• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.6 s.111
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• pp.643-650
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• 2006

This paper is concerned with the vibration analysis of a simply-supported rectangular plate with a circular cutout. Even though there have been many methods developed for the free vibration of the rectangular plate with a rectangular cutout, very few research has been carried out for the rectangular plate with a circular cutout. In this paper, a new methodology called independent coordinate coupling method, which was developed to save the computational effort for the free vibration analysis of rectangular plate with a rectangular cutout, is applied to the case of circular cutout. The independent coordinate coupling method employs the global coordinate system for the plate and the local coordinate system for the cutout. In the case of the rectangular plate with a circular cutout, the global coordinate system is the Cartesian coordinate system and the local coordinate system is the polar coordinate system. By imposing the compatibility condition, the relationship between the global coordinates and the local coordinates is derived. This equation is then used for the calculation of the mass and stiffness matrices resulting in eigenvalue problem. The numerical results show the efficacy of the proposed method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1177-1182
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• 2006

This paper is concerned with the vibration analysis of a simply-supported rectangular plate with a circular cutout. Even though there have be en many methods developed for the free vibration of the rectangular plate with a rectangular cutout., very few research has been carried out for the rectangular plate with a circular cutout. In this paper, a new methodology called independent coordinate coupling method, which was developed to save the computational effort for the free vibration analysis of rectangular plate with a rectangular cutout, is applied to the case of circular cutout. The independent coordinate coupling method employs the global coordinate system for the plate and the local coordinate system for the cutout. In the case of the rectangular plate with a circular cutout, the global coordinate system is the Cartesian co ordinate system and the local coordinate system is the polar coordinate system. By imposing the compatibility condition, the relationship between the global coordinates and the local coordinates is derived. This equation is then used for the calculation of the mass and stiffness matrices resulting in eigenvalue problem. The numerical results show the efficacy of the proposed method.

• Journal of Korean Society for Atmospheric Environment
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• v.16 no.4
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• pp.339-350
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• 2000

The three-dimensional new corrdinate system over a single hill double hills and complex terrain with a single hill and a rectangular obstacle was generated using a body-fitted coordinate system. Control of the coordinate line distribution in the field was executed by generalizing the elliptic generating system to Poisson equation. ▽2ξ=P. The new coordinate system was well fitted to the surface boundary of single hill and double hills. But in the case of complex terrain with hill and rectangular obstacle there was smoothing tendency around the rectangular obstacle. In order to show the validity of the body-fitted coordinate system the heat diffusion equation was transformed and the temperature distribution was calculated over the various terrain. The results showed the temperature distribution was very symmetrical and stable around hills and obstacle. As a result the couple of a body-fitted coordinate system and the heat diffusion equation were executed successfully. Wind field over complex terrain with hill and rectangular obstacle which represent urban area was simulated stably in body-fitted coordinate system. The qualitative result show the enhancement of wind speed at the upwind direction of a hill and a rectangular obstacle and the recirculation zone at the downwind direction.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.37-51
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• 2012

By comparing the development history of rectangular coordinate system in Cartography and Mathematics, we assert in this manuscript that the rectangular coordinate system is not so much related to analytic geometry but comes from the space perceiving ability inherent in human beings. We arrived at this conclusion by the followings: First, although the Cartography have much influenced to various area of Mathematics such as trigonometry, logarithm, Geometry, Calculus, Statistics, and so on, which were developed or progressed around the advent of analytic geometry, the mathematical coordinate system itself had not been completely developed in using the origin or negative axis until 100 years and more had passed since Descartes' publication. Second, almost mathematicians who contributed to the invention of rectangular coordinate system had not focused their studying on rectangular coordinate system instead they used it freely on solving mathematical problem.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.1 no.2
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• pp.42-59
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• 1983

This article investigates the situation of the Plane Rectangular Coordinate derived from the Gauss Double Projection whereby the positioning of triangulation point in Korea has been represented on. Analyzing and assessing it have been performed by means of new computational method such as computer programing. On the basis of the results brought about, it is found that a new Plane Rectangular Coordinate as well as map projection and scale factor of geodetic length may be adapted to improve the distortion along the geodetic line on a certain zone of map projection in order to enhance the accuracy and the utility of the practical surveying works. The proposals for this study are as follows; (1) projection: Gauss-Kruger's projection (2) Coordinate system: Plane Rectangular coordinate with 8 origin system (3) Scale factor of geodetic length in origin; $m_0=0.9999$

• Korean Journal of Remote Sensing
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• v.8 no.2
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• pp.93-104
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• 1992

Although the Transverse Mercator(TM) coordinate is used on standard topogrphic maps of Korea as a supplement to regular latitude-longitude coordinate, the use of this TM coordinate system is rather limited to a single coordinate zone that spans only two degrees of longitude. With growing applications of a variety of digiral geographic data, such as satellite remote sensor data, a Cartesian or rectangular coordinate system is more effective to deal with such data type than angular coordinate system. An unified rectangular coordinate system based on the Transverse Mercator projection is designed to cover the whole area of the Korea Peninsula as a single coordinate zone. Considering the width of the peninsula and the distribution of scale error, the origin of the coordinate is determined to 127$^{\circ}$30' east and 38$^{\circ}$ north. Coordinate conversion procedure is discussed along with the corresponding scale error term.

• Journal of Korea Water Resources Association
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• v.53 no.12
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• pp.1049-1057
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• 2020

This study aimed to develop a flow measurement method using drone in flood season. Measuring flow in all branches is difficult to conduct annually due to budget and labor limitation, safety and river works. Especially when heavy rain like storm comes, changes in stage-discharge relationship should be reviewed; however, it is usually impeded by the aforementioned issues. To solve the problem, it developed a simple measuring method with a minimum of labor and time. A numeric map and numeric orthophoto coordinate of South Korea are mostly based on Transverse Mercator Projection (TM) in accordance with rectangular coordinate system and use World Geodetic Reference System 1980 (GRS80) oval figure for conversion. Applying a concept of aerial photogrammetry, it located four visible Ground Control Points (GCP) near the river at Uijeongbu-si (Singok Bridge) and Yeongdong-gun (Youngdong 2nd Bridge) station and measured the coordinates using VRS DGPS. Hovering at a same level, drones took orthophoto of water surface at an interval of 3 seconds. It defined the pictures with GRS80 TM coordinate system, a rectangular coordinate system and then conducted an orthometric correction using GCP coordinates. According to X and Y coordinate analysis, it estimated the distance between the floating positions at 3 seconds-intervals and calculated the flow through the flow area according to the flow path. This study attested applicability of the flow measurement method using drone in flood season by applying the rectangular coordinate system based on the concept of aerial photogrammetry.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.2 no.2
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• pp.1-13
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• 1984

Projection has been used in order to indicate the horizontal position of triangulation stations which had been existed on the earth surface. In our country, the plane Rectangular coordinate of the triangulation station is computed by means of Gauss Double projection. But it proves to contain many errors according to the difference in Latitude and longitude. Therefore, in this study Transverse Mercator projection which is known to contain less error than Gauss Double projection in an applied region is introduced, and the results obtain by two these projections and the value today in our country are compared and analysed. when an another plane Rectangular Coordinate system is added to the present 3-plane Rectangular Coordinate system, there is an object inshowing the best position.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.2
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• pp.69-79
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• 1994

The conventional machine vision system which has uniform rectangular grid requires tremendous amount of computation for processing and analysing an image especially in 2-D image transfermations such as scaling, rotation and 3-D reconvery problem typical in robot application environment. In this study, the imaging system with nonuiformly distributed image sensors simulating human visual system, referred to as Ploar Exponential Grid(PEG), is compared with the existing conventional uniform rectangular grid system in terms of image resolution and computational complexity. By mimicking the geometric structure of the PEG sensor cell, we obtained PEG-like images using computer simulation. With the images obtained from the simulation, image resolution of the two systems are compared and some basic image processing tasks such as image scaling and rotation are implemented based on the PEG sensor system to examine its performance. Furthermore Fourier transform of PEG image is described and implemented in image analysis point of view. Also, the range and heading-angle measurement errors usually encountered in 3-D coordinates recovery with stereo camera system are claculated based on the PEG sensor system and compared with those obtained from the uniform rectangular grid system. In fact, the PEC imaging system not only reduces the computational requirements but also has scale and rotational invariance property in Fourier spectrum. Hence the PEG system has more suitable image coordinate system for image scaling, rotation, and image recognition problem. The range and heading-angle measurement errors with PEG system are less than those of uniform rectangular rectangular grid system in practical measurement range.

• Journal of the Korean Society of Safety
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• v.18 no.1
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• pp.101-107
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• 2003

Dynamic behavior of flexible rectangular liquid storage structures is analysed by the developed method. The rectangular liquid storage structures are assumed to be fixed to the ground and a moving coordinate system is used. The irrotational motion of invicid and incompressible ideal fluid is represented by two analytic solutions. One is the solution of the fluid motion in the rigid rectangular liquid storage structure due to ground motions and the other is the solution of the fluid motion by the motion of the wall in the flexible rectangular liquid storage structure. The motion of structure is modeled by finite elements. The fluid-structure interaction effect is reflected into the coupled equation of motion as added fluid mass matrix. The free surface sloshing motion and hydrodynamic pressure acting on the wall in the flexible rectangular liquid storage structure due to the horizontal ground motion are obtained by the developed method and verified.