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Journal articles on the topic 'Rotating coordinate system'
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1
Zel'dovich, Ya B., L. V. Rozhanskii, and A. A. Starobinskii. "Rotating bodies and electrodynamics in a rotating coordinate system." Radiophysics and Quantum Electronics 29, no. 9 (1986): 761–68. http://dx.doi.org/10.1007/bf01034472.
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Liu, Yan, Zhendong Ge, Yingtao Yuan, et al. "Study of the Error Caused by Camera Movement for the Stereo-Vision System." Applied Sciences 11, no. 20 (2021): 9384. http://dx.doi.org/10.3390/app11209384.
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The stereo-vision system plays an increasingly important role in various fields of research and applications. However, inevitable slight movements of cameras under harsh working conditions can significantly influence the 3D measurement accuracy. This paper focuses on the effect of camera movements on the stereo-vision 3D measurement. The camera movements are divided into four categories, viz., identical translations and rotations, relative translation and rotation. The error models of 3D coordinate and distance measurement are established. Experiments were performed to validate the mathematical models. The results show that the 3D coordinate error caused by identical translations increases linearly with the change in the positions of both cameras, but the distance measurement is not affected. For identical rotations, the 3D coordinate error introduced only in the rotating plane is proportional to the rotation angle within 10° while the distance error is zero. For relative translation, both coordinate and distance errors keep linearly increasing with the change in the relative positions. For relative rotation, the relationship between 3D coordinate error and rotation angle can be described as the nonlinear trend similar to a sine-cosine curve. The impact of the relative rotation angle on distance measurement accuracy does not increase monotonically. The relative rotation is the main factor compared to other cases. Even for the occurrence of a rotation angle of 10°, the resultant maximum coordinate error is up to 2000 mm, and the distance error reaches 220%. The results presented are recommended as practice guidelines to reduce the measurement errors.
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Hou, Yanli, Xianyu Su, and Wenjing Chen. "Alignment Method of an Axis Based on Camera Calibration in a Rotating Optical Measurement System." Applied Sciences 10, no. 19 (2020): 6962. http://dx.doi.org/10.3390/app10196962.
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The alignment problem of a rotating optical measurement system composed of a charge-coupled device (CCD) camera and a turntable is discussed. The motion trajectory model of the optical center (or projection center in the computer vision) of a camera rotating with the rotating device is established. A method based on camera calibration with a two-dimensional target is proposed to calculate the positions of the optical center when the camera is rotated by the turntable. An auxiliary coordinate system is introduced to adjust the external parameter matrix of the camera to map the optical centers on a special fictitious plane. The center of the turntable and the distance between the optical center and the rotation center can be accurately calculated by the least square planar circle fitting method. Lastly, the coordinates of the rotation center and the optical centers are used to provide guidance for the installation of a camera in a rotation measurement system. Simulations and experiments verify the feasibility of the proposed method.
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Mou, Qishan. "A candle in a rotating coordinate system." Physics Teacher 35, no. 9 (1997): 542–43. http://dx.doi.org/10.1119/1.2344801.
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Zhu, Yuanchao, Dazhao Zhang, Yanlin Lai, and Huabiao Yan. "Shape adjustment of "FAST" active reflector." Highlights in Science, Engineering and Technology 1 (June 14, 2022): 391–400. http://dx.doi.org/10.54097/hset.v1i.493.
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Abstract. In this paper, the relevant working principle of "FAST" Chinese Eye is studied, and a mathematical model is established to solve the equation of the ideal paraboloid. The ideal paraboloid model is obtained by rotating the paraboloid around the axis in the two-dimensional plane. On this basis, the specific solutions of each question are discussed, and the parabolic equation, the receiving ratio of the feed cabin to the reflected signal, the numbering information and coordinates of the main cable node and other parameters are obtained. This paper for solving directly above the benchmark of spherical observation of celestial bodies when ideal parabolic equation, according to the geometrical optics to knowledge should be clear all the signals of the incoming signal after the ideal parabolic will converge to the focal point of basic rules, then through converting ideal parabolic model of ideal parabolic equation in a two-dimensional plane, An optimization model was established to minimize the absolute value of the difference between the arc length and the arc length of the parabola in the diameter of 300 meters. The known conditions were substituted into Matlab to solve the equation of the ideal parabola by rotating the parabola around the axis: . In order to determine the ideal paraboloid of the celestial body, a new spatial cartesian coordinate system is first established with the line direction between the celestial body and the spherical center as the axis, so that the observed object is located directly above the new coordinate system. The same model in question 1 is established to obtain the vertex coordinates of the ideal paraboloid at this time. Then the vertex coordinates are converted to the coordinates in the original space cartesian coordinate system by rotation transformation between space cartesian coordinate systems. The solution of its vertex coordinates (-49.5287, -37.0203, -294.1763).
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Kazachkov, Ivan. "Modeling of the Flow due to Double Rotations Causing Phenomenon of Negative Pressure." WSEAS TRANSACTIONS ON FLUID MECHANICS 18 (December 31, 2023): 259–71. http://dx.doi.org/10.37394/232013.2023.18.25.
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This paper is devoted to mathematical modeling and computational experiments of a flow with negative pressure. A previously unknown class of fluid flow under the action of counter-current centrifugal forces is in focus. Volumetric forces in a non-conducting fluid can arise from gravity, vibrations, or rotations. In this paper, we consider controlled variable volumetric forces in a system with two rotations around the vertical axis and the tangential axis of a horizontal disk rotating around the vertical axis. The study of the coordinate system during double rotation showed that the double rotation about two perpendicular axes, one of which moves along a tangential direction to the rotating horizontal disk, is equal to the rotation around the oscillating axis inclined at some angle to the vertical axis.
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Klier, Eliana M., Hongying Wang, and J. Douglas Crawford. "Interstitial Nucleus of Cajal Encodes Three-Dimensional Head Orientations in Fick-Like Coordinates." Journal of Neurophysiology 97, no. 1 (2007): 604–17. http://dx.doi.org/10.1152/jn.00379.2006.
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Two central, related questions in motor control are 1) how the brain represents movement directions of various effectors like the eyes and head and 2) how it constrains their redundant degrees of freedom. The interstitial nucleus of Cajal (INC) integrates velocity commands from the gaze control system into position signals for three-dimensional eye and head posture. It has been shown that the right INC encodes clockwise (CW)-up and CW-down eye and head components, whereas the left INC encodes counterclockwise (CCW)-up and CCW-down components, similar to the sensitivity directions of the vertical semicircular canals. For the eyes, these canal-like coordinates align with Listing’s plane (a behavioral strategy limiting torsion about the gaze axis). By analogy, we predicted that the INC also encodes head orientation in canal-like coordinates, but instead, aligned with the coordinate axes for the Fick strategy (which constrains head torsion). Unilateral stimulation (50 μA, 300 Hz, 200 ms) evoked CW head rotations from the right INC and CCW rotations from the left INC, with variable vertical components. The observed axes of head rotation were consistent with a canal-like coordinate system. Moreover, as predicted, these axes remained fixed in the head, rotating with initial head orientation like the horizontal and torsional axes of a Fick coordinate system. This suggests that the head is ordinarily constrained to zero torsion in Fick coordinates by equally activating CW/CCW populations of neurons in the right/left INC. These data support a simple mechanism for controlling head orientation through the alignment of brain stem neural coordinates with natural behavioral constraints.
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Arjun, Tan. "From the Pear-shape of the Earth to a Tetrahedroid-shape of the Earth." APPLIED SCIENCE PERIODICAL XXVI, no. 4, November 2024 (2024): 15–23. https://doi.org/10.5281/zenodo.14802427.
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<em>The notion of the ‘Pear-shape of the Earth’ is widely known to the public at large. However, a similar concept called the ‘Tetrahedroid-shape of the Earth’, is not. This concept was recently revived by Mentock, who argued that the tetrahedroid Earth was more appropriate than the pear-shaped Earth. In this study, we construct three model orientations of the tetrahedron within a circumscribed spherical Earth to see which orientation best locates the geoid highs with its four vertices. In the first model (Model A), one vertex is situated at the North Pole, a second on the Greenwich meridional plane and the two others at azimuthal angles of 120° and 240° respectively. Two other models are generated from Model A to better locate the vertices with the geoid highs. The method consists of converting the spherical coordinates of the vertices to rectangular coordinates; then rotating the coordinates system by a desired angle; and finally, converting the new rectangular coordinates back to the spherical coordinates. The origin of the rectangular coordinate system is at the center of the Earth, with z-axis pointing towards the North Star, the x-axis lying in the Greenwich meridional plane, and y-axis fixed by the right-hand rule. Model B is created by rotating the coordinate system about the y-axis counter-clockwise by -20°; and Model C is created by rotating the coordinate system about the x-axis counter-clockwise by -20°. The locations of the vertices in Models B and C show improved agreements with the geoid highs.</em>
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Fuh, Jon‐Shen, Brahmananda Panda, and David A. Peters. "Assembly of Finite‐Element Helicopter Subsystems with Large Relative Rotations." Journal of the American Helicopter Society 35, no. 2 (1990): 60–68. http://dx.doi.org/10.4050/jahs.35.60.
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A general finite‐element procedure is presented for modeling rotorcraft undergoing elastic deformations in addition to large rigid body motions with respect to inertial space. Special attention is given to the coupling of the rotor and fuselage subsystems subject to large relative rotations. Initially, the rotor and fuselage subsystems are assembled separately as small‐rotation finite‐element models in a moving coordinate system. In order to handle large rigid body rotations, the coordinate systems are tied to the structure using one of several alternate constraint methods. Finally, the equations which allow large rotations are constrained together using a rotating to nonrotating transformation which allows rotor azimuth angle as a degree of freedom. The resulting system of equations, which has not been implemented, is applicable to both helicopter trim and large angle maneuver analyses.
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Shabana, Ahmed A., and Aki M. Mikkola. "Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity." Journal of Mechanical Design 125, no. 2 (2003): 342–50. http://dx.doi.org/10.1115/1.1564569.
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A large rigid body rotation of a finite element can be described by rotating the axes of the element coordinate system or by keeping the axes unchanged and change the slopes or the position vector gradients. In the first method, the definition of the local element parameters (spatial coordinates) changes with respect to a body or a global coordinate system. The use of this method will always lead to a nonlinear mass matrix and non-zero centrifugal and Coriolis forces. The second method, in which the axes of the element coordinate system do not rotate with respect to the body or the global coordinate system, leads to a constant mass matrix and zero centrifugal and Coriolis forces when the absolute nodal coordinate formulation is used. This important property remains in effect even in the case of flexible bodies with slope discontinuities. The concept employed to accomplish this goal resembles the concept of the intermediate element coordinate system previously adopted in the finite element floating frame of reference formulation. It is shown in this paper that the absolute nodal coordinate formulation that leads to exact representation of the rigid body dynamics can be effectively used in the analysis of complex structures with slope discontinuities. The analysis presented in this paper also demonstrates that objectivity is not an issue when the absolute nodal coordinate formulation is used due to the fact that this formulation automatically accounts for the proper coordinate transformations.
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Dong, Shidu. "Vision Measurement Scheme Using Single Camera Rotation." ISRN Machine Vision 2013 (June 5, 2013): 1–7. http://dx.doi.org/10.1155/2013/874084.
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We propose vision measurement scheme for estimating the distance or size of the object in static scene, which requires single camera with 3-axis accelerometer sensor rotating around a fixed axis. First, we formulate the rotation matrix and translation vector from one coordinate system of the camera to another in terms of the rotation angle, which can be figured out from the readouts of the sensor. Second, with the camera calibration data and through coordinate system transformation, we propose a method for calculating the orientation and position of the rotation axis relative to camera coordinate system. Finally, given the rotation angle and the images of the object in static scene at two different positions, one before and the other after camera rotation, the 3D coordinate of the point on the object can be determined. Experimental results show the validity of our method.
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Norouzi, Hamed, and Davood Younesian. "Forced Vibration Analysis of Spinning Disks Subjected to Transverse Loads." International Journal of Structural Stability and Dynamics 15, no. 03 (2015): 1450049. http://dx.doi.org/10.1142/s0219455414500497.
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Forced vibration of a rotating disk subjected to a stationary transverse load is studied in this paper. Time and frequency responses are obtained and effects of the rotating speed on the natural frequencies are evaluated. Finite element method (FEM) is employed as the solution technique and natural frequencies are obtained for different speeds. Forced vibration is then considered and disk responses are determined using the Galerkin method. The solution is determined in two different coordinate systems. In the first one, the disk is assumed to be rotating in an inertial coordinate system, while in the second coordinate system, a rotating peripheral force is applied on a stationary disk. The objective here in this paper is to compare the two modeling scenarios and is to find limiting range of the rotational speed for employing the stationary coordinate system.
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Fukushima, Toshio. "Coordinate system in general relativity." Symposium - International Astronomical Union 128 (1988): 105–6. http://dx.doi.org/10.1017/s0074180900119357.
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The proper reference frame comoving with a system of mass-points is defined as a general relativistic extension of the relative coordinate system in the Newtonian mechanics. The coordinate transformation connecting this and the background coordinate systems is presented explicitly in the post-Newtonian formalism. The conversion formulas of some physical quantities caused by this coordinate transformation are discussed. The concept of the rotating coordinate system is reexamined within the relativistic framework. A modification of the introduced proper reference frame named the Natural Coordinate System (NCS) is proposed as the basic coordinate system in the astrometry. By means of the concept of the natural coordinate system, the relation between the solar system barycentric coordinate system and the terrestrial coordinate system is given explicitly. To illustrate the concept of NCS, we quote in the following the definition of the non-rotating NCS comoving with the Earth, i.e. the Terrestrial Coordinate System (TCS) (Fukushima et al., 1986a, 1986b):1) Consider a fictitious spacetime with the metric obtained by subtracting the direct terms due to the Earth from the true metric in the solar system Barycentric Coordinate System (BCS).2) The time coordinate axis of the TCS is defined as the worldline of the geocenter, i.e. the timelike geodesic of the geocenter in the above ficititious spacetime.3) The unit of time in the TCS, terrestrial second sT, is defined as the unit of time in the BCS, barycentric second, multiplied by a certain factor so that there exist periodic differences only between the time coordinate of any event in the TCS, i.e. TDT, and the corresponding time coordinate in the BCS, i.e. TDB.4) The space coordinate axes of the TCS are defined as three geometrically straight lines satisfying that they and the time coordinate axis of the TCS are orthogonal to each other at the geocenter in the above fictitious spacetime, and that the coordinate triad constructed by them is symmetric.5) The unit of length in the TCS, terrestrial meter mT, is defined as the length so that c = 299792458 mT/sT.
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Kazachkov, Ivan V. "Stability Analysis for Complex Rotational Flow." WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS 16 (August 10, 2021): 62–72. http://dx.doi.org/10.37394/232011.2021.16.7.
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Based on the earlier developed mathematical model of the complex flow due to the double rotations in two perpendicular directions, the stability analysis is performed in the paper. The Navier-Stokes equations are derived in the coordinate system rotating around the two perpendicular different axes, the vertical one of them is arranged on some distance from the other axis of rotation, the horizontal axis is directed along the tangential line to the circle of the vertical rotation. The two centrifugal and Coriolis forces create the unique features in high oscillating flow, with localities of the stretched liquid, due to their action varying by the circumferential cylindrical coordinate in the channel flow. Stability analysis for the complex rotational flow under double rotations creating strongly varying mass forces and stretching of the liquid is considered at first
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BINI, DONATO, LUCA LUSANNA, and BAHRAM MASHHOON. "LIMITATIONS OF RADAR COORDINATES." International Journal of Modern Physics D 14, no. 08 (2005): 1413–29. http://dx.doi.org/10.1142/s0218271805006961.
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The construction of a radar coordinate system about the world line of an observer is discussed. Radar coordinates for a hyperbolic observer as well as a uniformly rotating observer are described in detail. The utility of the notion of radar distance and the admissibility of radar coordinates are investigated. Our results provide a critical assessment of the physical significance of radar coordinates.
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Li, Yunfeng, Yundong Li, Huabin Wen, and Wenbo Ning. "Dynamical response of a rotating cantilever pipe conveying fluid based on the absolute nodal coordinate formulation." Journal of Mechanics 37 (2021): 359–72. http://dx.doi.org/10.1093/jom/ufab005.
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Abstract A dynamical model of a rotating cantilever pipe conveying fluid is derived based on the absolute nodal coordinate formulation. The free vibration and dynamical response of the system are investigated in this paper. Based on the absolute nodal coordinate method and the extended Lagrangian equation proposed by Irschik for the nonmaterial system, the motion equation of the rotating flexible cantilever pipe conveying fluid is built. The influence of the rotational angular velocity and flow velocity on the natural frequency of the system is analyzed. The critical nondimensional circular frequency of in-plane vibration and critical nondimensional flow velocity are investigated. The static deformation is shown under different flow velocities and angular velocities. The nonlinear transient analyses of a rotating flexible cantilever pipe are completed with the variation of parameters. During the rotation, the Coriolis force of fluid acting on the pipe has a great effect on the static deformation.
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Kadzhaya, I. M., and G. B. Furman. "Zeeman effect in NQR in the rotating coordinate system." Soviet Physics Journal 34, no. 1 (1991): 12–14. http://dx.doi.org/10.1007/bf00914113.
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Chen, Xue-feng, Jian-guo Hu, Yan-sheng Xu, Zhong-ming Xu, and Hong-bo Wang. "Study on Elastic Dynamic Model for the Clamping Mechanism of High-Speed Precision Injection Molding Machine." Shock and Vibration 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/427934.
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This work centered on the double-toggle clamping mechanism with diagonal-five points for the high-speed precise plastic injection machine. Based on Lagrange equations, the differential equations of motion for the beam elements are established, in a rotating coordinate system and an absolute coordinate system, respectively. 43 generalized coordinates and a model matrix for the mechanism are created and some coordinate matrices are derived. By coupling the coordinate transformation and matrix manipulation, a high nonlinear and strong time-variant elastic dynamic model is obtained. Based on the dynamic model, a Kineto-Elasto Dynamics (KED) analysis and a Kineto-Elasto Static (KES) analysis are carried out, respectively. By comparing and analyzing the simulation results of KED and KES, the regularity of elastic vibration of the clamping mechanism in high-speed clamping process has been revealed.
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Filippatos, Angelos, Tino Wollmann, Minh Nguyen, et al. "Design and Testing of a Co-Rotating Vibration Excitation System." Sensors 19, no. 1 (2018): 92. http://dx.doi.org/10.3390/s19010092.
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A vibration excitation system (VES) in a form of an active coupling is proposed, designed and manufactured. The system is equipped with a set of piezoelectric stack actuators uniformly distributed around the rotor axis and positioned parallel to each other. The actuator arrangement allows an axial displacement of the coupling halves as well as their rotation about any transverse axis. Through the application of the VES an aimed vibration excitation is realised in a co-rotating coordinate system, which enables a non-invasive and precise modal analysis of rotating components. As an example, the VES is applied for the characterisation of the structural dynamic behaviour of a generic steel rotor at different rotational speeds. The first results are promising for both stationary and rotating conditions.
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Wei, Yongchao, Chunyan Deng, Xingkun Wu, and Liangzhong Ao. "Three Dimensional Measurement System for the Dynamic Deformation of Aero-engine Blade Profile." International Journal on Artificial Intelligence Tools 29, no. 07n08 (2020): 2040014. http://dx.doi.org/10.1142/s021821302040014x.
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In order to solve the technical problem of three-dimensional profile measurement of aero-engine blades with high speed rotation, an optical dynamic measurement system for aero-engine blades was developed. Firstly, the system is calibrated by the algorithm of spatial truncation phase calibration to establish the index between truncation phase and spatial coordinates. During the measurement, the deformation map of the rotating measured blade is obtained by synchronous projection and snapshot. By using the fast Fourier algorithm, the truncation phase is obtained, and then the profile information of blade can be obtained through the truncation phase and spatial coordinate index. Through the design and construction of the blade simulation platform and dynamic measurement experiment system, the three-dimensional profile data of the blade at different rotating speeds are obtained, compared and analyzed, and then the overall profile deformation law is discovered, which verifies the effectiveness and feasibility of the algorithm. The system can obtain the dynamic profile information of the whole blade completely, and provide innovative technical means for blade design verification and performance analysis.
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Zhao, Jianping, Yong Cheng, Gen Cai, et al. "A Calibration Method for a Self-Rotating, Linear-Structured-Light Scanning, Three-Dimensional Reconstruction System Based on Plane Constraints." Sensors 21, no. 24 (2021): 8359. http://dx.doi.org/10.3390/s21248359.
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This paper proposes a calibration method for a self-rotating, linear-structured-light (LSL) scanning, three-dimensional reconstruction system based on plane constraints. The point cloud of plane target collected by the self-rotating, LSL scanning, 3D reconstruction system should be constrained to the basic principle of the plane equation; it can quickly and accurately calibrate the position parameters between the coordinate system of the LSL module and the coordinate system of the self-rotating, LSL scanning, 3D reconstruction system. Additionally, the transformation equation could be established with the calibrated optimal position parameters. This paper obtains the above-mentioned position parameters through experiments and uses the calibrated self-rotating, LSL scanning, 3D reconstruction system to perform three-dimensional scanning and reconstruction of the test piece. The experimental results show that the calibration method can effectively improve the measurement accuracy of the system.
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Zhang, Jun Li, Yu Ren Li, Long Fei Fu, and Fan Gao. "The Implementation of Permanent Magnet Synchronous Motor Direct Torque Control." Advanced Materials Research 712-715 (June 2013): 2757–60. http://dx.doi.org/10.4028/www.scientific.net/amr.712-715.2757.
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In order to deeply understand the characteristics of the permanent magnet synchronous motor direct torque control method, its mathematical models were established in the two-phase stationary coordinate system, the two-phase synchronous rotating coordinate system, and x-y stator synchronous rotating coordinate system. The implementation process of direct torque control method in varied stator winding connection was analyzed in detail. In order to improve the speed and torque performance of the permanent magnet synchronous motor, the direct torque control block diagram and the space voltage vector selection table were given. Finally, the summary and outlook of reducing torque ripple in the permanent magnet synchronous motor direct torque control methods.
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Lizunov, Petro, and Valentyn Nedin. "The gyroscopic forces influence on the oscillations of the rotating shafts." Strength of Materials and Theory of Structures, no. 105 (November 30, 2020): 223–31. http://dx.doi.org/10.32347/2410-2547.2020.105.223-231.
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The results of numerical investigation of shafts transverse oscillations with account of gyroscopic inertia forces are presented. It is shown what the action and how the gyroscopic forces influence on the transverse oscillations of the shafts during rotation. The study has been done with computer program with a graphical interface that is developed by authors. The process of numerical solution of the differential equations of oscillations of rotating rods using the method of numerical differentiation of rod's bend forms by polynomial spline-functions and the Houbolt time integration method is described. A general block diagram of the algorithm is shown. This algorithm describes the process of repeated (cyclical) solving the system of differential equations of oscillations for every point of mechanical system in order to find the new coordinates of positions of these points in each next point of time t+Dt. The computer program in which the shown algorithm is realized allows to monitor for the behavior of moving computer model, which demonstrates the process of oscillatory motion in rotation. Moreover, the program draws the graphics of oscillations and changes of angular speeds and accelerations in different coordinate systems. Defines the dynamic stability fields and draw the diagrams of found fields. Using this program, the dynamics of a range of objects which are modeled by long elastic rods have been studied. For some objects is shown that on special rotational speeds of shafts with different lengths, in the rotating with shaft coordinate system, the trajectories of center of the section have an ordered character in the form of n-pointed star in time interval from excitation to the start of established circular oscillation with amplitude that harmoniously changes in time. It is noted that such trajectories are fact of the action of gyroscopic inertia forces that arise in rotation.
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Brumberg, V. A. "Relativistic Hierarchy of Reference Systems and Time Scales." International Astronomical Union Colloquium 127 (1991): 36–49. http://dx.doi.org/10.1017/s0252921100063557.
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AbstractRelativistic hierarchy of reference systems (RS) developed in recent years by different authors is examined in detail. Metric expressions and transformation relations for solar system barycentric RS (BRS), heliocentric RS (HRS), Earth-Moon local RS (LRS), geocentric RS (GRS), topocentric RS (TRS)and Earth satellite RS (SRS) may be obtained explicitly in harmonic coordinates of GRT. The time coordinate of any RS involves the corresponding time scale. Particular attention is given to the closed form representation of GRS avoiding expansions in powers of the geocentric coordinates. GRS has been constructed in both versions of dynamically non-rotating GRS (DGRS) or kinematically non-rotating GRS (KGRS). DGRS and KGRS differ in their space axes orientation by the amount of the geodesic precession. Similarly, taking into account the motion of the Sun around the center of the Galaxy one should distinguish between dynamically non-rotating BRS (DBRS) and kinematically non-rotating BRS (KBRS) differing in their space axes orientation by the amount of the galactic precession. Reduction to the galactic time and the galactic space axes may be needed in the nearest future.
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ALBA, DAVID, and LUCA LUSANNA. "CHARGED PARTICLES AND THE ELECTRO-MAGNETIC FIELD IN NONINERTIAL FRAMES OF MINKOWSKI SPACE–TIME II: "APPLICATIONS: ROTATING FRAMES, SAGNAC EFFECT, FARADAY ROTATION, WRAP-UP EFFECT"." International Journal of Geometric Methods in Modern Physics 07, no. 02 (2010): 185–213. http://dx.doi.org/10.1142/s0219887810004051.
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We apply the theory of noninertial frames in Minkowski space–time, developed in the previous paper, to various relevant physical systems. We give the 3 + 1 description without coordinate singularities of the rotating disk and the Sagnac effect, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system. Then we study properties of Maxwell equations in noninertial frames like the wrap-up effect and the Faraday rotation in astrophysics.
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Joh, Chee-Young, and Chong-Won Lee. "Use of dFRFs for Diagnosis of Asymmetric/Anisotropic Properties in Rotor-Bearing System." Journal of Vibration and Acoustics 118, no. 1 (1996): 64–69. http://dx.doi.org/10.1115/1.2889636.
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The diagnostic method, which utilizes the dFRFs defined in the stationary and rotating coordinate systems, is tested with a laboratory flexible rotor-bearing system, in order to verify its effectiveness in detection of the asymmetry in shaft and the anisotropy in stator. The experimental results indicate that the dFRFs can be effectively used for the diagnosis of anisotropy and/or asymmetry in rotor systems by the investigation of two kinds of dFRF estimates using the complex input and output signals defined in the stationary and rotating coordinate systems.
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Lizunov, Petro, and Valentyn Nedin. "Transmission shafts vibrations in transient rotating modes." Strength of Materials and Theory of Structures, no. 110 (June 26, 2023): 229–37. http://dx.doi.org/10.32347/2410-2547.2023.110.229-237.
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The paper presents the investigation results of the transmission shaft dynamic behavior in transient modes of motion with change of the rotational speeds. Such modes occur during the transmission shaft transmits torque from engine to executive device. This process can be accompanied by vibration with change of frequency and amplitude of shaft oscillation. Therefore, the question of studying the dynamic behavior of such systems with identifying the impact of rotational speeds changing on them is relevant. In this regard, the study was done by developed software, in which a technique of computer simulation of the oscillating motion of considerable rotating rods under the action of inertia forces is implemented. Such software gives the possibility to model the oscillatory motion of rotating rods and determine the parameters by which the dynamic stability loss of the studying system can occur. Using this software, the diagrams of rod oscillating motion of the rotating shaft were drawn for definite parameters of the considered system. The process of oscillation is considered in space. The mathematical model of transverse oscillations is described by system of differential equations in rotating coordinate system that is tied to the shaft, but diagrams of oscillations is shown in inertial coordinate system. It is shown that when the speed of rotation changes, namely at the time interval of its increase, this process continues with growth of oscillation frequency during the acceleration time. Also shown that the amplitude of oscillations increases, too. After pass to next constant speed of rotation, the frequency of oscillations, as shown in diagrams, decreases back. Such increase of oscillation frequency during the acceleration can lead to undesirable consequences of destructive nature.
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ALBA, DAVID, and LUCA LUSANNA. "GENERALIZED RADAR 4-COORDINATES AND EQUAL-TIME CAUCHY SURFACES FOR ARBITRARY ACCELERATED OBSERVERS." International Journal of Modern Physics D 16, no. 07 (2007): 1149–86. http://dx.doi.org/10.1142/s021827180701064x.
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All existing 4-coordinate systems centered on the world-line of an accelerated observer are only locally defined, as for Fermi coordinates both in special and general relativity. As a consequence, it is not known how non-inertial observers can build equal-time surfaces which (a) correspond to a conventional observer-dependent definition of synchronization of distant clocks, and (b) are good Cauchy surfaces for Maxwell equations. Another type of coordinate singularities generating the same problems are those connected to the relativistic rotating coordinate systems used in the treatment of the rotating disk and the Sagnac effect. We show that the use of Hamiltonian methods based on 3+1 splittings of space–time allows one to define as many observer-dependent globally defined radar 4-coordinate systems as nice foliations of space–time with space-like hyper-surfaces admissible according to Møller (for instance, only the differentially rotating relativistic coordinate system, but not the rigidly rotating ones of non-relativistic physics, are allowed). All these conventional notions of an instantaneous 3-space for an arbitrary observer can be empirically defined by introducing generalizations of the Einstein ½ convention for clock synchronization in inertial frames. Each admissible 3+1 splitting has two naturally associated congruences of time-like observers: as a consequence every 3+1 splitting gives rise to non-rigid non-inertial frames centered on any one of these observers. Only for Eulerian observers are the simultaneity leaves orthogonal to the observer world-line. When there is a Lagrangian description of an isolated relativistic system, its reformulation as a parametrized Minkowski theory allows one to show that all the admissible synchronization conventions are gauge equivalent, as also happens in the canonical metric and tetrad gravity, where, however, the chrono-geometrical structure of space–time is dynamically determined. The framework developed in this paper is not only useful for a consistent description of the rotating disk, but is also needed for the interpretation of the future ACES experiment on the synchronization of laser-cooled atomic clocks and for the synchronization of the clocks on the three LISA spacecrafts.
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Zhang, Jiangang, Xitong Zhang, Ningning Wang, Haihu Liu, and Guang Xi. "Lattice Boltzmann modeling of particle dynamics in rotating coordinate system." Physics of Fluids 33, no. 12 (2021): 123316. http://dx.doi.org/10.1063/5.0075177.
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SAIFULIN, Ruslan, Evgenyi KOTOV, Gulmira NURMAGAMBETOVA, and Tomasz PAJCHROWSKI. "Model of an Induction Motor in a Rotating Coordinate System." Trudy Universiteta, no. 4 (2021): 292–97. http://dx.doi.org/10.52209/1609_1825_2021_4_292.
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Paterson, Carl, and Robin Smith. "Helicon waves: propagation-invariant waves in a rotating coordinate system." Optics Communications 124, no. 1-2 (1996): 131–40. http://dx.doi.org/10.1016/0030-4018(95)00636-2.
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Aslanyan L. S. and Ayvazyan A.E. "Spatial dynamics of light quasispin vector in an anisotropic medium with twisting." Optics and Spectroscopy 130, no. 8 (2022): 945. http://dx.doi.org/10.21883/eos.2022.08.54767.3295-22.
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On the Poincar's sphere the spatial evolution of the light's polarization state has been studied quantitatively in the smoothly inhomogeneous anisotropic media with gyrotropy. The main features of the dependence on the sample?s thickness, the gyration vector and the azimuth of the polarization of the incident linearly polarized wave were revealed. An analytical solution of the system of coupled equations relative to Cartesian components of light's wave electric component obtained by transition to rotating coordinate system has been used for analysis. Keywords: Poincar' sphere, polarization evolution, medium with gyrotropy, rotating coordinate system.
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Newton, Paul K., and Houman Shokraneh. "Interacting dipole pairs on a rotating sphere." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2094 (2008): 1525–41. http://dx.doi.org/10.1098/rspa.2007.0209.
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The evolution, interaction and scattering of 2 N point vortices grouped into equal and opposite pairs ( N -dipoles) on a rotating unit sphere are studied. A new coordinate system made up of centres of vorticity and centroids associated with each dipole is introduced. With these coordinates, the nonlinear equations for an isolated dipole diagonalize and one directly obtains the equation for geodesic motion on the sphere for the dipole centroid. When two or more dipoles interact, the equations are viewed as an interacting billiard system on the sphere—charged billiards—with long-range interactions causing the centroid trajectories to deviate from their geodesic paths. Canonical interactions are studied both with and without rotation. For two dipoles, the four basic interactions are described as exchange-scattering , non-exchange-scattering , loop-scattering (head on) and loop-scattering (chasing) interactions. For three or more dipoles, one obtains a richer variety of interactions, although the interactions identified in the two-dipole case remain fundamental.
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Chelnokov, Yu N. "Quaternion Methods and Regular Models of Celestial and Space Flight Mechanic: Using Euler (Rodrigues-Hamilton) Parameters to Describe Orbital (Trajectory) Motion. II: Perturbed Spatial Restricted Three-Body Problem." Известия Российской академии наук. Механика твердого тела, no. 1 (January 1, 2023): 3–32. http://dx.doi.org/10.31857/s0572329922600293.
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The article considers the problem of regularizing the features of the classical equations of celestial mechanics and space flight mechanics (astrodynamics), which use variables that characterize the shape and size of the instantaneous orbit (trajectory) of the moving body under study, and Euler angles that describe the orientation of the used rotating (intermediate) coordinate system or the orientation of the instantaneous orbit, or the plane of the orbit of a moving body in an inertial coordinate system. Singularity-type features (division by zero) of these classical equations are generated by Euler angles and complicate the analytical and numerical study of orbital motion problems. These singularities are effectively eliminated by using the four-dimensional Euler (Rodrigues-Hamilton) parameters and Hamiltonian rotation quaternions. In this (second) part of the work, new regular quaternion models of celestial mechanics and astrodynamics are obtained that do not have the above features and are built within the framework of a perturbed spatial limited three-body problem (for example, the Earth, the Moon (or the Sun) and a spacecraft (or an asteroid)): equations of trajectory motion written in non-holonomic or orbital or ideal coordinate systems, for the description of the rotational motion of which the Euler (Rodrigues-Hamilton) parameters and quaternions of Hamilton rotations are used. New regular quaternion equations of the perturbed spatial restricted three-body problem are also obtained, constructed using two-dimensional ideal rectangular Hansen coordinates, Euler parameters and quaternion variables, as well as using complex compositions of Hansen coordinates and Euler parameters (Cayley-Klein parameters). The advantage of the proposed orbital motion equations constructed using the Euler parameters over the equations constructed using the Euler angles is due to the well-known advantages of the quaternion kinematic equations in the Euler parameters included in the proposed equations over the kinematic equations in the Euler angles included in the classical equations.
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Fukushima, T., M. K. Fujimoto, H. Kinoshita, and S. Aoki. "Coordinate systems in the general relativistic framework." Symposium - International Astronomical Union 114 (1986): 145–68. http://dx.doi.org/10.1017/s0074180900148120.
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The treatment of the coordinate systems is briefly reviewed in the Newtonian mechanics, in the special theory of relativity, and in the general relativistic theory, respectively. Some reference frames and coordinate systems proposed within the general relativistic framework are introduced. With use of the ideas on which these coordinate systems are based, the proper reference frame comoving with a system of mass-points is defined as a general relativistic extension of the relative coordinate system in the Newtonian mechanics. The coordinate transformation connecting this and the background coordinate systems is presented explicitly in the post-Newtonian formalism. The conversion formulas of some physical quantities caused by this coordirate transformation are discussed. The concept of the rotating coordinate system is reexamined within the relativistic framework. A modification of the introduced proper reference frame is proposed as the basic coordinate system in the astrometry. The relation between the solar system barycentric coordinate system and the terrestrial coordinate system is given explicitly.
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Liu, Jin, Fan Zhang, Aleksey Kudreyko, Wenjia Ren, and Haima Yang. "Novel laser tracking measurement system based on the position sensitive detector." Mathematical Biosciences and Engineering 20, no. 1 (2022): 572–86. http://dx.doi.org/10.3934/mbe.2023026.
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<abstract> <p>The rapid development of modern industrial technology has led to the increase of machinery precision. Laser tracking measurement systems represent a novel type of coordinate measurement method, which was developed on the basis of metrology. In this paper, we aim to define a single-station 3D coordinate rotating laser tracking measurement system based on the principle of the space coordinate method. In view of the current architecture and optical path of the system, we establish the ideal mathematical model of the system and derive the coordinate expression for arbitrary measured points in the measurement space. The output response of the photoelectric position detector to the rotating laser and the linearity of the position signal in the detection circuit have been detected via a concrete experiment. A laser tracking system was used to track the target mirror mounted on the coordinate measuring machine measuring spindle. It is shown that stable tracking is possible during the 3D movement of a cat's eye retroreflector if its velocity is 0.2 m/s and the distance to the moving object is 1–2 m. The corresponding velocity of the object must be 0.4 m/s. Our system provides a feasible implementation method for the tracking of the moving target space position.</p> </abstract>
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Davies-Jones, Robert. "Formulas for Parcel Velocity and Vorticity in a Rotating Cartesian Coordinate System." Journal of the Atmospheric Sciences 72, no. 10 (2015): 3908–22. http://dx.doi.org/10.1175/jas-d-15-0015.1.
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Abstract Formulas in an Eulerian framework are presented for the absolute velocity and vorticity of individual parcels in inviscid isentropic flow. The analysis is performed in a rectangular Cartesian rotating coordinate system. The dependent variables are the Lagrangian coordinates, initial velocities, cumulative temperature, entropy, and a potential. The formulas are obtained in two different ways. The first method is based on finding a matrix integrating factor for the Euler equations of motion and a propagator for the vector vorticity equation. The second method is a variational one. Hamilton’s principle of least action is used to minimize the fluid’s absolute kinetic energy minus its internal energy and potential energy subject to the Lin constraints and constraints of mass and entropy conservation. In the first method, the friction and diabatic heating terms in the governing equations are carried along in integrands so that the generalized formulas lead to Eckart’s circulation theorem. Using them to derive other circulation theorems, the helicity-conservation theorem, and Cauchy’s formula for the barotropic vorticity checks the formulas further. The formulas are suitable for generating diagnostic fields of barotropic and baroclinic vorticity in models if some simple auxiliary equations are added to the model and integrated stably forward in time alongside the model equations.
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Bramson, Brian. "Newtonian quantum gravity: axisymmetric, spinning systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2078 (2006): 503–20. http://dx.doi.org/10.1098/rspa.2006.1775.
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Consider a rotating, gravitating system whose mass centre and intrinsic spin define a natural axis of symmetry. A pair of quantum–mechanical polar coordinates, a continuous radial coordinate and an angular coordinate with discrete eigenvalues, are tied to the system's geometry. The gravitational scalar potential generated by the system is a quantum operator that is a function of the two polar coordinates. Exact expressions for the potential's gradient and Laplacian are derived, which involve forward, backward and central differences. The system's binding energy, an integral over Euclidean 3-space, comprises a radial part and an integral over the unit 2-sphere. The latter is shown to amount to a summation over the angular eigenvalues. The result is applied to the Newtonian analogues of Kerr black holes, a class of gravitational potentials with classical, ring singularities. It is shown that any fermionic, Kerr – Newton particle has a finite binding energy. This is remarkable because the classical binding energy is divergent. Furthermore, the binding energy tends to a constant in the limit of large spin.
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Zou, Yanbiao, and Xiangzhi Chen. "Hand–eye calibration of arc welding robot and laser vision sensor through semidefinite programming." Industrial Robot: An International Journal 45, no. 5 (2018): 597–610. http://dx.doi.org/10.1108/ir-02-2018-0034.
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PurposeThis paper aims to propose a hand–eye calibration method of arc welding robot and laser vision sensor by using semidefinite programming (SDP).Design/methodology/approachThe conversion relationship between the pixel coordinate system and laser plane coordinate system is established on the basis of the mathematical model of three-dimensional measurement of laser vision sensor. In addition, the conversion relationship between the arc welding robot coordinate system and the laser vision sensor measurement coordinate system is also established on the basis of the hand–eye calibration model. The ordinary least square (OLS) is used to calculate the rotation matrix, and the SDP is used to identify the direction vectors of the rotation matrix to ensure their orthogonality.FindingsThe feasibility identification can reduce the calibration error, and ensure the orthogonality of the calibration results. More accurate calibration results can be obtained by combining OLS + SDP.Originality/valueA set of advanced calibration methods is systematically established, which includes parameters calibration of laser vision sensor and hand–eye calibration of robots and sensors. For the hand–eye calibration, the physics feasibility problem of rotating matrix is creatively put forward, and is solved through SDP algorithm. High-precision calibration results provide a good foundation for future research on seam tracking.
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Wei, Mao, Hu Xiaochun, Guo Xinjian, and Fan Yu. "A New Concept of Constructing an Accurate Coordinate System From Ground-Based Optical Observations." Symposium - International Astronomical Union 141 (1990): 129–30. http://dx.doi.org/10.1017/s0074180900086484.
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Based on the expected precision and characteristics of the Low Latitude Meridian Circle (LLMC), and the development of CCD astrometry at Yunnan Observatory, an internally consistent and non-rotating optical celestial coordinate system can be set up through observations with the LLMC and CCDs. To obtain this goal, the main work we plan to do are (1) to establish a fundamental stellar reference system of several thousand stars based on the absolute obsrvations with the LLMC; (2) to provide the accurate zero-point corrections for the system from observations of minor planets with the LLMC and CCDs; (3) to determine the precessional rotation of the system with respect to an extragalactic reference system with the LLMC and CCDs, thus transforming the system into a quasi-inertial coordinate system; and (4) to obtain the atmospheric refraciton corrections from the observations with the LLMC.
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Hussien, Ihsan Y., and Shwan F. Mahmood. "FLOW COMPUTATION THROUGH THE PASSAGE BOUNDED BY THE DISH AND SUPPORTS OF THE AWACS." Journal of Engineering 13, no. 01 (2007): 1373–95. http://dx.doi.org/10.31026/j.eng.2007.01.16.
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A numerical method has been introduced to predict the flow through a complex geometry bounded by the fuselage, airfoil supports and rotating dish of the AWACS. The finite volume computational approach is used to carry out all computations with staggered grid arrangement. The (k-ε) turbulence model is utilized to describe the turbulent flow. The solution algorithm is based on the technique of automatic numerical grid generation of curvilinear coordinate system having coordinate lines coincident with the boundary counters regardless of its shape. A general coordinate transformation is used to represent complex geometries accurately and the grid is generated using a system of elliptic partial differential equations technique. The extension of the SIMPLE algorithm for compressible flow is used to obtain the required solution.. The results obtained in the present work show that the moving boundary (the rotating dish) has small effects on the free stream and the effects vanish after short distance away from the lower surface of the rotating dish along the span distance. The results of the proposed numerical method show good agreement with available results obtained in literatures.
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Shang, Chun Min, Dong Mei Zhang, and Xin Ming Zhang. "Rotating Angle Error Influence to Grinding Aspheric Optical Component." Advanced Materials Research 937 (May 2014): 396–99. http://dx.doi.org/10.4028/www.scientific.net/amr.937.396.
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An analyzing rotating error method has presented based on grinding aspheric optical component. A coordinate transform has been done between the new and original coordinates system in view of the rotating error in installing parts, further, the rotating angle error model has deduced between actual curve and theoretical curve. The surface error formulas can be used for variety of rotary conic aspheric curve, depending on the requirements of the parts surface accuracy, quantitative adjustment target can be given in installation and adjustment process before grinding. Based on the rotating error formulas, the calculating example shows that installation angle bas various different influence to surface shape error, the error decreases with the θ decreasing, the surface error is reduced a magnitude accordingly when the angle is reduced to a magnitude. The parts surface error is up from-0.0030mm to-0.0448mm when the rotating angle increasing from 0.1° to 1°. When θ is constant, the surface shape error increases with steepness increasing, installing rotating angle requirement is more stringent for all the large steepness parts.
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JANASZEK, Michał. "EXTENDED CLARKE TRANSFORMATION FOR n-PHASE SYSTEMS." Proceedings of Electrotechnical Institute 63 (December 15, 2016): 5–26. http://dx.doi.org/10.5604/01.3001.0009.4333.
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The article describes how to convert space vectors written in a stationary multiphase system, consisting of a number of phases where n > 3, to the stationary alfa beta orthogonal coordinate system. The transformation of vectors from a stationary n-phase system to the stationary alfa beta orthogonal coordinate system is defined The inverse transformation of a vector written in the orthogonal coordinate system to a stationary n-phase system is also defined. The application of the extended Clarke transformation allows control calculations to be performed in both stationary alfa beta or rotating dq orthogonal coordinate systems. This gives the possibility of performing different control strategies. It has a practical application for drive systems with five-phase, six-phase or dual three-phase motors.
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Hurlebaus, Stefan, and Lothar Gaul. "Calculating the Eigenfrequency of Rotating Acoustic Annulus Inside Labyrinth Seals of Turbomachines." Journal of Engineering for Gas Turbines and Power 127, no. 1 (2005): 178–81. http://dx.doi.org/10.1115/1.1787501.
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This brief note describes a method for calculating the eigenfrequencies of a rotating acoustic air column inside labyrinth seals in turbomachinery. The method is applied to nonrotating air columns as well as to rotating air columns considering a body fixed and a spatial fixed coordinate system.
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Glushko, S. P. "Calculation of Angular Coordinates for the Control System of a Two-Link Industrial Robot Manipulator." Advanced Engineering Research 22, no. 4 (2023): 346–52. http://dx.doi.org/10.23947/2687-1653-2022-22-4-346-352.
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Introduction. One of the tasks of two-link manipulators of industrial robots that move the end-effector along complex trajectories (e.g., robot welder) is associated with the need for careful programming of their movement. For these purposes, manual programming methods or training methods are used. These methods are quite labor-intensive, and they require highly qualified service personnel. A possible solution to the problem of programming the manipulator movements is the simulation of motion with the calculation of angular coordinates. This can help simplify the geometric adaptation of the manipulator in the process of debugging the control program. Therefore, this work aimed at calculating coordinates for programming the control system of a two-link manipulator operating in an angular coordinate system and moving the end-effector along a complex trajectory (e. g., when welding car bodies). Materials and Methods. A two-link robot manipulator designed for cyclically repeating actions in an angular coordinate system was considered. The manipulator consisted of two rotating links: “arm” and “elbow”, which were fixed on the base. The base could rotate, which provided a third degree of freedom. This configuration increased the working area of the manipulator and minimized the area for its placement in production. The movement of the manipulator end-effector could be performed if the kinematics provided its positioning along three Cartesian and three angular coordinates. For software control of robots, including welding robots operating in an angular coordinate system and performing the movement of the end-effector along a complex trajectory, it was required to calculate the angular coordinates of the movement of the end-effector of a two-link articulated manipulator. The robot control system should determine the position of the tool in the angular coordinate system, converting it for user friendliness into x, y and z coordinates of the Cartesian coordinate system. Results. The relations of angular and Cartesian coordinates have been obtained. They can be used for calculating when programming the control system of a two-link manipulator of an industrial robot and organizing the exchange of information between the user and the control system, as well as for checking the accuracy and debugging the movement of the end-effector of an industrial robot through feedback. Discussion and Conclusion. The presented results can be used for software control of a welding robot operating in an angular coordinate system and performing a complex trajectory of the end-effector of a two-link articulated manipulator (gripper). A manipulator operating in an angular coordinate system can be used for contact spot welding when moving the end-effector along a complex trajectory using a positioning or contouring control system. These systems control the movement of the end-effector along a given trajectory with the help of technological commands.
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AWAD, ADEL M. "THE FIRST LAW, COUNTERTERMS AND KERR-AdS5 BLACK HOLES." International Journal of Modern Physics D 18, no. 03 (2009): 405–18. http://dx.doi.org/10.1142/s0218271809014522.
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We apply the counterterm subtraction technique to calculate the action and other quantities of the Kerr-AdS black hole in five dimensions using two boundary metrics: the Einstein universe and the rotating Einstein universe with an arbitrary angular velocity. In both cases, the resulting thermodynamic quantities satisfy the first law of thermodynamics. We point out that the reason for the violation of the first law in previous calculations was that the rotating Einstein universe, used as a boundary metric, was rotating with an angular velocity that depended on the black hole rotation parameter. Using a new coordinate system with a boundary metric that has an arbitrary angular velocity, one can show that the resulting physical quantities satisfy the first law.
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Xing, Shi Tong, Hui Yang, Gang Zheng, and Hai Ma Yang. "The Scattering of Carbon Nanotubes on the Gaussian Beam." Applied Mechanics and Materials 229-231 (November 2012): 171–74. http://dx.doi.org/10.4028/www.scientific.net/amm.229-231.171.
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The first-order approximation description of Gaussian beam in the two parallel Cartesian coordinates was introduced. On the basis of Generalized Mie theory, adopting the relation between the spherical vector wave functions belonging to a rotating Cartesian coordinate system, the electromagnetic fields of Gaussian beam with spherical vector wave functions was deduced at any right coordinates system. Then taking advantage of the cylindrical vector wave functions given by Stratton, the relationship of the spherical vector wave functions expressed in cylindrical vector wave functions was deduced. Finally the electromagnetic fields of infinitely long cylinder was expanded by the cylindrical vector, and the approximate expression of the cylinder to the far zone scattered field was solved.
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Maeda, Hideki, and Jiří Podolský. "Charged rotating BTZ solution revisited: new coordinates and algebraic classifications." Classical and Quantum Gravity 41, no. 11 (2024): 115012. http://dx.doi.org/10.1088/1361-6382/ad422d.
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Abstract We revisit the charged rotating Bañados–Teitelboim–Zanelli (BTZ) solution in the three-dimensional Einstein–Maxwell-Λ system. After the erroneous announcement of its discovery at the end of the original BTZ paper in 1992, the solution was first obtained by Clément in the paper published in 1996 by coordinate transformations from the charged non-rotating BTZ solution. While Clément’s form of the solution is valid only for Λ < 0 , we present a new form for a wider range of Λ by uniform scaling transformations and a reparametrization. We also introduce new coordinates corresponding to the Doran coordinates in the Kerr spacetime, in which the metric and also its inverse are regular at the Killing horizon, and described by elementary functions. Lastly, we show that (i) the algebraic Cotton type of the spacetime is type III on the Killing horizon and type I away from the horizon, and (ii) the energy-momentum tensor for the Maxwell field is of the Hawking–Ellis type I everywhere.
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Zhou, Xue Song, Da Yan Wang, and You Jie Ma. "Deduction of Coordinate Transform for Instantaneous Reactive Power Theory." Applied Mechanics and Materials 641-642 (September 2014): 1219–22. http://dx.doi.org/10.4028/www.scientific.net/amm.641-642.1219.
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By means of building up a three-dimension coordinate system in vector space, the coordinate transform used in instantaneous reactive power theory (IRPT) proposed by H. Akagi is deduced and through spatial coordinate transform two equivalent three-dimension coordinate systems are obtained. After rigorous mathematical deduction the transformation factor for above-mentioned three-dimension coordinate systems is achieved, thus the coefficient deduction for IRPT is solved and the zero-sequence quantity expressing three-phase asymmetrical system is directly obtained. By use of the theory of rotating phasor, the basic principle of instantaneous spatial vector detection method based on IRPT is explained. The authors’ analysis is available for understanding and improvement of this harmonic current detection method.
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Bao, Sheng, Xi Zhang, and Ping Fa Feng. "A Method for Enhancing the Accuracy of On-Machine Inspection for Five-Axis CNC Machines." Advanced Materials Research 426 (January 2012): 351–54. http://dx.doi.org/10.4028/www.scientific.net/amr.426.351.
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The efficiency of manufacturing structural parts can be improved by using on-machine inspection system. It is difficult to separate the valid information from hundreds of points and correct the errors by rotating and translating the workpiece coordinate system directly, especially for five-axis CNC machines. In this paper, a practical method is designed to correct errors easily. By using the least square method, an error reference frame is constructed, and the relation between the compensation values and coordinates of the theoretical points is derived. An example of aircraft structural parts is presented to validate the design.