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Journal articles on the topic 'Cylindrical coordinate system'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Hadjinicolaou, Maria, and Eleftherios Protopapas. "Eigenfunction Expansions for the Stokes Flow Operators in the Inverted Oblate Coordinate System." Mathematical Problems in Engineering 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/9049131.

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When studying axisymmetric particle fluid flows, a scalar function,ψ, is usually employed, which is called a stream function. It serves as a velocity potential and it can be used for the derivation of significant hydrodynamic quantities. The governing equation is a fourth-order partial differential equation; namely,E4ψ=0, whereE2is the Stokes irrotational operator andE4=E2∘E2is the Stokes bistream operator. As it is already known,E2ψ=0in some axisymmetric coordinate systems, such as the cylindrical, spherical, and spheroidal ones, separates variables, while in the inverted prolate spheroidal coordinate system, this equation acceptsR-separable solutions, as it was shown recently by the authors. Notably, the kernel space of the operatorE4does not decompose in a similar way, since it accepts separable solutions in cylindrical and spherical system of coordinates, whileE4ψ=0semiseparates variables in the spheroidal coordinate systems and itR-semiseparates variables in the inverted prolate spheroidal coordinates. In addition to these results, we show in the present work that in the inverted oblate spheroidal coordinates, the equationE′2ψ=0alsoR-separates variables and we derive the eigenfunctions of the Stokes operator in this particular coordinate system. Furthermore, we demonstrate that the equationE′4ψ=0 R-semiseparates variables. Since the generalized eigenfunctions ofE′2cannot be obtained in a closed form, we present a methodology through which we can derive the complete set of the generalized eigenfunctions ofE′2in the modified inverted oblate spheroidal coordinate system.

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2

Kim, Kun-Woo, Jae-Wook Lee, Jin-Seok Jang, Joo-Young Oh, Ji-Heon Kang, Hyung-Ryul Kim, and Wan-Suk Yoo. "Construction of unwinding equation of motion for thin cable in spherical coordinate system." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 7 (May 11, 2017): 1208–20. http://dx.doi.org/10.1177/0954406217705406.

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The transient-state unwinding equation of motion for a thin cable can be derived by using Hamilton’s principle for an open system, which can consider the mass change produced by the unwinding velocity in a control volume. In general, most engineering problems can be analyzed in Cartesian, cylindrical, and spherical coordinate systems. In the field of unwinding dynamics, until now, only Cartesian and cylindrical coordinate systems have been used. A spherical coordinate system has not been used because of the complexity of derivatives. Therefore, in this study, the unwinding motion of a thin cable was analyzed using a spherical coordinate system in both water and air, and the results were compared with the results in Cartesian and cylindrical coordinate systems. The unwinding motions in the spherical, Cartesian, and cylindrical coordinate systems were nearly same in both water and air. The error related to the total length was within 0.5% in water, and the error related to the maximum balloon radius was also within 0.5 % in air. Therefore, it can be concluded that it is possible to solve the transient-state unwinding equation of motion in a spherical coordinate system.

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3

Dong, Guo Jun, Cheng Shun Han, and Shen Dong. "Solution for Best Fitting Spherical Curvature Radius and Asphericity of Off-Axis Aspherics of Optical Aspheric Surface Component." Key Engineering Materials 364-366 (December 2007): 499–503. http://dx.doi.org/10.4028/www.scientific.net/kem.364-366.499.

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This study aimed to establish the coordinate transformation between the off-axis aspherics coordinate system σ and the axial symmetry aspherics coordinate system σ by transforming coordinates and present the computation models of asphericity in rectangular coordinate system and cylindrical coordinate system respectively. The asphericity expressions in both coordinate systems were applicable to the comparative sphere calculation of Off-axis aspherics with different figures. We selected an Initiation sphere in view of technology, along with equations in a right coordinate system for certain caliber and structure. Then, by numerical computation, we selected the best fitting sphere and simplifed the complex models by choosing a right coordinate system. At last, the solution for asphericity and the best fitting sphere curvature radius of off-axis aspherics were introduced by examples.

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4

Obukhov, A. G., and N. V. Chunikhina. "EQUATION OF CONTINUITY IN THE CYLINDRICAL COORDINATES SYSTEM." Oil and Gas Studies, no. 3 (July 1, 2016): 119–22. http://dx.doi.org/10.31660/0445-0108-2016-3-119-122.

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Sophisticated viscous compressible heat-conducting gases arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the full Navier - Stokes equations to describe such gas flows is advisable to use a cylindrical coordinate system. This paper describes the transformation of the first equation of the full Navier - Stokes equations. The result of the transformation is to write the continuity equation in the cylindrical coordinate system.

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5

Wei, Xiu Ting, Qiang Du, and Jing Cheng Liu. "The Application of UG NX Second Development in Centrifugal Pump Impeller Vane 3D Solid Modeling." Applied Mechanics and Materials 20-23 (January 2010): 1286–91. http://dx.doi.org/10.4028/www.scientific.net/amm.20-23.1286.

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The hydraulic model of the impeller and points of its vane surface given in the cylindrical coordinates, we can not directly use those data to accomplish the 3D solid modeling of the impeller in CAD systems. Based the Access and the UG NX, this paper puts forwards a new method for modeling centrifugal pump impeller vanes and presents the implementing procedure. And the method includes the following steps: 1) defining the data structure of hydraulic models; 2)converting the vane surface data from the cylindrical coordinate system to the cartesian coordinate system; 3)constructing the vane’s working surface and back surface along the axial transversals; 4) accomplishing the impeller’s 3D solid model by UG NX Second Development. The practical application demonstrates that the proposed method can shorten the cycle of impeller modeling and improve the design precision.

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6

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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7

Lei, Xiao Ling, and Bo Tao. "Study on the Diffusion Equations of Water Pollutants in Various Water Areas with Different Waterflow States." Advanced Materials Research 183-185 (January 2011): 1030–34. http://dx.doi.org/10.4028/www.scientific.net/amr.183-185.1030.

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The development and application of the diffusion equations of water pollutants are synthetically discussed. Depending on Cartesian Coordinate system, the water pollutants diffusion equations in different waterflow states are reviewed. And further development of the water pollutants diffusion equations in different waterflow states is extended to Cylindrical Coordinate system and Spherical Coordinate system respectively. This makes the simulating and modeling of water pollutants diffusion much more accurate and convenient in various water areas with different waterflow states by using different coordinate systems.

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8

Khomasuridze, N. "Effective Solution of a Class of Boundary Value Problems of Thermoelasticity in Generalized Cylindrical Coordinates." gmj 11, no. 3 (September 2004): 495–514. http://dx.doi.org/10.1515/gmj.2004.495.

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Abstract A class of static boundary value problems of thermoelasticity is effectively solved for bodies bounded by coordinate surfaces of generalized cylindrical coordinates ρ, α, 𝑧 (ρ, α are orthogonal curvilinear coordinates on the plane and 𝑧 is a linear coordinate). Besides in the Cartesian system of coordinates some boundary value thermoelasticity problems are separately considered for a rectangular parallelepiped. An elastic body occupying the domain Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < 𝑧1}, is considered to be weakly transversally isotropic (the medium is weakly transversally isotropic if its nine elastic and thermal characteristics are correlated by one or several conditions) and non-homogeneous with respect to 𝑧.

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9

Barannikova, D. D., and A. G. Obukhov. "THE THIRD PROJECTION OF THE MOTION EQUATION IN THE CYLINDRICAL COORDINATE SYSTEM." Oil and Gas Studies, no. 1 (March 1, 2017): 109–12. http://dx.doi.org/10.31660/0445-0108-2017-1-109-112.

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Sophisticated viscous compressible heat-conducting gases arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the full Navier-Stokes equations to describe such gas flows is advisable to use a cylindrical coordinate system. This paper describes the transformation of the third projection of the equation of motion of the full Navier-Stokes equations. The result of the transformation is to record the third projection of the equation of motion of a continuous medium in a cylindrical coordinate system.

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10

Wang, Wan-xian. "Expansion of the Green’s function in a cylindrical coordinate system." Quarterly of Applied Mathematics 48, no. 3 (September 1, 1990): 499–501. http://dx.doi.org/10.1090/qam/1074964.

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11

AKIMOTO, Toshio. "Mapping of the Cyclodextrin Cavity Using the Cylindrical Coordinate System." YAKUGAKU ZASSHI 125, no. 12 (December 1, 2005): 971–80. http://dx.doi.org/10.1248/yakushi.125.971.

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12

Barannikova, D. D., and A. G. Obukhov. "THE SECOND PROJECTION OF THE MOTION EQUATION IN THE CYLINDRICAL COORDINATE SYSTEM." Oil and Gas Studies, no. 5 (November 1, 2016): 83–85. http://dx.doi.org/10.31660/0445-0108-2016-5-83-85.

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The complex flows of viscous compressible heat-conducting gas arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the complete Navier-Stokes equations system to describe such gas flows it is advisable to use a cylindrical coordinate system. This paper describes a transformation of the second projection of the motion equation of the complete Navier-Stokes equations system. The result of this transformation is writing of the second projection of the equation of a continuous medium motion in the cylindrical coordinate system.

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13

Mohanty, R. K., Rajive Kumar, and Vijay Dahiya. "Cubic Spline Iterative Method for Poisson’s Equation in Cylindrical Polar Coordinates." ISRN Mathematical Physics 2012 (February 12, 2012): 1–11. http://dx.doi.org/10.5402/2012/234516.

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Using nonpolynomial cubic spline approximation in x- and finite difference in y-direction, we discuss a numerical approximation of O(k2+h4) for the solutions of diffusion-convection equation, where k>0 and h>0 are grid sizes in y- and x-coordinates, respectively. We also extend our technique to polar coordinate system and obtain high-order numerical scheme for Poisson’s equation in cylindrical polar coordinates. Iterative method of the proposed method is discussed, and numerical examples are given in support of the theoretical results.

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14

Nesterovich, N. V., and A. G. Obukhov. "EQUIATION OF ENERGY WITH ALLOWANCE OF EFFECTS OF DISSIPATION IN CYLINDRYCAL COORDINATE SYSTEM." Oil and Gas Studies, no. 5 (November 1, 2017): 109–13. http://dx.doi.org/10.31660/0445-0108-2017-5-109-113.

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Complex flows of a viscous compressible heat-conducting gas in ascending swirling flows have a pro-nounced axial symmetry. Therefore, for the numerical solution of the complete system of Navier - Stokes equations to describe such gas flows, it is desirable to use a cylindrical coordinate system. The paper describes the transformation of the energy equation for a complete system of Navier - Stokes equations with allowance for the dissipative properties of a moving continuous medium. The result of the transformation is the formulation of the energy equation in a cylindrical coordinate system.

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15

Obukhov, A. G., and R. E. Volkov. "FIRST PROJECTION OF THE EQUATION OF MOTION IN THE CYLINDRICAL COORDINATE SYSTEM." Oil and Gas Studies, no. 4 (September 1, 2016): 90–92. http://dx.doi.org/10.31660/0445-0108-2016-4-90-92.

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It is proved that complex flows of the viscous compressible heat-conducting gas, arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the full Navier-Stokes equations for description of such gas flows it are advisable to use a cylindrical coordinate system. This paper describes the transformation of the first projection of the equation of motion of the full Navier-Stokes equations system. The result of the transformation is a record of the first projection of the equation of a continuous medium motion in the cylindrical coordinate system.

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16

Abdelwahed, Hesham G. "Properties of Damped Cylindrical Solitons in Nonextensive Plasmas." Zeitschrift für Naturforschung A 73, no. 10 (October 25, 2018): 905–10. http://dx.doi.org/10.1515/zna-2018-0157.

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AbstractWave properties of damped solitons in a collisional unmagnetised four-component dusty fluid plasma system containing nonextensive distributed electrons, mobile ions and negative-positive dusty grains have been examined. The reductive perturbation (RP) analysis is used under convenient geometrical coordinate transformation; we have derived three-dimensional damped Kadomtsev-Petviashvili (3D-CDKP) equation to study dissipative dust ion acoustic (DIA) mode properties. It is found that the properties of damped cylindrical solitons in nonextensive plasmas in cylindrical coordinates are obtained. The effects of collisional parameters on damped soliton pulse structures are studied. More specifically, the cylindrical geometry with the time on solitary propagation is examined. This investigation may be viable in plasmas of Earth’s mesosphere.

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17

Legkostup, V. V., and V. E. Markevich. "Methodology of determining of the transfer function of engagement kinematics of accelerations of an aircraft and its elliptic coordinates used for thr guidance based on time difference of arrival." «System analysis and applied information science», no. 1 (April 26, 2021): 12–20. http://dx.doi.org/10.21122/2309-4923-2021-1-12-20.

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This paper discusses the problem of determining a kinematics (in terms of transfer function, as far as possible) of parameters of the motion of an aircraft expressed in the curvilinear coordinate system and control accelerations expressed in a rectangular coordinate system. Examples of curvilinear coordinate systems using in practice can be polar, biangular, two-center bipolar, elliptic, parabolic cylindrical, spherical, ellipsoidal, coordinate systems. A technique for obtaining a kinematic link for the control problem of an unmanned aerial vehicle in the elliptic coordinate system was described. It allowed to obtain simpler view of the kinematic link which could provide navigation an aircraft along the hyperbola deriving from the time difference of arrival navigation system. It can. As a result, it is possible to reduce the number of the navigation radio beacons.

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18

Zheng, Guowu, and Kangshen Chen. "The studies of cylindrical microstrip line with the FD-TD method in cylindrical coordinate system." International Journal of Infrared and Millimeter Waves 13, no. 9 (September 1992): 1421–31. http://dx.doi.org/10.1007/bf01009998.

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19

Matveev, A. Yu, I. P. Gavrilova, A. V. Kovyazin, and E. V. Brovkov. "CONSTRUCTION OF FRAME GEODETIC NETWORK FOR ENGINEERING SURVEY OF RAIL TRANSPORT FACILITIES." Engineering survey 12, no. 5-6 (August 16, 2018): 58–71. http://dx.doi.org/10.25296/1997-8650-2018-12-5-6-58-71.

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Increasing the speed of trains along railroad tracks and the development of satellite geodetic technologies put forward new requirements for the production of the engineering survey at the rail transport facilities. Ensuring the safety of high-speed traffic is directly related to the accuracy of determining the coordinates and heights of the reference geodetic networks created for the design, construction, reconstruction and operation of railways. A large length of Railways in Russia requires solving a number of problems in the conditions of increasing the accuracy of determining the coordinates. High-speed route crosses several regions with its own local coordinate systems. Simplify the design and cadastral works and reduce to minimum linear distortions when performing geodetic measurements, allows the creation of a local coordinate system, unified for the entire route. The technology of creating a unified local coordinate system for linear objects passing through several 6-degree zones in the projection of GaussKruger and objects located at an angle to the axial Meridian is considered on the example of the railway Moscow — Saint-Petersburg — Vyborg. At the basis of a unified local system of the object, it is proposed to use an oblique cylindrical cartographic projection. Implemented a coordinate system in the form of the software, allowing to perform transformations between the local system, the world and state coordinate systems. The paper also considers the practical experience of creating a high-precision geodetic reference network for a high-speed railway traffic route, which can be used for various linear engineering structures. The created frame network can serve as a geodetic base for performing laser scanning, monitoring facilities, creating geoinformation systems and solving other problems that arise during the operation of an engineering facility.

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20

Mehta, Nirajkumar. "FDM for Alumina based Induction Furnace Wall using Cylindrical Coordinate System." International Journal for Research in Applied Science and Engineering Technology 8, no. 2 (February 29, 2020): 338–46. http://dx.doi.org/10.22214/ijraset.2020.2051.

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21

Luo Shi-Rong and Lyu Bai-Da. "Generalized M2 factor of truncated beams in the cylindrical coordinate system." Acta Physica Sinica 53, no. 1 (2004): 82. http://dx.doi.org/10.7498/aps.53.82.

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22

Iwatsuki, M., and N. Okiyama. "A new formulation of visual servoing based on cylindrical coordinate system." IEEE Transactions on Robotics 21, no. 2 (April 2005): 266–73. http://dx.doi.org/10.1109/tro.2004.837242.

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23

Shi, Xungang, and Lixin Wu. "A spectral method for unbounded flow in a cylindrical coordinate system." ESAIM: Proceedings 1 (1996): 577–85. http://dx.doi.org/10.1051/proc:1996031.

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24

Wang, Wan-xian. "The potential for a homogeneous cylinder in a cylindrical coordinate system." Quarterly of Applied Mathematics 49, no. 1 (January 1, 1991): 163–71. http://dx.doi.org/10.1090/qam/1096238.

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25

Guo-xiang, Huang, Lou Sen-yue, and Dai Xian-xi. "Model Equations and Their Solitary Wave Solutions in Cylindrical Coordinate System." Communications in Theoretical Physics 13, no. 1 (January 1990): 103–7. http://dx.doi.org/10.1088/0253-6102/13/1/103.

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26

Li, Hui, Li-zhu Hao, Xiao-bo Chen, and Hui-long Ren. "The computation of forward speed Green function in cylindrical coordinate system." European Journal of Mechanics - B/Fluids 69 (May 2018): 76–86. http://dx.doi.org/10.1016/j.euromechflu.2018.01.005.

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27

Fukagata, Koji, and Nobuhide Kasagi. "Highly Energy-Conservative Finite Difference Method for the Cylindrical Coordinate System." Journal of Computational Physics 181, no. 2 (September 2002): 478–98. http://dx.doi.org/10.1006/jcph.2002.7138.

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28

Sárközi, Réka, Péter Iványi, and Attila Béla Széll. "Formex algebra adaptation into parametric design tools and rotational grids." Pollack Periodica 15, no. 2 (August 2020): 152–65. http://dx.doi.org/10.1556/606.2020.15.2.14.

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Abstract:This paper describes the adaptation of the formex configuration processing to the computer program Grasshopper 3D and focuses on the applied mathematical solutions. Formex algebra is a mathematical system, primarily used for planning structural systems like truss-grid domes and vaults, together with the programming language Formian. The goal of the research is to allow architects to plan truss-grid structures easily with parametric design tools based on the versatile formex algebra mathematical system. To produce regular structures, coordinate system transformations are used. Owing to the abilities of the parametric design software, it is possible to apply further modifications on the structures and gain special forms. The paper covers the basic dome types, and it introduces additional dome-based structures using special coordinate-system solutions based on a spherical coordinate system, vault structures and their modifications based on a cylindrical coordinate system and circular structures and their modifications based on polar coordinates. Moreover two rotational grid tools are introduced, which uses coordinate system transformations on a unique way to create surfaces of revolutions based on the given generating curve and create grid structures on these surfaces. It also describes the solution technique to implement the triangular grid version of every one of these tools based on diamatic domes. The adaptation of formex algebra and the parametric workflow of Grasshopper together give the possibility of quick and easy design and optimization of special truss-grid domes.

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Xu, Xiu Long, Zhen Ying Xu, Ran Ran Xu, Jia Kun Jiang, and Xiao Dong Guo. "A Real-Time Location and Reset Method of Cylindrical FPSO." Key Engineering Materials 464 (January 2011): 103–6. http://dx.doi.org/10.4028/www.scientific.net/kem.464.103.

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In this paper, a real-time location and reset method of cylindrical FPSO is presented based on GPS. In this method, the coordinate system of PFSO is determined by three GPS locators installed on the platform. Then, through coordinate transformation according to the marine engineering coordinate system established before, we can get the displacement and the orientation of FPSO, so as to achieve its real-time location. Finally, this displacement and orientation information is assigned to relative thrusters, which are evenly distributed with an angle 22.5°on both sides of the “+” and “-” X and Y axis, according to the calculating results of the optimization model.

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Park, Jae Wan, Seok Jin Lee, and Chil Woo Lee. "Upper-Body Pose Recognition Using Cylinder Pattern Model." Applied Mechanics and Materials 571-572 (June 2014): 781–87. http://dx.doi.org/10.4028/www.scientific.net/amm.571-572.781.

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In this paper, we propose cylindrical coordinate system which can analyze upper-body pose of the depth images correctly. This method extracts the part of human body from the depth images, and we configure the center of the part as origin of the cylindrical coordinate system. And we configure multi-layered cylinders based on the origin, then, we can analyze pose using the pattern which is crossed depth images namely cylinders and upper-body. Since the crossed point of the cylinders and upper-body is obtained as brightness values, it can extract to convert feature vector of the cylindrical coordinate system. The extracted feature vectors of the cylindrical coordinate system are presented to feature space of circular and are categorized pose patterns. The pose patterns are learned using average value of the feature vectors, and the pose patterns are categorized as pose to compare to pre-defined pose patterns using Euclidean distance. In this paper, we applied dynamic cylinder model to the region of the upper-body, so we can be classified as head, body and arms through simple computation, and to extract pose information is possible effectively. In this paper, the effect that can get through proposing pose estimation method is as following. At the first, pose estimation is possible by using only minimum feature points which apply cylinder model in region that connect human's torso, head and arms. The second is as following. When we obtain the feature points, because of applying cylinder model, we can extract user's feature points and angle of rotation easily. And in this paper, we don't consider the status of the user's body is titled using only the upper-body poses of the state rightly standing pose toward the front. Because it has disadvantage which cannot distinguish between changes according to the tile of the torso, but we can detect the vectors of the hands and arm using cylindrical coordinate system. Therefore, in the future, we will study to be able to recognize the pose in the tilted status.

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Zhu, Da-Wei, Hai-Lin Chen, Zi-Yu Pan, Bo-Ao Xu, and Bin Chen. "An Efficient Laguerre-Based FDTD Iterative Algorithm in 3D Cylindrical Coordinate System." International Journal of Antennas and Propagation 2019 (September 25, 2019): 1–14. http://dx.doi.org/10.1155/2019/9542976.

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Here an efficient Laguerre-based finite-difference time-domain iterative algorithm is proposed. Different from the previously developed iterative procedure used in the efficient FDTD algorithm, a new perturbation term combined with the Gauss–Seidel iterative procedure is introduced to form the new Laguerre-based FDTD algorithm in the 3D cylindrical coordinate system. Such a treatment scheme can reduce the splitting error to a low level and obtain a good convergence; in other words, it can improve the efficiency and accuracy than other algorithms. To verify the performance of the proposed algorithm, two scattering numerical examples are given. The computation results show that the proposed algorithm can be better than the ADI-FDTD algorithm in terms of efficiency and accuracy. Meanwhile, the proposed algorithm is extremely useful for the problems with fine structures in the 3D cylindrical coordinate system.

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Campos, L. M. B. C., and P. J. S. Gil. "On spiral coordinates with application to wave propagation." Journal of Fluid Mechanics 301 (October 25, 1995): 153–73. http://dx.doi.org/10.1017/s0022112095003843.

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We introduce a possibly new system of orthogonal curvilinear coordinates, whose coordinate curves are logarithmic spirals in the plane, supplemented by a cylindrical coordinate for three dimensions. It is shown that plane spiral coordinates form a oneparameter family, with equal scale factors along the two orthogonal coordinate curves, and constant Christoffel symbols. The equations of magnetohydrodynamics, which include those of fluid mechanics, are written in spiral coordinates and used to find a state of magnetohydrostatic equilibrium under a radial gravity field and spiral magnetic field, and to solve the equation of non-dissipative Alfvén waves in a spiral magnetic field in terms of Bessel functions. This exact solution specifies the evolution of wave perturbations (velocity and magnetic field) and energy variables (kinetic and magnetic energy densities and energy flux) with distance, for waves of arbitrary frequency. Both the frequency and the spiral angle are varied in plots of the waveforms, which show the effect on Alfvén wave propagation of three simultaneous effects: change in the mass density of the medium and in the strength and direction of the external magnetic field.

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Freimanis, Juris. "Polarized radiative transfer equation in some nontrivial coordinate systems." Proceedings of the International Astronomical Union 7, S283 (July 2011): 360–61. http://dx.doi.org/10.1017/s1743921312011428.

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AbstractExplicit expressions for the differential operator of stationary quasi-monochromatic polarized radiative transfer equation in Euclidean space with piecewise homogeneous real part of the effective refractive index are obtained in circular cylindrical, prolate spheroidal, elliptic conical, classic toroidal and simple toroidal coordinate system.

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Knez, Dariusz. "STRESS STATE ANALYSIS IN ASPECT OF WELLBORE DRILLING DIRECTION." Archives of Mining Sciences 59, no. 1 (March 1, 2014): 71–76. http://dx.doi.org/10.2478/amsc-2014-0005.

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Abstract Drilling directional wells challenges designers. Apart from known problems until now they face exact description of stress distribution in near wellbore region issue. Paper presents analysis of stress state taking into account drilling direction. The transposed in-situ stress state relative to the borehole coordinate system (Cartesian borehole coordinate system) and the total stress component at the borehole wall (cylindrical coordinate system) exhibits cyclic behaviour with respect to drilling direction of borehole. It allows to find optimal wellbore path

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Hemenway, Paul D., Arthur L. Whipple, and Raynor L. Duncombe. "Mapping Coordinate System Irregularities On The Celestial Sphere." Symposium - International Astronomical Union 133 (1988): 159–64. http://dx.doi.org/10.1017/s0074180900139567.

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Various techniques have been used to evaluate and describe coordinate system irregularities. The basic techniques have developed from simple differences to differences in coordinate “bins” to full spherical and cylindrical harmonic treatments. We are undertaking a 15-year program of minor planet observation with the express purpose of finding basic parameters of the adopted fundamental system with respect to a dynamical reference frame. The program is expected to provide a few hundred observations per year of 34 minor planets selected for their distribution of physical and orbital characteristics. The ability of the program to contribute to our knowledge of the rotation of the fundamental system and systematic irregularities within the system will depend on the accuracies of the observations and the distribution of the observations over the orbits and over the celestial sphere. We are considering the use of splines as a method of evaluating systematic corrections to the extant fundamental system. The initial development of the formalism and prospects for evaluation are presented.

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Yang, Ling Hui, Li Jun Wang, Hai Qing Liu, Yong Jie Ren, Jia Rui Lin, and Yin Guo. "Design and Calibration of Real-Time 3D Coordinate Measurement System Based on Multi-Angle Intersection and Cylindrical Imaging." Applied Mechanics and Materials 870 (September 2017): 147–52. http://dx.doi.org/10.4028/www.scientific.net/amm.870.147.

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This paper presents a high-resolution real-time 3D coordinate measurement system based on multi-angle intersection and cylindrical imaging. The measuring angle is detected by the linear camera equipped with cylindrical lenses, whose field of view is a 3D space rather than 2D plane. This camera has prominent advantages in precise coordinate measurement and dynamic position tracking due to the high resolution and outstanding frame rate of linear CCD. Each camera is a 1D angle measuring unit which confirms an angle thereby a plane passing through the light spot. With three cameras arrangement in front of the measurement field, the 3D coordinate of the light spot can be reconstructed by multi-angle intersection. An accurate and generic calibration method is introduced to calibrate this camera. The proposed calibration method is based on nonparametric ideas to find the mapping from incoming scene rays to photo-sensitive elements, and this method (black box calibration) is still effective even if the lens distortion is high and asymmetric. It is applicable to a central (single viewpoint) camera equipped with any lenses. The proposed calibration method is applied to the 3D coordinate measurement system. The coordinate measurement accuracy of the designed system is better than 0.49mm.

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Siraeva, D. T., and Y. V. Yulmukhametova. "Transformations of gas dynamics equations and basis operators of a admitted 11-dimensional Lie algebra." Multiphase Systems 15, no. 3-4 (2020): 217–22. http://dx.doi.org/10.21662/mfs2020.3.133.

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In this paper, the gas dynamics equations are considered. The system is closed by a general equation of state. This equations describe a model of an inviscid non-heat-conducting gas motion in the absence of external force fields and external energy sources. The system is invariant under the 11-parameter group with the corresponding 11-dimensional Lie algebra. The gas dynamics equations, equations of motion, and basis operators of the Lie algebra are written in Cartesian, Cylindrical, and Spherical coordinate systems. The steps involved when changing the coordinate system are illustrated in detail.

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Zhumagulov, Kuanyshbay, Yermek Sarsikeyev, and Dameli Kapanova. "Calculation of the Magnetic Field of the Stator Windings of the Synchronous Machine." MATEC Web of Conferences 155 (2018): 01048. http://dx.doi.org/10.1051/matecconf/201815501048.

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Medvedev, P. A., and M. V. Novgorodskaya. "Development of mathematical model Gauss – Kruger coordinate system for calculating planimetric rectangular coordinates using geodesic coordinates." Geodesy and Cartography 926, no. 8 (September 20, 2017): 10–19. http://dx.doi.org/10.22389/0016-7126-2017-926-8-10-19.

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Algorithms with improved convergence for the calculation of rectangular coordinates in the Gauss – Kruger coordinate system according to the parameters of any ellipsoid were designed. The approach of definition the spherical components in the classic series defined variables x, y, represented by the difference between the degrees of longitude l, followed by the replacement of their sums by formulas of spherical trigonometry. For definition of the amounts of spherical components of the relevant decompositions patterns of transverse-cylindrical sphere plane projection in the condition of the initial data equality on the ellipsoid and sphere radius N were used. Analysis of othertransformation methods of classical expansions in series, used in derivation of both logarithmical and non-logarithmical working formulas is carried outfor comparison with developed algorithms. The technique of algorithms development with usage of hyperbolic tangent function, applied by L. Kruger, Yu. Karelin, A. Schödlbauer is considered and their analysis is carried out. Advantages of Krasovskii – Isotov formulas for six-degree strips are pointed out. The usage of the spherical function sin τ in the expansion made it possible not only to obtain a rapidly convergent series, but also to represent the spherical part of the solution of the problem with the help of trigonometric identities in different types. It is proved that derived for the calculation algorithms with the proposed estimates of their accuracy, are optimal in removing points from the central meridian to l ≤ 6°. For the difference of longitudes l > 6°, the expansions of the unknown quantities into Fourier series should be applied. An example of the calculation of coordinates in the system SK-2011 is given. Theoretical studies have been carried out and shortened formulas with a reliability estimate for the determination of coordinates in the area l ≤ 3° have been proposed.

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Shao, W., and B. Z. Wang. "Order-Marching Time-Domain Method in Cylindrical Coordinate System for Eigenvalue Problems." Journal of Electromagnetic Waves and Applications 21, no. 14 (January 1, 2007): 2025–31. http://dx.doi.org/10.1163/156939307783152849.

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41

Hoppe, R. H. W., W. G. Litvinov, and T. Rahman. "Problems of Stationary Flow of Electrorheological Fluids in a Cylindrical Coordinate System." SIAM Journal on Applied Mathematics 65, no. 5 (January 2005): 1633–56. http://dx.doi.org/10.1137/s0036139903432883.

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Tynyna, Serhii, Ihor Chobotko, Liliya Frolova, and Tetyana Butyrina. "Modeling of influence of stresses on indicators of resistance of mining rocks to mechanical destruction." E3S Web of Conferences 109 (2019): 00104. http://dx.doi.org/10.1051/e3sconf/201910900104.

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The article deals with the problem of determining the expression for the components of the stress tensor of a rock mass that is exposed to rock-breaking tools. In solving this problem, the natural tension of the rocks and the stresses arising ahead, in the plane and on the boundary of the face of the cylindrical excavation were taken into account. Formulation presented in the form of a semi-infinite cylinder whose axis coincides with the axis ̅Z of the coordinate system. The solution is obtained in a cylindrical coordinate system in the form of analytical expressions, which is carried out by numerical integration of improper integrals.

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Dierkes, Dominik, and Martin Oberlack. "Euler and Navier–Stokes equations in a new time-dependent helically symmetric system: derivation of the fundamental system and new conservation laws." Journal of Fluid Mechanics 818 (March 31, 2017): 344–65. http://dx.doi.org/10.1017/jfm.2017.74.

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The present contribution is a significant extension of the work by Kelbin et al. (J. Fluid Mech., vol. 721, 2013, pp. 340–366) as a new time-dependent helical coordinate system has been introduced. For this, Lie symmetry methods have been employed such that the spatial dependence of the originally three independent variables is reduced by one and the remaining variables are: the cylindrical radius $r$ and the time-dependent helical variable $\unicode[STIX]{x1D709}=(z/\unicode[STIX]{x1D6FC}(t))+b\unicode[STIX]{x1D711}$, $b=\text{const.}$ and time $t$. The variables $z$ and $\unicode[STIX]{x1D711}$ are the usual cylindrical coordinates and $\unicode[STIX]{x1D6FC}(t)$ is an arbitrary function of time $t$. Assuming $\unicode[STIX]{x1D6FC}=\text{const.}$, we retain the classical helically symmetric case. Using this, and imposing helical invariance onto the equation of motion, leads to a helically symmetric system of Euler and Navier–Stokes equations with a time-dependent pitch $\unicode[STIX]{x1D6FC}(t)$, which may be varied arbitrarily and which is explicitly contained in all of the latter equations. This has been conducted both for primitive variables as well as for the vorticity formulation. Hence a significantly extended set of helically invariant flows may be considered, which may be altered by an external time-dependent strain along the axis of the helix. Finally, we sought new conservation laws which can be found from the helically invariant Euler and Navier–Stokes equations derived herein. Most of these new conservation laws are considerable extensions of existing conservation laws for helical flows at a constant pitch. Interestingly enough, certain classical conservation laws do not admit extensions in the new time-dependent coordinate system.

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HILL, J. M., and Y. M. STOKES. "A NOTE ON NAVIER–STOKES EQUATIONS WITH NONORTHOGONAL COORDINATES." ANZIAM Journal 59, no. 3 (January 2018): 335–48. http://dx.doi.org/10.1017/s144618111700058x.

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There are many fluid flow problems involving geometries for which a nonorthogonal curvilinear coordinate system may be the most suitable. To the authors’ knowledge, the Navier–Stokes equations for an incompressible fluid formulated in terms of an arbitrary nonorthogonal curvilinear coordinate system have not been given explicitly in the literature in the simplified form obtained herein. The specific novelty in the equations derived here is the use of the general Laplacian in arbitrary nonorthogonal curvilinear coordinates and the simplification arising from a Ricci identity for Christoffel symbols of the second kind for flat space. Evidently, however, the derived equations must be consistent with the various general forms given previously by others. The general equations derived here admit the well-known formulae for cylindrical and spherical polars, and for the purposes of illustration, the procedure is presented for spherical polar coordinates. Further, the procedure is illustrated for a nonorthogonal helical coordinate system. For a slow flow for which the inertial terms may be neglected, we give the harmonic equation for the pressure function, and the corresponding equation if the inertial effects are included. We also note the general stress boundary conditions for a free surface with surface tension. For completeness, the equations for a compressible flow are derived in an appendix.

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Zhu, Jianxin, and Wencheng Lin. "Efficient Computation of Heat Distribution of Processed Materials under Laser Irradiation." Mathematics 9, no. 12 (June 12, 2021): 1368. http://dx.doi.org/10.3390/math9121368.

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In this paper, a solution is provided to solve the heat conduction equation in the three-dimensional cylinder region, where the laser intensity of the material irradiation surface is expressed as a Gaussian distribution. Based on the symmetry of heat distribution, firstly, the form of the heat equation in the common rectangular coordinate system is changed to another form in the two-dimensional cylindrical coordinate system. Secondly, the ADI with the backward Euler method and with Crank–Nicolson method are established to discretize the model in the cylindrical coordinate system, after which the simulation results are obtained, where the first kind of boundary value condition is used to verify the accuracy of these two algorithms. Then, the above two methods are used to solve the model with the third kind of boundary value condition. Finally, the comparison is performed with the results obtained by the MATLAB’s PDETOOL, which shows that the solution is more feasible and efficient.

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Yang, Wei Ling, and Chun Lan Jiang. "Study on Intersection Criterion of MEFP Warhead to Target." Applied Mechanics and Materials 110-116 (October 2011): 3243–48. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.3243.

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Putting forward the straight-line trajectory of MEFP （multi-explosively formed penetrators, also called attack unit） in the target coordinate by means of building ground coordinate and target coordinate and the conversion of ground coordinate to target coordinate in the Area Blank off Weapon System. According to the intersection criterion that there are only two points between the attack unit straight-line trajectory and the cylindrical surface of the target, whether attack unit hits the target or not is decided. The intersection criterion is applied on the simulation of all kinds of different distributed plans.

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Chang, Der-Form, and Jyhwen Wang. "Optimized Upper Bound Analysis of Axisymmetric Extrusion Using Spherical Velocity Field." Journal of Manufacturing Science and Engineering 128, no. 1 (June 14, 2005): 4–10. http://dx.doi.org/10.1115/1.2112947.

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This paper presents an upper bound approach to analyze axisymmetric extrusion processes. A cylindrical and a spherical coordinate system are defined to represent the die geometry and the velocity field, respectively. For various curved dies, minimized upper bound results can be obtained by relating these two coordinate systems. Based on this modeling technique, the effects of die geometry, reduction ratio, and friction are investigated. Axisymmetric extrusion through various curved dies can be easily optimized with the proposed methodology.

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Baločková, Lenka. "The Method for Solving Kinematics of an Industrial Robot." Applied Mechanics and Materials 282 (January 2013): 274–81. http://dx.doi.org/10.4028/www.scientific.net/amm.282.274.

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This article deals with an overview of kinematic structures of industrial operating robots in cartesian, cylindrical, spherical and angular coordinating system. The second half of the article deals with solution of direct kinematics. Each of the coordinate systems is graphically shown and verbally described. Basic transformation matrices are used for the solution of direct kinematics and subsequently the Denavit-Hartenberg method, placing coordinate systems of robotic structure RRRT, is described in details. Calculated workspaces of kinematic structure RRRT are shown at the end of this article.

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Li, You Tang, Chang Feng Yan, and Wu Yin Jin. "The Method of Torsional Cylindrical Shaft with Annular Notch in Quadric Coordinate." Materials Science Forum 561-565 (October 2007): 2225–28. http://dx.doi.org/10.4028/www.scientific.net/msf.561-565.2225.

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The notch is not only one of the primary reasons of component fracture, but also the key factor in life assessment of shaft. The stress and displacement field near the tip of annular notch should be obtained at first for safe design and life assessment. A quadric coordinate system suited for annular notch is proposed and the stress and displacement component of cylindrical shaft with annular notch are derived by using the modified Galerkin displacement function. This method can be used to solve various problems of cylindrical shaft with annular notch by selecting an appropriate displacement function and provides the basis for safe design and life assessment of this kind of components. A solution of torsional problems of cylindrical shaft with annular notch is calculated as a demonstration of the method presented.

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Wang, Bao-Lin. "Transient thermal cracking associated with non-classical heat conduction in cylindrical coordinate system." Acta Mechanica Sinica 29, no. 2 (April 2013): 211–18. http://dx.doi.org/10.1007/s10409-013-0010-9.

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