic reconnection may provide an alternative explanation. The rotation of the polarization vector in Mrk421 suggests the presence of a helical magnetic field in the jet. In blazars with lower-frequency peaks and the radio galaxy Centaurus A, the non-detection of X-ray polarization by IXPE constrains the X-ray emission mechanism.

Faraday effect of light caused by plane gravitational wave

A gravitational field can cause a rotation of the polarisation vector of light. This phenomenon is known as the gravitational Faraday effect. We study the gravitational Faraday effect of linearly polarised light propagating in the gravitational field of a weak plane gravitational wave (GW) with “+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$+$$\\end{document}", “×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes $$\\end{document}", and elliptical polarisation modes. The corresponding gravitational Faraday rotation angle is proportional to the GW amplitude and to the squared distance traveled by the light and inversely proportional to the GW squared wavelength. The Faraday rotation is maximal if the light propagates along directions perpendicular to the GW propagation and tilted by π/4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi /4$$\\end{document} to the directions of its polarisation. There is no a gravitational Faraday rotation when light and a GW propagate along the same directions, or when light propagates along directions of a GW polarisation. Helicity of an elliptically polarised GW gives cubic order contribution to the Faraday rotation.