Rotating Reference Frame Research Articles

Inducing Performance of Commercial Surgical Robots in Space.

Pre-existing surgical robotic systems are sold with electronics (sensors and controllers) that can prove difficult to retroactively improve when newly developed methods are proposed. Improvements must be somehow "imposed" upon the original robotic systems. What options are available for imposing performance from pre-existing, common systems and how do the options compare? Optimization often assumes idealized systems leading to open-loop results (lacking feedback from sensors), and this manuscript investigates utility of prefiltering, such other modern methods applied to non-idealized systems, including fusion of noisy sensors and so-called "fictional forces" associated with measurement of displacements in rotating reference frames. A dozen modern approaches are compared as the main contribution of this work. Four methods are idealized cases establishing a valid theoretical comparative benchmark. Subsequently, eight modern methods are compared against the theoretical benchmark and against the pre-existing robotic systems. The two best performing methods included one modern application of a classical approach (velocity control) and one modern approach derived using Pontryagin's methods of systems theory, including Hamiltonian minimization, adjoint equations, and terminal transversality of the endpoint Lagrangian. The key novelty presented is the best performing method called prefiltered open-loop optimal + transport decoupling, achieving 1-3 percent attitude tracking performance of the robotic instrument with a two percent reduced computational burden and without increased costs (effort).

Optical counterpart of a Foucault pendulum.

The twin beam vortex interferometer with a phase-conjugating mirror in a rotating reference frame is analyzed. The circular motion of the interference pattern occurs due to the exchange of angular momenta between photons and the interferometer. Using the concept of the ideal phase-conjugating mirror, it is shown that the motion of the helical interference pattern of interacting vortex photons with topological charge ℓ may be used for detection of slow rotations. The higher density of interference fringes may improve sensitivity by a factor containing 2ℓ compared to conventional Michelson interferometry.

Topology optimization for fluid flow devices modeled through the Multiple Reference Frame approach

Fluid flow devices have been algorithmically designed through optimization methods, and this task is relatively complex for flow machines. Particularly, one recent development is the use of the topology optimization method for this task, which is capable of achieving possibly non-intuitive geometries and even auxiliary structures, such as splitter blades without ever imposing them as a condition for the design. The design of the rotating part of the rotor has already been previously considered. However, in the presence of stationary parts surrounding the rotor, such as diffuser blades, the fluid flow behavior may change, meaning that it may be interesting to consider this different dynamic in the design. One possible approach for this is the Multiple Reference Frame approach, which considers the fluid flow dynamics inside the rotor being computed in the rotating reference frame, whilst the fluid flow dynamics outside the rotor is being computed in the stationary reference frame. In particular, this implies the need for some changes in the topology optimization formulation, also impacting the choice of objective functions. Therefore, here the topology optimization method is formulated for the Multiple Reference Frame approach, and a new combination for the multi-objective function is proposed. The discrete design variable configuration from the Topology Optimization of Binary Structures approach is adopted with some adjustments to account for the Multiple Reference Frame approach. The fluid flow is chosen to be laminar or turbulent. Numerical examples are presented in 2D for the rotor-diffuser in order to consider some aspects that affect the overall topology optimization design.

Oceanic response to typhoons in the Northwest Pacific using Aquarius and SMAP data (2011–2020)

Typhoons, such as tropical cyclones, can produce a variety of ocean responses through drastic changes in atmospheric and oceanic environments. However, the uncertainty in satellite salinity data increases during the passage of a typhoon and may limit its potential application. To investigate whether the satellite salinity data can explain oceanic responses to typhoons in the Northwest Pacific, we validated the satellite salinity using Argo float data for the past decade (2011–2020). The Soil Moisture Active Passive (SMAP) and Aquarius salinity were relatively accurate in subtropical regions at low latitudes under high sea surface temperature conditions in summer. This demonstrates the validity of the satellite salinity data in typhoon studies. We analyzed the oceanic responses to 20 representative typhoons over the past decade. Both the Aquarius and SMAP satellites observed a decrease in the SSS on the left side of the typhoon in contrast to the high salinity on the right side of the typhoon. The locations of SSS freshening coincided with those of higher precipitation to the left of the typhoon centers. We also observed that the higher the precipitation rate, the lower the satellite salinity. The ratio of the salinity freshening to the precipitation rate was significant at approximately –0.0401 psu mm-1 h-1. Changes in the vertical profiles of the Argo data supported this partial freshening of salinity as well as the characteristic surface cooling and deepening of the mixed layer after the passage of the typhoon. We further demonstrated that the atmospheric environments in a rotated coordinate system along the typhoon paths showed clear salinity freshening in the forward and slightly left sides of the typhoon center. The spatial distinction of the wind and precipitation fields along the typhoon paths induced the characteristic synoptic response of salinity prior to the arrival of each typhoon. Our results provide reasonable observational evidence of oceanic responses to typhoons in the Northwest Pacific and contribute to the understanding of atmospheric and oceanic processes related to tropical storms.

Some Dynamic Aspects of a Sextic Galactic Potential in a Rotating Reference Frame

This work aims to explore some dynamic aspects of the problem of star motion that is impacted by the rotation of the galaxy, which we model as a bisymmetric potential based on a two-dimensional harmonic oscillator with sextic perturbations. We demonstrate analytically that the motion is non-integrable when certain conditions are met. The analytical results for the non-integrability are confirmed by showing the irregularity of the behavior of the motion through utilizing the Poincaré surface of a section as a numerical method. The motion equilibrium positions are detected, and their stability is discussed. We show that the force generated by the rotating frame acts as a stabilizer for the maximum equilibrium points. We display graphically that the size of the stability regions relies on the angular velocity magnitude for the frame. Through the application of Lyapunov’s theorem, periodic solutions can be constructed which are close to the equilibrium positions. Furthermore, we demonstrate that there are one or two families of periodic solutions relying on whether the equilibrium point is a saddle or stable, respectively.

A 5G rotated frame radiator for ultra wideband microwave communication

AbstractA 5G rotated frame radiator for multiple applications is presented in the following paper. The presented geometry is capable of radiating the large frequency band from 2.91 to 12.17 GHz, which covers the 5G-(I) sub-6 GHz band, X-band communication with high efficiency. The impedance bandwidth of the radiator is 128%, with an electrical size of 0.24 λ × 0.24 λ × 0.15 λ in lambda. The antenna is simulated with an FR4 substrate using CST Simulator. 06-stages evolution process is also investigated by simulations, and corresponding S-parameter results are presented. Antenna's design comprises a patch in a rotated square fractal-like frame fed by a microstrip line. The proposed structure also demonstrates stable radiation patterns across the operating bandwidth. The proposed radiator has a high gain of 3.8 dBi, and an efficiency of 85%, which claimed that UWB range of the designed antenna. Therefore, it is useful for 5G-(I) sub-6 GHz band, X-band applications, including mobile, radar, and satellite microwave communication.

INTELLIGENT COMPUTING PARADIGM FOR SECOND-GRADE FLUID IN A ROTATING FRAME IN A FRACTAL POROUS MEDIUM

The numerical methods such as the artificial neural networks with greater probability and nonlinear configurations are more suitable for estimation and modeling of the problem parameters. The numerical methods are easy to use in applications as these methods do not require costly and time-consuming tests like the experimental study. In this study, we use the Levenberg–Marquardt-based backpropagation Process (LMP) to create a computing paradigm that makes use of the strength of artificial neural networks (ANN), known as (ANN-LMP). Here we use the ANN-LMP to obtain the solution of the second-grade fluid in a rotating frame in a porous material with the impact of a transverse magnetic field. The 1000 data set points in the interval [Formula: see text] are used for the network training to determine the effect of various physical parameters of the flow problem under consideration. The experiment is executed of six scenarios with different physical paramaters. ANN-LMP is used for evaluating the mean square errors (MSE), training (TR), validation (VL), testing (TT), performance (PF) and fitting (FT) of the data. The problem has been verified by error histograms (EH) and regression (RG) measurements, which show high consistency with observed solutions with accuracy ranging from E-5 to E-8. Characteristics of various concerned parameters on the velocity and temperature profiles are studied.

Behaviour of self excited synchronous generator loaded by different sizing induction motors

The modeling of both the synchronous generator and induction motor which is represented by the rotor reference frame was studied where the modeling was established using MATLAB /SIMULINK software package for an isolated synchronous generator direct-on-line with different sized induction motors; 20, 50, and 100 Hp, at manually adjusted excitation voltage values which were maintained constant at 3.35, 4.55, and 6.21 V, respectively. The purpose of this work is to study the impact of a sudden increase in the load torque; from 0 to 150 % with an increase of 25 %, of full load torque was studied at a constant motor speed of 188.49 rad sec-1. On the other hand, the impact of a sudden decrease in the rotor speed by about 20 % from its rated value; from 188.49 to 150.79 rad sec-1 was also studied at full load torque of the same different-sized induction motors. These values were manually recorded and response variables of the generator including terminal voltage, current, output power, electromagnetic torque, and load angle were determined and represented as a function of time. The results illustrated the Changes in the terminal voltage, the current, the output power, the electromagnetic torque, and the load angle as parameters of a synchronous generator for different-sized induction motors.

Особенности численного моделирования работы воздушно-тепловой завесы в OpenFOAM

The issues of mathematical modeling of turbulent heat-conductive flow of compressible viscous medium in the internal volume of the body of an air-thermal curtain equipped with a tangential fan are considered. The solution of the problem is constructed on the basis of averaged Reynolds (Favre) Navier-Stokes equations. The solution of the problem is obtained using the MRF (Multiple Reference Frame) approach, which uses a rotating reference frame, and using a transformation of the basic Navier-Stokes equations in the rotation zone. In order to correctly describe the working processes occurring in the internal volume of the air-thermal curtain and in the environment, modular multiblock meshes are applied in the work, including those allowing to separate rotating and stationary areas. The solution of the set tasks is constructed using the tools of the OpenFOAM package. As a result of the work, the peculiarities of the flow structure in the flowing part of the air-heat curtain are described in detail, and the gas velocities achieved at different fan speeds are estimated. The self-similarity of velocity profiles at the air curtain nozzle outlet is shown.

On the Necessity of Canonical Momentum Over mv Momentum, Illustrated with Perturbations on the Classical Ideal Gas

Through the formalism of the partition function, perturbations on the classical ideal gas are considered. The perturbations include externally applied fields and rotating the reference frame. The rotating reference frame offers a stark pedagogical opportunity to show why statistical mechanics requires canonical momentum in contrast to mv momentum.

Intelligent Attitude Fault-Tolerant Control of Space Tumbling Target Fly-Around Based on RBF Neural Network

The flying around monitoring task of space tumbling target is one of the key links of its on-orbit service. Considering the practical constraints of system inertia uncertainty, external disturbance, actuator saturation, and fault in engineering practice, a robust composite controller based on radial basis function (RBF) neural network is proposed. First, in a new line of sight rotation (RLOS) coordinate system, the relative attitude kinematics and dynamics equations between the tracker and tumbling target based on the error quaternion are established; second, the RBF neural network is used to estimate the additive and multiplicative faults of the system, and the fast nonsingular terminal sliding mode surface (FNTSMS) is combined with the active disturbance rejection control (ADRC) technology to design a finite-time fault-tolerant control (FTC) strategy with high accuracy, strong robustness, and anti-saturation based on the RBF neural network. It is proven that the designed robust fault-tolerant controller can ensure that the system state error converges to a small region containing the origin in a limited time under the Lyapunov framework. Finally, the effectiveness and superiority of the control strategy were verified by numerical simulation.

A Simplified DTC-SVPWM Scheme for Induction Motor Drives Using a Single PI Controller

Apart from variable switching frequency, a major issue in direct torque controlled (DTC) induction motor drives is the high torque ripple, which can be minimized by incorporating suitable pulsewidth modulation schemes such as space vector pulsewidth modulation (DTC-SVPWM) and duty ratio control DTC. However, the simplicity and robustness of the DTC scheme are compromised due to the high computational complexity and requirement of a number of motor parameters for the control. In this article, a simple and elegant control algorithm for the realisation of the DTC-SVPWM that is less dependent on motor parameters is proposed. The stator flux-linkage space vector angle needed to generate the reference torque for the DTC operation is computed based on the basic torque equation and the reference stator phase voltage needed for the SVPWM is determined in turn in every sampling period. For the modulation, a carrier-based space vector pulsewidth modulation (CSVPWM) scheme is adopted to get low torque ripple at constant switching frequency. The proposed speed control scheme avoids the use of rotor parameters and rotating reference frame transformations. It requires no sector identification and only one PI controller is needed for the speed control. Though the scheme has comparable torque ripple as that of the conventional DTC-SVPWM scheme, it significantly reduces the computational burden. Hardware results on a three-phase, 2 HP, 415 V induction motor are presented to validate the performance of the proposed control scheme.

FANet: An Arbitrary Direction Remote Sensing Object Detection Network Based on Feature Fusion and Angle Classification

High-precision remote sensing image object detection has broad application prospects in military defense, disaster emergency, urban planning, and other fields. However, the arbitrary orientation, dense arrangement, and small size of objects in remote sensing images lead to poor detection accuracy of existing methods. To achieve accurate detection, this paper proposes an arbitrary directional remote sensing object detection method, called FANet, based on feature fusion and angle classification. Initially, the angle prediction branch is introduced, and the circular smooth label method is used to transform the angle regression problem into a classification problem, which solves the difficult problem of abrupt changes in the boundaries of the rotating frame while realizing the object frame rotation. Subsequently, to extract robust remote sensing objects, innovative introduce pure convolutional model as a backbone network, while Conv is replaced by GSConv to reduce the number of parameters in the model along with ensuring detection accuracy. Finally, the strengthen connection feature pyramid network (SC-FPN) is proposed to redesign the lateral connection part for deep and shallow layer feature fusion, and add jump connections between the input and output of the same level feature map to enrich the feature semantic information. In addition, add a variable parameter to the original localization loss function to satisfy the bounding box regression accuracy under different IoU thresholds, and thus obtain more accurate object detection. The comprehensive experimental results on two public datasets for rotated object detection DOTA and HRSC2016 demonstrate the effectiveness of our method.

Relative velocity in pseudo-Riemannian spacetime

We give a coordinate independent definition of relative velocity of test particle in pseudo-Riemannian spacetime as measured along the observer’s line-of-sight in general and several instructive cases. In doing this, the test particle is considered as a luminous object, otherwise, if it is not, we assume that a light source is attached to it, which has neither mass nor volume. Then we utilize the general solution of independent definition of relative velocity of a luminous source in generic pseudo-Riemannian spacetime. As a corollary, we discuss the implications for the Minkowski metric, the test particle and observer at rest in an arbitrary stationary metric, the uniform gravitational field, the rotating reference frame, the Schwarzschild metric, the Kerr-type metrics, and the spatially homogeneous and isotropic Robertson-Walker (RW) spacetime of standard cosmological model. In the last case, it leads to cosmological consequence that the resulting, so-called, kinetic recession velocity of an astronomical object is always subluminal even for large redshifts of order one or more, so that it does not violate the fundamental physical principle of causality. We also calculate the measure of carrying away of a galaxy at redshift z by the expansion of space, which proves, in particular, that cosmological expansion of a flat 3D–space is fundamentally different from a kinematics of galaxies moving in a non-expanding flat 3D-space. So, it is impossible to mimic the true cosmological redshift by a Doppler effect caused by motion of galaxies in a non-expanding 3D-space, flat or curved. We also give a reappraisal of the `standard ́ kinematic interpretation of redshifts in RW spacetime as accumulated Doppler-shifts.

Two-dimensional non-Abelian topological insulators and the corresponding edge/corner states from an eigenvector frame rotation perspective

We propose the concept of two-dimensional (2D) non-Abelian topological insulators which can explain the energy distributions of the edge states and corner states in systems with parity-time symmetry. From the viewpoint of non-Abelian band topology, we establish the constraints on the 2D Zak phase and polarization. We demonstrate that the corner states in some 2D systems can be explained as the boundary mode of the one-dimensional edge states arising from the multiband non-Abelian topology of the system. We also propose the use of the off-diagonal Berry phase as complementary information to assist the prediction of edge states in non-Abelian topological insulators. Our work provides an alternative approach to study edge and corner modes and this idea can be extended to three-dimensional systems.

Observation of Non-Abelian Charged Nodes Linking Nonadjacent Gaps.

Nodal links are special configurations of band degeneracies in the momentum space, where nodal line branches encircle each other. In PT symmetric systems, nodal lines can be topologically characterized using the eigenvector frame rotations along an encircling loop and the linking structure can be described with non-Abelian frame charges involving adjacent bands. While the commutation rules between the frame charges are well established, the underlying relationship between distant band gap closing nodes remains to be explored. In this Letter, we present a photonic multiple nodal links system, where the nodal lines of nonadjacent bands are investigated with symmetry constraints on frame charges. Through an orthogonal nodal chain, the nodal line from the lower two bands predicts the existence of nodal lines formed between the higher bands. We designed and fabricated a metamaterial, with which the multiple nodal links and the topological connection between nonadjacent nodal lines are experimentally demonstrated.

Numerical modeling and nonlinear analysis of semi-rigid jointed steel frames

This paper investigates the effect of semi-rigid connection, geometric nonlinearity and material nonlinearity in steel frame analysis. To study the independent and combined effects of different nonlinearities, elastic and inelastic analyses are carried out using general purpose finite element software SAP2000. Connections are modeled as rotational springs and frame as one dimensional beam element. Verification and application of the simplified numerical model developed in the present study is demonstrated by considering different examples and comparing the results of present study with those available in the published literature. Numerical alternatives, key features about modeling and necessary input parameters are discussed in detail. Rotational springs are characterized by linear, bilinear, multi-linear or nonlinear moment-rotation relationships of the connection. Results in terms of beam moment and nodal displacement are presented for both elastic and inelastic analyses. With the increase in connection flexibility, beam mid-span moments and displacements increase, but beam-end moments decrease. It is observed that the influence of connection nonlinearity dominates over material and geometric nonlinearities.

Toolpath generation for ultraprecision machining: Freeform surface generation and extrapolation

The rise in complexity of freeform optics drives the development of equally complex manufacturing processes needed to produce them. Complex optical designs, however, require equally complex machining toolpaths and techniques that can generate them. This paper and subsequent research develops and investigates toolpath generation techniques for explicitly defined surfaces of the form Z(X,Y). A generalized approach is developed for the toolpath generation of optical surfaces themselves as well as techniques for transitioning between surfaces in an array. All surfaces herein are continuous, well-behaved, and differentiable – constraints satisfied by most optical prescriptions today. The current paper describes the toolpath generation and extrapolation process for a tilted freeform surface defined inside a non-circular boundary. Boundaries are defined so that some non-convexity is acceptable, and it is simple to determine whether a toolpath coordinate lies inside or outside them. Using the proposed coordinate frame transformation and boundary definition, it is shown that by tilting a surface and boundary together, the tilted surface retains its original form and boundary in a rotated coordinate frame. With the proposed extrapolating surface, it is possible to modify a freeform surface outside its defined boundary so it is smooth and well-behaved inside its overall region of interest – an important consideration for both toolpath generation and opto-mechanical design. By combining freeform and extrapolating surfaces together, a smooth piecewise surface is generated whose overall continuity increases as the order of the extrapolating surface increases. As a result, it is possible to increase the overall continuity of a toolpath along its cutting direction. To verify the utility of the proposed extrapolating surface, experimental data are presented for several spiral toolpaths generated for a 6th order polynomial surface prescription defined inside a rectangular boundary. Subsequent research, using the techniques herein as a starting point, develop and investigate blending multiple freeform surfaces together.

Matrix regularization for tensor fields

Abstract We propose a novel matrix regularization for tensor fields. In this regularization, tensor fields are described as rectangular matrices, and area-preserving diffeomorphisms and local rotations of the orthonormal frame are both realized as unitary similarity transformations of matrices in a unified way. We also show that the matrix commutator corresponds to the covariantized Poisson bracket for tensor fields in the large-N limit.

A Modified Multi-Level Inverter System for Grid-Tied DES Applications

Energy harvesting from renewable energy sources is trending in the world due to inventions in modern technology. This paper proposes a grid-tied single-phase modified W-type 81-level inverter. Inverter design equations to calculate various parameters, such as the number of voltage levels and the number of DC power sources, along with the feedback controller equations, are developed to integrate the proposed topology with an electric power grid. The modeling of the control system for the proposed topology is carried out in the synchronously rotating reference frame for single-phase systems. The PWM generation part of the proposed inverter system makes use of the binary search nearest level algorithm to efficiently track the grid voltage signal. The proposed system integrates the inverter with the grid without the need for an output filter. The efficiency analysis shows that the proposed system delivers active and reactive power to the grid with an efficiency of around 90% and a THD of 1.04%. The voltage and current waveforms for the dynamic active and reactive power flow reveal that the proposed system exhibits a good transient and steady-state response. The overall system is simulated in MATLAB/Simulink and the results are verified using a hardware implementation of the prototype circuit.