Mapping Ground-based Coronagraphic Images to Helioprojective-Cartesian Coordinate System by Image Registration by Feiyang Sha, Yu Liu, Lidong Xia, Yao Chen, Qing Zhou, Yangrui Chen, Chuyu Zhong, Xuefei Zhang, Tengfei Song, Mingzhe Sun, Xiaoyu Yu, Haitang Li, Jacob Oloketuyi, Qiang Liu, Xinjian Wang, Qiwang Luo, Xiaobo Li

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Simplified method for analytically determining the external magnetostatic field of uncertain extended technical objects based on near-field measurements by B. I. Kuznetsov, T. B. Nikitina, I. V. Bovdui, K. V. Chunikhin, V. V. Kolomiets, I. V. Nefodova

“…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. Methodology. Forward problems of magnetostatics solved based on developed method of analytical calculation of magnetostatic field induction of spherical and spheroidal sources in Cartesian coordinate system based on near-field measurements. …”
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阿基米德螺旋面异常数据的剔除方法 by 邹红玲, 郭阳宽, 祝连庆, 陈青山, 孟浩

“…A method of removing abnormal data is presented.It is used for lots of data on Archimedes surfaces measured by CMM.The data from cartesian-coordinate system is transformed into cylindrical coordinate system at first.Then the Archimedes surface is transformed into plane.At last,the abnormal data is removed by repeatedly using least square method and Laiyite principle.Experiments show that this method is feasibility.…”
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On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows by J. Venetis

“…In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.…”
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Effect of Different Parameters on Powell-Eyring Fluid Peristaltic Flow with the Influence of a Rotation and Heat Transform in an Inclined Asymmetric Channel by Rana Ghazi Ibraheem, Liqaa Zeki Hummady

“…Long wavelength and low Reynolds number are assumed, where the perturbation approach is used to solve the nonlinear governing equations in the Cartesian coordinate system to produce series solutions. distributions of velocity and pressure gradients are expressed mathematically. …”
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Numerical Solution of Three-Dimensional Transient Heat Conduction Equation in Cylindrical Coordinates by Endalew Getnet Tsega

“…The solutions obtained by the numerical method in cylindrical coordinates were displayed in the Cartesian coordinate system graphically. The method requires relatively very small time steps for a given mesh spacing to avoid computational instability. …”
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Modeling of Compound Curves on Railway Lines by Wladyslaw Koc

“…An analytical method for designing track geometric systems was used, adapted to the mobile satellite measurement technique, in which calculations are carried out in the appropriate local Cartesian coordinate system. The basis of this system is the symmetrically arranged adjacent main directions of the route, and the beginning is located at the point of intersection of these directions. …”
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Magnetic field analytical calculation method for radial unite of a combined magnetic bearing by Xiaojun Ren, Ming Feng, Tianming Ren

“…The magnetic field of magnetic bearing with large diameter rotor is analysed and calculated in Cartesian coordinate system. Considering the influence of curvature the magnetic field distribution of magnetic bearing with small diameter rotor is deduced and calculated analytically in polar coordinate system. …”
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Distribution of autochthonous dendro-species in the Management Unit „Ozren“-Petrovo – implementation of GIS technology by Đorđije Milanović, Vladimir Stupar, Jugoslav Brujić, Davor Nikić

“…Species were mapped using the GIS technology, with the square network 1x1 km, which was laid into the National Cartesian coordinate system, in zone 6. In the total of 109 squares, 93 species of trees and shrubs were recorded. …”
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Experimental and Theoretical Investigations of the Impact Localization of a Passive Smart Composite Plate Fabricated Using Piezoelectric Materials by M. M. S. Dezfouli, Mohd Roshdi Hassan, Mohd Hafidz Ruslan, Sohif Mat, B. Bakhtyar

“…The locations of the impacts are determined based on the crossing points of two circles and the origin of an intended Cartesian coordinate system that is concentric with one of the sensors. …”
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Positioning Error Compensation for Industrial Robots Based on Stiffness Modelling by Yingjie Li, Guanbin Gao, Fei Liu

“…Finally, these two models are transformed into a Cartesian coordinate system, and a positioning error compensation method based on these two models is presented. …”
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Real-Time Sliding Mode and Moving Sliding Mode Control of 3-DOF Linear Parallel Robot by Muhammet Aydın

“…Considering the point where the robot will be fixed, control was provided for the third region of the x-y cartesian coordinate system for position control. According to the results, the robot reached the desired reference values faster in the MSMC, with a difference of approximately 2 s. …”
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Influence of Secondary Currents on Solute Dispersion in Curved Open Channels by Myung Eun Lee, Gunwoo Kim

“…SSFD coefficient tensor in a streamwise curvilinear coordinate system of curved channel was transformed to those components of fixed Cartesian coordinate system, and 2D numerical model with finite element method was established in the Eulerian-Cartesian coordinate. …”
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Effect of Inclined Magnetic Field on Peristaltic Flow of Carreau Fluid through Porous Medium in an Inclined Tapered Asymmetric Channel by Tamara Sh. Ahmed

“…By exploitation, the perturbation technique for little values of weissenberg number, the nonlinear governing equations in the two-dimensional Cartesian coordinate system is resolved under the assumptions of long wavelength and low Reynolds number. …”
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Sensitivity of Line-of-Sight Estimation to Measurement Errors in L-Shaped Antenna Arrays for 3D Localization for In-Orbit Servicing by Botond Sándor Kirei, Vlad Rațiu, Ovidiu Rațiu

“…First, the proposed 3D localization model in the Cartesian coordinate system is given, where, for simplicity, the origin of the coordinate system is the origin of the L-shaped antenna array. …”
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Heat Exchange and Flow Resistance in a Heat Exchanger Based on a Minimal Surface of the Gyroid Type—Results of Experimental Studies by Krzysztof Dutkowski, Marcin Kruzel, Marcin Walczak

“…TPMS is a minimal surface replicated in the three main directions of the Cartesian coordinate system. The minimal surface is a surface stretched between two objects, known as the smallest possible area (e.g., a soap bubble with a saddle shape stretched between two parallel circles). …”
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System Elegant-frequency Characteristics, Wave-sign Diagrams and Stability Criterion by ZHU Ming, YU Jiaxuan, MIAO Yuhui, ZHU Jiahui

“…Then, a functional transformation is applied to plot characteristic curves in a Cartesian coordinate system of linear division, similar to those in a Bode diagram, by which gain-phase frequency characteristics are converted into elegant-frequency characteristics. …”
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Sensitivity Analysis of Vibrating Laminated Composite Rec-tangular Plates in Interaction with Inviscid Fluid Using EFAST Method by Korosh Khorshidi, Moein Taheri, Mohsen Ghasemi

“…Theoretical formulations, both for the laminated rectangular plates in interaction with inviscid, incompressible and irrotational fluid and the sensitivity analysis technique are summarized here. A Cartesian coordinate system is used to describe governing equations of fluid-structure interaction. …”
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An improved experimental-theoretical method for calculating the particle trajectory in a pneumatic separating channel by A. I. Burkov, A. L. Glushkov, V. A. Lazykm

“…At the third stage, the system of differential equations of particle motion in a pneumatic separating channel relative to a Cartesian coordinate system is made and their trajectories are calculated. …”
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Geodesics in the closed accelerating University by V.V. Arkhipov, T.M. Orymbay, P.A. Kisabekova

“…The pseudo-Cartesian coordinate system is introduced for saving formal equality of space dimensions of the space-time. …”
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