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Journal articles on the topic 'Vector-coordinate method'

Author: Grafiati

Published: 28 May 2022

Last updated: 31 July 2025

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1

Hathaway, R. J., and J. C. Bezdek. "Grouped coordinate minimization using Newton's method for inexact minimization in one vector coordinate." Journal of Optimization Theory and Applications 71, no. 3 (1991): 503–16. http://dx.doi.org/10.1007/bf00941400.

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2

Yan, Chaode, Wang Guo, and Aimin Li. "THE COORDINATE TRANSFORMATION METHOD OF HIGH RESOLUTION DEM DATA." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences IV-3 (April 23, 2018): 239–44. http://dx.doi.org/10.5194/isprs-annals-iv-3-239-2018.

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Coordinate transformation methods of DEM data can be divided into two categories. One reconstruct based on original vector elevation data. The other transforms DEM data blocks by transforming parameters. But the former doesn’t work in the absence of original vector data, and the later may cause errors at joint places between adjoining blocks of high resolution DEM data. In view of this problem, a method dealing with high resolution DEM data coordinate transformation is proposed. The method transforms DEM data into discrete vector elevation points, and then adjusts positions of points by bi-lin

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3

Ziegler, Franz, and Piotr Borejko. "The Method of Generalized Ray-Revisited." Journal of Mechanics 16, no. 2 (2000): 125–26. http://dx.doi.org/10.1017/s1727719100001696.

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In Section 2, ROTATION OF COORDINATES, the Authors derived the emittance functions in the Weyl-Sommerfeld representation of the wave potentials for a horizontal instantaneous single force from those known for a vertical force from conditions of invariance of the phase and amplitude of plane waves under coordinate rotation, Eqs. (10) ∼ (13) and (18) ∼ (20). That transformation implies the validity of the commonly applied identity for the (force) vector components when rotating the vector in the opposite sense to the coordinate rotation. Further, in the three-dimensional case, the vertical force

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4

Tleuzhanov, A. B., and D. B. Toybazarov. "METHODOLOGICAL FEATURES OF TEACHING THE VECTOR METHOD IN A SCHOOL GEOMETRY COURSE." Vestnik of M. Kozybayev North Kazakhstan University, no. 4 (60) (February 1, 2024): 70–77. http://dx.doi.org/10.54596/2958-0048-2023-4-70-77.

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The article describes the main methodological features of teaching “vector methods” in a school geometry course. In order to increase the efficiency of teaching students the vector method, the connections between the vector method and coordinate methods are analyzed. Examples of solving algebraic and geometric problems using the vector method were shown, showing the scope of vector studies covered in the school course. A brief overview of the history of the development of the vector method is given. The article is recommended for students, school teachers, methodologists and all interested par

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Chelnokov, Yu N., and A. V. Molodenkov. "Quaternion Algorithm for Initial Alignment of Strapdown INS Using the A. N. Tikhonov Regularization Method." Mekhatronika, Avtomatizatsiya, Upravlenie 22, no. 4 (2021): 217–24. http://dx.doi.org/10.17587/mau.22.217-224.

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For the functioning of algorithms of inertial orientation and navigation of strapdown inertial navigation system (SINS), it is necessary to conduct a mathematical initial alignment of SINS immediately before the operation of these algorithms. An efficient method of initial alignment (not calibration!) of SINS is the method of vector matching. Its essence is to determine the relative orientation of the instrument trihedron Y (related to the unit of SINS sensors) and the reference trihedron X according to the results of measuring the projections of at least two non-collinear vectors of the axes

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6

Han, Zhao Lin, and Mao Xing Yuan. "Research on the Vector Measure Method of Coordinate Measuring Machine." Key Engineering Materials 561 (July 2013): 572–75. http://dx.doi.org/10.4028/www.scientific.net/kem.561.572.

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When we use Coordinate Measuring Machine to measure some points of the workpieces, the wrong measuring method will get the poor repeatability and poor reproducibility of measurement results. Now the vector measure of the CMM is a more convenient way. The main principles are analyzed in this paper, and a workpiece is measured for example.

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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

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Jin, Xin, Xin Liu, Jinyun Guo, Maosheng Zhou, and Kezhi Wu. "A Novel All-Weather Method to Determine Deflection of the Vertical by Combining 3D Laser Tracking Free-Fall and Multi-GNSS Baselines." Remote Sensing 14, no. 17 (2022): 4156. http://dx.doi.org/10.3390/rs14174156.

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The bright stars in the clear night sky with weak background lights should be observed in the traditional deflection of the vertical (DOV) measurement so that the DOV cannot be observed under all-weather conditions, which limits its wide applications. An all-weather DOV measurement method combining three-dimensional (3D) laser tracking free-fall and multi-GNSS baselines is proposed in this paper. In a vacuum environment, the 3D laser tracking technique is used to continuously track and observe the motion of free-fall with high frequency and precision for obtaining 3D coordinate series. The plu

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9

Mohazzabi, P. "Tutorial / Article didactique Derivatives of curvilinear coordinate unit vectors: A concise matrix-vector approach." Canadian Journal of Physics 77, no. 12 (2000): 969–83. http://dx.doi.org/10.1139/p99-073.

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The time evolution of a curvilinear coordinate system can be identifiedwith an angular velocity matrix or vector, which contains the complete differentiationrule for all unit coordinate vectors of the curvilinear system, providinga concise method for their computations. When generalized the technique provides a powerful tool fordifferentiation, with respect to any parameter, of not only unit coordinate vectors but any vector that remains fixed in a general orthogonal curvilinear coordinate system. Several curvilinear systems, as well as the normal and tangentialcoordinate system are examined.P

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10

Liu, Hong Jun, Jing Yu Cao, and Ji Bin Zhao. "Research of the Tool Orientation Optimization with Kinematical Constraints." Advanced Materials Research 712-715 (June 2013): 2143–48. http://dx.doi.org/10.4028/www.scientific.net/amr.712-715.2143.

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Drastic change of the tool axis vector for five-axis CNC machining due to avoid global interference, proposed gentle forward, over-backward correction method to optimize the tool axis vector. Established a machine tool axis of rotation angular velocity constraints, and feed coordinate system, through the feed coordinate system adjust the inclination angle and swing angle of the existing tool axis vector to make the tool axis vector change between each adjacent cutter contact points satisfy the machine axis of rotation kinematics constraints and to ensure the continuity of feed rate during proc

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11

Ton, That-Dong, and Min-Fu Hsieh. "A Deadbeat Current and Flux Vector Control for IPMSM Drive with High Dynamic Performance." Applied Sciences 12, no. 8 (2022): 3789. http://dx.doi.org/10.3390/app12083789.

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In this paper, a new deadbeat stator current and flux linkage vector control (DB-CFVC) scheme for interior permanent magnet synchronous machines (IPMSM) is proposed. The control structure is simplified by implementing the proposed flux linkage vector control method in the α-β stationary coordinate. Unlike conventional deadbeat methods, the dynamic performance of the proposed DB-CFVC can be enhanced while voltage command saturation and over output current are avoided. This is achieved with a “reinforced” phase angle reference of stator flux linkage vector by considering rotor speed error and ma

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12

Tang, Xiao, Zhi Zhang, Xueliang Liu, Chang Liu, Ming Jiang, and Yue Song. "A Novel Field-Oriented Control Algorithm for Permanent Magnet Synchronous Motors in 60° Coordinate Systems." Actuators 12, no. 2 (2023): 92. http://dx.doi.org/10.3390/act12020092.

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In this study, a novel field-oriented control (FOC) algorithm was proposed in a 60° coordinate system for controlling the speed of permanent magnet synchronous motors. The FOC algorithm consists of several parts in which the reference currents and feedback currents are transformed into the representation form in a 60° coordinate system. Current regulators are typically used in a 60° coordinate system to directly obtain the reference voltage vector. The proposed FOC structure was established by incorporating the space vector pulse width modulation algorithm in a 60° coordinate system. The propo

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13

Riznyk, V. V. "FORMALIZATION CODING METHODS OF INFORMATION UNDER TOROIDAL COORDINATE SYSTEMS." Radio Electronics, Computer Science, Control, no. 2 (July 7, 2021): 144–53. http://dx.doi.org/10.15588/1607-3274-2021-2-15.

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Contents. Coding and processing large information content actualizes the problem of formalization of interdependence between information parameters of vector data coding systems on a single mathematical platform. Objective. The formalization of relationships between information parameters of vector data coding systems in the optimized basis of toroidal coordinate systems with the achievement of a favorable compromise between contradictory goals. Method. The method involves the establishing harmonious mutual penetration of symmetry and asymmetry as the remarkable property of real space, which a

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14

Zhang, Yudong, Shiying Wang, Claude Esling, et al. "A method to identify dislocations in a known crystal structure by transmission electron microscopy." Journal of Applied Crystallography 44, no. 6 (2011): 1164–68. http://dx.doi.org/10.1107/s0021889811041173.

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This paper proposes a method to identify the type and the Burgers vector of dislocations visualizedviatransmission electron microscopy (TEM). The first step is to determine experimentally the orientation, with respect to the sample holder, of a grain of known crystal structure whose dislocation slip systems have been previously reported. With this determined orientation of the grain, the method calculates the orientation of the projections of the possible dislocation line vectors in the transmission electron microscope screen coordinate system and then compares them with the observed dislocati

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15

BONDAR, Olga, Oksana ZADOROZHNA, and Irina YAKUNINA. "Method of applied direction of mathematics in the aviation institution of higher education." Scientific Bulletin of Flight Academy. Section: Pedagogical Sciences 10 (2021): 13–19. http://dx.doi.org/10.33251/2522-1477-2021-10-13-19.

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The elements of the method of applied direction of mathematics in the aviation institution of higher education developed by us are considered. We use this technique in higher mathematics classes at the Flight Academy of the National Aviation University. Examples of a combination of fundamental mathematical concepts and practical methods of their application are given. We illustrate in detail the coordinate systems used in aviation. Among these systems are mobile and fixed coordinate systems. Problems of higher mathematics related to one or another coordinate system are indicated. For example,

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16

Fallahi, Behrooz, S. Lai, and C. Venkat. "A Finite Element Formulation of a Flexible Slider Crank Mechanism Using Local Coordinates." Journal of Dynamic Systems, Measurement, and Control 117, no. 3 (1995): 329–35. http://dx.doi.org/10.1115/1.2799123.

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The need for higher manufacturing throughput has lead to the design of machines operating at higher speeds. At higher speeds, the rigid body assumption is no longer valid and the links should be considered flexible. In this work, a method based on the Modified Lagrange Equation for modeling a flexible slider-crank mechanism is presented. This method possesses the characteristic of not requiring the transformation from the local coordinate system to the global coordinate system. An approach using the homogeneous coordinate for element matrices generation is also presented. This approach leads t

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17

Xu, Jianhua. "Multi-label Lagrangian support vector machine with random block coordinate descent method." Information Sciences 329 (February 2016): 184–205. http://dx.doi.org/10.1016/j.ins.2015.09.023.

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18

Zheng, Tianyou, Xun Liang, and Run Cao. "The coordinate descent method with stochastic optimization for linear support vector machines." Neural Computing and Applications 22, no. 7-8 (2012): 1261–66. http://dx.doi.org/10.1007/s00521-012-1139-3.

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19

Gulivets, О. А., and S. Y. Oliinyk. "NON-COORDINATE METHOD OF DIFFERENTIALIZATION OF VECTOR FUNCTIONS OF THE SCALARY ARGUMENT." Cherkasy University Bulletin: Physical and Mathematical Sciences, no. 1 (2019): 107–22. http://dx.doi.org/10.31651/2076-5851-2019-1-107-122.

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20

Abuhmaidan, Khaled, Monther Aldwairi, and Benedek Nagy. "Vector Arithmetic in the Triangular Grid." Entropy 23, no. 3 (2021): 373. http://dx.doi.org/10.3390/e23030373.

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Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at le

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21

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 vect

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22

Bhagavatula, Ramkamal, Olu A. Fashesan, Lloyd R. Heinze, and James F. Lea. "A Computational Method for Planar Kinematic Analysis of Beam Pumping Units." Journal of Energy Resources Technology 129, no. 4 (2007): 300–306. http://dx.doi.org/10.1115/1.2790981.

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A generalized computational method for planar kinematic analysis of pumping units is presented in this study. In this method, a local coordinate system is assigned to each body with respect to a fixed global coordinate system. The position of each point in a body is determined by specifying the global translational coordinates of the local coordinate system origin and its rotational angle relative to the global coordinate system. Constraint equations of motion are developed using the vector of coordinates of the connected bodies. These equations are solved to yield the position, velocity, and

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23

Huang, Xing, Tinghao Li, Hua Yi, Yupeng Zhou, Feng Xu, and Yatao Ren. "An Analytical Method for Solar Heat Flux in Spacecraft Thermal Management Under Multidimensional Pointing Attitudes." Energies 18, no. 15 (2025): 3956. https://doi.org/10.3390/en18153956.

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In order to provide a theoretical basis for the thermal analysis and management of spacecraft/payload interstellar pointing attitudes, which are used for inter-satellite communication, this paper develops an analytical method for solar heat flux under pointing attitudes. The key to solving solar heat flux is calculating the angle between the sun vector and the normal vector of the object surface. Therefore, a method for calculating the included angle is proposed. Firstly, a coordinate system was constructed based on the pointing attitude. Secondly, the angle between the coordinate axis vector

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24

Song, Shibin, Xiao Lu, and Haixia Wang. "A Pulsar Vector Observation-Based Link Acquisition Method for X-Ray Communications." International Journal of Aerospace Engineering 2023 (December 14, 2023): 1–9. http://dx.doi.org/10.1155/2023/5541338.

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X-ray communication (XCOM) is an emerging laser communication technique for deep space applications. Traditional link acquisition of laser communications depends significantly on Earth support and shows little autonomy. For XCOM, a pulsar vector observation-based link acquisition method is proposed, which utilizes noncooperative pulsars in deep space as beacons to acquire absolute attitude information and accomplish link acquisition. Firstly, a pulsar vector observation model was established based on the coordinate definition of the X-ray detector and X-ray collimator model. Secondly, a modifi

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25

Ryzhkov, Lev. "Vector methods for determination of rigid body orientation." MECHANICS OF GYROSCOPIC SYSTEMS, no. 41 (December 28, 2022): 102–11. http://dx.doi.org/10.20535/0203-3771412021269249.

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Vector methods for determining the orientation of a rigid body using information about vectors in the reference and body-related coordinate systems are considered. The analysis is based on the least squares method in vector-matrix form. This approach allows us to consider the application of different methods of solving the problem from a single standpoint: matrix (using the directional cosine matrix), geometric (using the Gibbs vector), quaternion (using the quaternion of rotation). Numerical evaluation of the accuracy of eight orientation determination algorithms obtained on the basis of thes

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Dong, Ying Hua, Jing Sheng Huang, Mei Yin Liu, and Lei Cao. "Study on Single-Axis Tracking PV System Measurement." Advanced Materials Research 724-725 (August 2013): 185–89. http://dx.doi.org/10.4028/www.scientific.net/amr.724-725.185.

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In this paper, the precision test method of single-axis PV track device is proposed by analyzing generator mechanism of PV module. In the process of the rotation of single-axis track device, the change of corner in space is considered. Suitable coordinate system is built in order to evaluate track device precision which normal vector of PV module and solar direction vector can be decomposed in this coordinate system. Meanwhile, the comparison on the tracking precision of PV track devices tested by different devices is made and the test uncertainty is researched as well. Experimental results ve

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Liang, Chao, and Xueshuang Xiang. "Convergence of an Anisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems." Numerical Mathematics: Theory, Methods and Applications 9, no. 3 (2016): 358–82. http://dx.doi.org/10.4208/nmtma.2016.m1505.

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AbstractThe anisotropic perfectly matched layer (APML) defines a continuous vector field outside a rectangle domain and performs the complex coordinate stretching along the vector field. Inspired by [Z. Chen et al., Inverse Probl. Imag., 7, (2013):663–678] and based on the idea of the shortest distance, we propose a new approach to construct the vector field which still allows us to prove the exponential decay of the stretched Green function without the constraint on the thickness of the PML layer. Moreover, by using the reflection argument, we prove the stability of the PML problem in the PML

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28

Damaskinos, Georgios, Celestine Mendler-Dünner, Rachid Guerraoui, Nikolaos Papandreou, and Thomas Parnell. "Differentially Private Stochastic Coordinate Descent." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 8 (2021): 7176–84. http://dx.doi.org/10.1609/aaai.v35i8.16882.

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In this paper we tackle the challenge of making the stochastic coordinate descent algorithm differentially private. Compared to the classical gradient descent algorithm where updates operate on a single model vector and controlled noise addition to this vector suffices to hide critical information about individuals, stochastic coordinate descent crucially relies on keeping auxiliary information in memory during training. This auxiliary information provides an additional privacy leak and poses the major challenge addressed in this work. Driven by the insight that under independent noise additio

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29

Kharchenko, Yevhen. "Construction of a Plane From an Angular Vector." Journal of Mathematics Research 12, no. 2 (2020): 45. http://dx.doi.org/10.5539/jmr.v12n2p45.

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The procedure of constructions of a plane from an angular vector in a rectangular coordinate system has been described. The method of creating of an angular vector from two rectilinear vectors has been considered. The property of equality of angular vectors has been described.

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30

Hu, Wenxue, Jiannan Chi, Jiahui Liu, and Zuoyun Yang. "A Novel Method for Space Circular Target Detection in Machine Vision." Sensors 22, no. 3 (2022): 769. http://dx.doi.org/10.3390/s22030769.

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Computer-vision-based space circular target detection has a wide range of applications in visual measurement, object detection, and other fields. The space circular target is projected into an ellipse in the camera for localization. Traditional methods based on monocular vision use a precise calculation model to calculate the center coordinate and normal vector of the space circular target according to the image’s elliptic parameters. However, this accurate calculation method has the disadvantage of poor anti-interference ability in practical application. Aiming at the shortcomings of the abov

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31

Zheng, Yanfeng, Hua-Ping Wan, Jingyao Zhang, Chao Yang, Yaozhi Luo, and Makoto Ohsaki. "Local-Coordinate Representation for Spatial Revolute Clearance Joints Based on a Vector-Form Particle-Element Method." International Journal of Structural Stability and Dynamics 21, no. 07 (2021): 2150093. http://dx.doi.org/10.1142/s0219455421500930.

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Previously, the contact states between the bearing and journal of a spatial revolute joint (SRJ) with both axial and radial clearances were solved in the global coordinate system (GCS), which is complex and requires iterations. In this paper, a local-coordinate representation for the SRJs with clearance is combined with a vector-form particle-element method, i.e. finite particle method (FPM), to provide a more practical means for evaluation of the dynamic effects due to clearance. Firstly, the fundamentals of the FPM for analysis of spatial mechanisms are briefed. Then, a local-coordinate repr

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32

Dmitrenko, A. A., S. Y. Sedyshev, Y. У. Kuleshov, and A. A. Bogatyrev. "Calculation of spatial target coordinates in range-difference passive radars by the Levenberg – Marquardt method." Doklady BGUIR 18, no. 5 (2020): 35–43. http://dx.doi.org/10.35596/1729-7648-2020-18-5-35-43.

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This article studies and analyzes the results of applying numerical iterative methods for solving nonlinear equation systems (Newton, modified Newton's method, gradient descent, sequential iterations, Levenberg – Marquardt), compiled and used to calculate the rectangular spatial coordinates of radio emission sources in range-difference passive radars of various configurations (incorporating from 3 to 4 receiving points). The aim of the research was to determine the optimal number of receiving points and to select the most effective algorithm for coordinate transformations of the vector of obse

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33

Kuznetsov, B. I., T. B. Nikitina, I. V. Bovdui, K. V. Chunikhin, V. V. Kolomiets, and I. V. Nefodova. "Simplified method for analytically determining the external magnetostatic field of uncertain extended technical objects based on near-field measurements." Electrical Engineering & Electromechanics, no. 3 (May 2, 2025): 65–75. https://doi.org/10.20998/2074-272x.2025.3.10.

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Introduction. An important scientific and technical problem of magnetism of uncertain extended energy-saturated objects - such as naval vessels and submarines is implementation of strict requirements for magnetic silence based on mathematical modeling of magnetic field, adequate to its real measurements. The purpose of the work is to develop a simplified analytical method for determining the external magnetostatic field of extended technical objects with uncertain magnetic field sources based on near-field measurement data using spherical and spheroidal sources in a Cartesian coordinate system

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Lisitsyn, V. M., G. G. Sebryakov, K. V. Obrosov, and V. A. Safonov. "METHOD FOR DETERMINING THE MISALIGNMENT OF OPTICAL-ELECTRONIC AND INERTIAL ORIENTATIONS HELICOPTER SYSTEMS." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 201 (March 2021): 3–11. http://dx.doi.org/10.14489/vkit.2021.03.pp.003-011.

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A unique method for determining the misalignment of the orientation of the instrumental coordinate systems of different posts of the optical-electronic system of a helicopter with each other and with an inertial navigation system is proposed. The method does not require preflight preparation, and is based on processing video information streams generated by thermal imaging and television channels of the optical-electronic system, and using information from an inertial navigation system. The method involves the helicopter performing a special maneuver, which is a rotation of the helicopter at a

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35

Minnaert, Ben, Giuseppina Monti, and Mauro Mongiardo. "Unified Representation of 3D Multivectors with Pauli Algebra in Rectangular, Cylindrical and Spherical Coordinate Systems." Symmetry 14, no. 8 (2022): 1684. http://dx.doi.org/10.3390/sym14081684.

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In practical engineering, the use of Pauli algebra can provide a computational advantage, transforming conventional vector algebra to straightforward matrix manipulations. In this work, the Pauli matrices in cylindrical and spherical coordinates are reported for the first time and their use for representing a three-dimensional vector is discussed. This method leads to a unified representation for 3D multivectors with Pauli algebra. A significant advantage is that this approach provides a representation independent of the coordinate system, which does not exist in the conventional vector perspe

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36

Lin, Cheng Wu, Tian Jiao Liu, and Jun Gui. "Double Closed-Loop Control of the Three-Level Rectifier Based on Synchronous PI Current Decoupling." Applied Mechanics and Materials 385-386 (August 2013): 1179–83. http://dx.doi.org/10.4028/www.scientific.net/amm.385-386.1179.

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This paper analyzes the mathematical model of the three-level PWM rectifier in the three-phase stationary coordinate system and the two-phase synchronous rotating coordinate system. On this basis, the synchronous PI current double closed-loop decoupling control strategy is used to eliminate the impact between the d-q axis and relieve independent control of two axes. In order to simplify the complexity of the vector synthesis, the three-level space vector modulation (SVPWM) algorithm is studied. Transform the three-level space reference vector synthesis to the two-level. The mathematical model

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Everett, L. J., and M. McDermott. "The Use of Vector Techniques in Variational Problems." Journal of Dynamic Systems, Measurement, and Control 108, no. 2 (1986): 141–45. http://dx.doi.org/10.1115/1.3143756.

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A convenient means for applying vector mathematics to variational problems is presented. The total and relative variations of a vector are defined and results which follow from these definitions are developed and proved. These results are then used to express the variation of a functional using vector techniques rather than the classical scalar or matrix techniques. The simple problems of deriving equations of motion for a rigid body and for a rigid double pendulum are presented as examples of the technique. The key advantages of the method are that (1) it allows the investigator who is famili

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38

Didenko, Anton, Vladislav Borisenko, and Jose Leoro. "Load distribution method in helicopter blade multibody dynamics system." E3S Web of Conferences 258 (2021): 09076. http://dx.doi.org/10.1051/e3sconf/202125809076.

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The paper focuses on the loads applied to the helicopter blade cross-sections in the multibody dynamics system. The main objective is to simplify the blade aerodynamics calculation and avoid time-consuming CFD methods. For this reason, the way of computing blade aerodynamics is proposed by using multibody dynamics methods with a linear-elastic blade model. As the primary tool for further research, the MCS Adams software package is selected. Splitting the main rotor blade into a finite number of sections, each having its own average value of installation and coning angles, simplifies the calcul

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Guo, Xiaogang, Zhijie Xu, Jianqin Zhang, Jian Lu, and Hao Zhang. "An OD Flow Clustering Method Based on Vector Constraints: A Case Study for Beijing Taxi Origin-Destination Data." ISPRS International Journal of Geo-Information 9, no. 2 (2020): 128. http://dx.doi.org/10.3390/ijgi9020128.

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Origin-destination (OD) flow pattern mining is an important research method of urban dynamics, in which OD flow clustering analysis discovers the activity patterns of urban residents and mine the coupling relationship of urban subspace and dynamic causes. The existing flow clustering methods are limited by the spatial constraints of OD points, rely on the spatial similarity of geographical points, and lack in-depth analysis of high-dimensional flow characteristics, and therefore it is difficult to find irregular flow clusters. In this paper, we propose an OD flow clustering method based on vec

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Liu, Ping, and Jian Qin Fu. "Modeling Method for Mechanism Configuration of the Articulated Industrial Robot." Advanced Materials Research 694-697 (May 2013): 1696–99. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.1696.

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Modeling method for mechanism configuration of the articulated industrial robot is proposed. Each link of mechanism configuration is modeled by a type of variable coordinate system based on UG system. The variable coordinate system is changed with a type of variable kinematical parameter of the links. Thus the position and direction vector of terminal link by reference to frame at any time can be obtained by using inquiry command in UG system. The typical modeling example of the FANUC articulated industrial robot which possesses 6 rotation freedoms in space is as shown in figure. It is appeara

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UVAROVA, M. N., and S. YU GRISHINA. "THE USE OF THE VECTOR-COORDINATE METHOD IN THE STUDY OF THE DISCIPLINES OF MATHEMATICS AND PHYSICS." Scientific Notes of Orel State University 2, no. 99 (2023): 338–41. http://dx.doi.org/10.33979/1998-2720-2023-99-2-338-341.

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The article discusses the methodological features of using the vector-coordinate method, the formation of interdisciplinary knowledge among students. The authors analyzed the applied component in solving physical problems, fixing the studied mathematical concepts and symbols through the transition from geometric relationships to analytical data.

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Kekre, Dr H. B., Dr Tanuja K. Sarode, and Jagruti K. Save. "An Efficient Method for Similarity Measure in Independent PCA based Classification." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 9, no. 3 (2013): 1099–109. http://dx.doi.org/10.24297/ijct.v9i3.3335.

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The paper presents a new approach of finding nearest neighbor in image classification algorithm by proposing efficient method for similarity measure. Generally in supervised classification, after finding the feature vectors of training images and testing images, nearest neighbor classifier does the classification job. This classifier uses different distance measures such as Euclidean distance, Manhattan distance etc. to find the nearest training feature vector. This paper proposes to use Mean Squared Error (MSE) to find the nearness between two images. Initially Independent Principal Component

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Tan, Shuqiu, Jiahao Pan, Jianxun Zhang, and Yahui Liu. "CASVM: An Efficient Deep Learning Image Classification Method Combined with SVM." Applied Sciences 12, no. 22 (2022): 11690. http://dx.doi.org/10.3390/app122211690.

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Recent advances in convolutional neural networks (CNNs) for image feature extraction have achieved extraordinary performance, but back-propagation algorithms tend to fall into local minima. To alleviate this problem, this paper proposes a coordinate attention-support vector machine-convolutional neural network (CASVM). This proposed to enhance the model’s ability by introducing coordinate attention while obtaining enhanced image features. Training is carried out by back-propagating the loss function of support vector machines (SVMs) to improve the generalization capability, which can effective

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Wang, Haoyu, Lewei Jiang, and Da Xie. "A study of fixed-sun mirror field alignment based on mathematical methods." Highlights in Science, Engineering and Technology 72 (December 15, 2023): 1311–17. http://dx.doi.org/10.54097/vt5qb130.

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Different shapes of heliostat mirrors and different arrangements of mirror fields are important factors affecting the thermal power output of tower-type solar power plants. In this paper, for a regional heliostat mirror field, a coordinate system of heliostat mirror field is established, through which the incident vector of sunlight, normal vector of heliostat mirror plane is calculated, and the mirror coordinate system is transformed to calculate the optical cosine efficiency, and the discrete lattice point method and ray-tracing method are used to calculate the shadow blocking efficiency and

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Luo, Xiangdong. "Construction of electric dyadic Green’s functions in free space based on elliptic cylindrical coordinate system." Journal of Physics: Conference Series 2898, no. 1 (2024): 012005. http://dx.doi.org/10.1088/1742-6596/2898/1/012005.

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Abstract A set of vector wave functions is defined in the elliptic cylindrical coordinate system. These vector wave functions can not only describe the propagation characteristics of electromagnetic waves in the elliptic cylindrical coordinate system but also meet the requirements of the electromagnetic field equation. By studying the orthogonality of these vector wave functions, the free space magnetic dyadic Green function is derived by the Ohm-Rayleigh method. The free space electric dyadic Green function is derived from the magnetic dyadic Green function. The special electromagnetic field

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Wang, Yan, Zhanfeng Li, Guanyu Lin, and Yu Huang. "High-Precision Angle Prediction of Sun for Space Remote Sensing Instrument." International Journal of Aerospace Engineering 2021 (September 30, 2021): 1–9. http://dx.doi.org/10.1155/2021/8733478.

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In order to grasp the timing of sun calibration in advance, this paper introduces a high-precision method to predict the solar angle by using the current broadcast time and orbital instantaneous root of the satellite platform. By calculating the sun’s apparent right ascension and apparent declination, the conversion matrix from the geocentric inertial coordinate system to the orbital coordinate system, and the satellite attitude correction matrix, the sun vector in the satellite body coordinate system is obtained. This method is used to predict the sun angle of a sun synchronous orbit in the s

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Ivanov, Vyacheslav N., and Alisa A. Shmeleva. "Geometric characteristics of the deformation state of the shells with orthogonal coordinate system of the middle surfaces." Structural Mechanics of Engineering Constructions and Buildings 16, no. 1 (2020): 38–44. http://dx.doi.org/10.22363/1815-5235-2020-16-1-38-44.

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The aim of this work is to receive the geometrical equations of strains of shells at the common orthogonal not conjugated coordinate system. At the most articles, textbooks and monographs on the theory and analysis of the thin shell there are considered the shells the coordinate system of which is given at the lines of main curvatures. Derivation of the geometric equations of the deformed state of the thin shells in the lines of main curvatures is given, specifically, at monographs of the theory of the thin shells of V.V. Novozhilov, K.F. Chernih, A.P. Filin and other Russian and foreign scien

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Hahanova, Anna V. "Developing method of vector synthesis deductive logic for computer systems fault analysis." Herald of Advanced Information Technology 5, no. 2 (2022): 102–12. http://dx.doi.org/10.15276/hait.05.2022.8.

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The article is devoted to the development of models and methods for fault analysis for examinate test patterns. Deductive fault simulation of digital devices is the most advanced technology that serves the field of design and testing of modern computer systems. At the same time, fault simulation solves the problem of assessing the quality of the test in the class of single constant defects. However, the computational complexity of obtaining deductive formulas, estimated as n3 , is a rather difficult task for high-dimensional RTL-level functional circuits, so the deductive method is usually use

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Zheng, Rui. "Laser marking method for nonferrous metal casting ingots based on improved RANSAC algorithm." Manufacturing Review 12 (2025): 7. https://doi.org/10.1051/mfreview/2025002.

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Non ferrous metal casting ingots must carry relevant production information, usually using manual pasting of copper coated paper, manual lifting of spray code, and pneumatic marking methods. These methods have a low degree of automation and severe material waste. To this end, genetic algorithm (GA) is used to guide sampling of random sample consensus algorithm (RANSAC) based on probability, and the two are combined for simulation to optimize the shortcomings of RANSAC algorithm in random sampling. On the ground of the optimized RANSAC to fit the plane equation, the normal vector of the plane i

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Zhang, Yu Dong, Shi Ying Wang, Claude Esling, Xiang Zhao, and Liang Zuo. "Determination of Crystallographic Elements (Dislocation and Surface Plane) from Automated TEM Orientation Determination." Materials Science Forum 702-703 (December 2011): 866–71. http://dx.doi.org/10.4028/www.scientific.net/msf.702-703.866.

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Abstract In the present work, we summarized two calculation methods to determine some specific crystallographic elements based on electron diffraction orientation measurements performed by TEM. The first one is to determine the type and the Burgers vector of dislocations for a known crystal structure. The method calculates the orientation of the projections of all the possible dislocation line vectors in the TEM screen coordinate system using the determined crystallographic orientation of the grain and then compares them with the observed ones to identify the observed dislocations. The second

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