• Title/Summary/Keyword: Runge-Kutta 적분 방법

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Accuracy Analysis of GLONASS Orbit Determination Strategies for GLONASS Positioning (GLONASS 측위를 위한 위성좌표 산출 정확도 향상 방안)

  • Lee, Ho-Seok;Park, Kwan-Dong;Kim, Hye-In
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.28 no.6
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    • pp.573-578
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    • 2010
  • Precise determination of satellite positions is necessary to improve positioning accuracy in GNSS. In this study, GLONASS orbits were predicted from broadcast ephemeris using the 4th-order Runge-Kutta numerical integration method and their accuracy dependence on the integration step and the integration time was analyzed. The 3D RMS (Root Mean Square) differences between the results from I-second integration step and 300-second integration step was about 3 cm, but the processing time was one hundred times less for the I-second integration time case. For trials of different integration times, the 3D RMS errors were 8.3 m, 187.3 m, and 661.5 m for 30-, 150-, and 300-minutes of integration time, respectively. Though this integration-time analysis, we concluded that the accuracy gets higher with a shorter integration time. Thus we suggest forward and backward integration methods to improve GLONASS positioning accuracy, and with this method we can achieve a 5-meter level of 3-D orbit accuracy.

Study of Chaotic Mixing for Manufacturing Uniform Mixtures in Extrusion Processes (Development of New Numerical Mapping Methods) (압출공정에서의 균일한 혼합체 제조를 위한 카오스 혼합연구)

  • 김은현
    • The Korean Journal of Rheology
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    • v.8 no.3_4
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    • pp.187-198
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    • 1996
  • 최근에 본 연구자에 의해서 단축 스크류 공정에서 카오스 스크류라고 명명되어진 카오스 혼합장치가 성공적으로 개발되었다. 기하학적 조건이나 공정조건에 대한 설계변수로 카오스 스크류를 설계하기 위하여 체류시간, 포인카레 단면 그리고 혼합패턴등에 대한 계산 과 해석이 이루어져야 하는데 이를 단지 Runge-Kutta 방법에 의해 속도장을 적분한다면 상당한 계산시간이 소비된다. 이러한 수치문제를 극복하기 위하여 본논문에서는 새로운 사 상법을 제안한다. 이 방법으  사용하면 벽면 근처의 특이점 영역에서도 수치문제가 해결된 다. 본 논문에서 제안하는 수치사상법은 Runge-Kutta 방법에 비하여 수치계산의 효율성과 정확도 면에서, 특히 유안요소법으로 얻은 속도장에 대하여 우수함이 밝혀졌다. 이러한 사상 법은 공간주기 유동장뿐만 아니라 시간주기 유동장에서 적용할수 있다.

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Nonlinear Free Surface Flows for an Axisymmetric Submerged Body (축대칭 몰수체에 대한 비선형 자유표면 유동)

  • Chang-Gu Kang
    • Journal of the Society of Naval Architects of Korea
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    • v.28 no.1
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    • pp.27-37
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    • 1991
  • In this paper the nonlinear free surface flows for an axisymmetric submerged body oscillating beneath the free surface are solved and the forces acting on the body are calculated. A boundary integral method is applied to solve the axisymmetric boundary value problem and the Runge-Kutta 4-th order method is used for the time stepping of the free surface location. The nonlinear forces acting on the axisymmetric body are computed and compared with published results.

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Dynamic Response of a Beam Structure with Discrete Supports Subjected to a Moving Mass (이동질량에 의한 이산지지 보 구조물의 동적응답)

  • Oh, B.J.;Ryu, B.J.;Lee, G.S.;Lee, Y.S.
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.21 no.3
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    • pp.264-270
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    • 2011
  • This paper deals with dynamic response of a beam structure with discrete spring-damper supports under a moving mass. Governing equations of motion taking into account of all inertia effects of the moving mass were derived by Galerkin's mode summation method, and Runge-Kutta integration method was applied to solve the differential equations. The effects of the speed of the moving mass, spring stiffness, damping coefficient, span number of a beam structure, mass ratio of the moving mass on the dynamic response of the beam structure have been studied. Some numerical results provide design engineers for the beam structure design with discrete supports under a moving mass.

Dynamic Response of a Beam with a Spring Support Subject to a Moving Mass (탄성스프링 지지를 갖고 이동질량을 받는 보의 동적응답)

  • Lee, J.W.;Ryu, B.J.;Lee, G.S.;Song, O.S.;Lee, Y.L.
    • Proceedings of the KSME Conference
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    • 2003.04a
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    • pp.868-873
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    • 2003
  • This paper deals with the linear dynamic response of an elastically restrained beam under a moving mass, where the elastic support was modelled by translational springs of variable stiffness. Governing equations of motion taking into account of all inertia effects of the moving mass were derived by Galerkin's mode summation method, and Runge-Kutta integration method was applied to solve the differential equations. The effects of the speed, the magnitude of the moving mass, stiffness and the position of the support springs on the response of the beam have been studied. A variety of numerical results allows us to draw important conclusions for structural design purposes.

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Collision Orbite for Small Mass Ratio in the Restricted Three Body Problem (제한 3체문제에서의 작은 질량비에 대한 충돌궤도)

  • 조중현;박상영;이병선;최규홍
    • Journal of Astronomy and Space Sciences
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    • v.5 no.1
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    • pp.19-30
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    • 1988
  • The existence of the j-type collision periodic orbit is examined on the condition of mass ratio 0.9878449 and Jacobian constant 2.9∼3.4. Using the Birckhoff's regularization method and the 5th order Runge-Kutta variable step-sized numerical roution introduced by Fehlberg (1968). we test their periodicities. As the results, 4 j-type collision orbits and 5 peculiar orbits are represented. There are good agreements in this collision orbits with the relationship between the period and the shape of orbit proposed by Pinotsis Zikides(1984).

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Dynamic Response and Vibration Characteristics of an Isolation Rail Track under a Traveling Mass (주행질량하의 방진 궤도레일의 동적응답 및 진동특성)

  • Oh, B.J.;Ryu, B.J.;Kim, J.H.;Lee, Y.S.
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.21 no.4
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    • pp.365-373
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    • 2011
  • This paper presents the dynamic response and the vibration characteristics for a rail-track supported by discrete springs and dampers. Recently, automatic conveyer system, rail-track, rack-master system demand the soundproof facilities and vibration suppression measures in order to satisfy the strict environmental standards. The equations of motions of the dynamic characteristics for a vibration suppression rail-track under a traveling mass were derived by Galerkin's mode summation method considering gravity, centrifugal force, Coriolis force, inertia force of the moving mass, transverse inertia of the rail-track. Also, numerical results were calculated by Runge-Kutta integration method. In order to investigate vibration characteristics and dynamic responses, modal testing and measurement of the responses of the rail-track were performed. Through the experiment and numerical simulations, numerical results have a good agreement with experimental ones.

Elastica of Simple Variable-Arc-Length Beams (단순지지 변화곡선 길이 보의 정확탄성곡선)

  • 이병구;박성근
    • Computational Structural Engineering
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    • v.10 no.4
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    • pp.177-184
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    • 1997
  • In this paper, numerical methods are developed for solving the elastica of simple beams with variable-arc-length subjected to a point loading. The beam model is based on Bernoulli-Euler beam theory. The Runge-Kutta and Regula-Falsi methods, respectively, are used to solve the governing differential equations and to compute the beam's rotation at the left end of the beams. Extensive numerical results of the elastica responses, including deflected shapes, rotations of cross-section and bending moments, are presented in non-dimensional forms. The possible maximum values of the end rotation, deflection and bending moment are determined by analyzing the numerical data obtained in this study.

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Transverse and Diagonal Mode Structures of Three-dimensional Detonation Wave (3차원 데토네이션 파의 수평 및 대각선 모드 파면 구조)

  • Cho Deok-Rae;Choi Jeong-Yeol
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • v.y2005m4
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    • pp.343-346
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    • 2005
  • Three dimensional structures of detonation wave propagating through a square-shaped duct were investigated using computational method and parallel processing. Inviscid fluid dynamics equations coupled with $variable-{\gamma}$ formulation and simplified one-step Arrhenius chemical reaction model were analysed by MUSCL-type TVD scheme and four stage Runge-Kutta time integration. The unsteady computational results in three dimension show the detailed mechanism of transverse mode and diagonal mode of detonation wave instabilities resulting same cell length but different cell width in smoked-foil record.

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PRECISE ORBIT PROPAGATION OF GEOSTATIONARY SATELLITE USING COWELL'S METHOD (코웰방법을 이용한 정지위성의 정밀궤도예측)

  • 윤재철;최규홍;김은규
    • Journal of Astronomy and Space Sciences
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    • v.14 no.1
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    • pp.136-141
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    • 1997
  • To calculate the position and velocity of the artificial satellite precisely, one has to build a mathematical model concerning the perturbations by understanding and analysing the space environment correctly and then quantifying. Due to these space environment model, the total acceleration of the artificial satellite can be expressed as the 2nd order differential equation and we build an orbit propagation algorithm by integrating twice this equation by using the Cowell's method which gives the position and velocity of the artificial satellite at any given time. Perturbations important for the orbits of geostationary spacecraft are the Earth's gravitational potential, the gravitational influences of the sun and moon, and the solar radiation pressure. For precise orbit propagation in Cowell' method, 40 x 40 spherical harmonic coefficients can be applied and the JPL DE403 ephemeris files were used to generate the range from earth to sun and moon and 8th order Runge-Kutta single step method with variable step-size control is used to integrate the the orbit propagation equations.

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