• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.5B
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• pp.493-496
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• 2009

In this study, we derive the extended mild-slope equation in terms of the velocity potential using the Euler-Lagrange equation. First, we follow Kim and Bai (2004) who derive the complementary mild-slope equation in terms of the stream function using the Euler-Lagrange equation and we compare their equation to the existing extended mild-slope equations of the velocity potential. Second, we derive the extended mild-slope equation in terms of the velocity potential using the Euler-Lagrange equation. In the developed equation, the higher-order bottom variation terms are newly developed and found to be the same as those of Massel (1993) and Chamberlain and Porter (1995). The present study makes wide the area of coastal engineering by developing the extended mild-slope equation with a way which has never been used before.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.899-909
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• 1992

An iterative solution technique is presented to analyze the dynamic systems of rigid bodies subjected to kinematic constraints. Lagrange multipliers associated with the constraints are iteratively computed by monotonically reducing an appropriately defined constraint error vector, and the resulting equation of motion is solved by a well-established ODE technique. Constraints on the velocity and acceleration as well as the position are made to be satisfied at joints at each time step. Time integration is efficiently performed because decomposition or orthonormalization of the large matrix is not required at all. An acceleration technique is suggested for the faster convergence of the iterative scheme.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.5
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• pp.683-690
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• 1985

본 논문에는 Euler매개변수를 회전좌표계로 사용하여 구속된 3차원 기계시스템의 역동학력 해 을 수행한 연구결과가 수록되었다. 해석을 위해 문제에 등장하는 비선형 Holonomic구속조건식 들과 운동방정식들을 Cartesian일반좌표계을 사용하여 표시하였으며, 일반좌표계를 구성하는 각 강체의 좌표계로는 변위를 나타내기 위한 3개의 좌표와 회전을 나타내기 위한 4개의 Euler매 개변수가 사용되었다. 구속조건식들과 미분방정식 형태의 운동방정식들을 결합하여 시스템 전 체의 운동방정식을 유도하기 위해 Lagrange승수 기법을 사용하였다. 각 강체의 주어진 시간에 서의 위치, 속도, 가속도는 기구학적 해석(kinematic analysis)을 통해 얻어지고, 이 자료들을 전 체운동방정식에 대입하여 Lagrnage승수의 값을 계산하여 6개의 자유도를 가진 로봇 기구를 원 하는대로 운전하는에 필요한 각 관절의 토오크를 계산하였으며, 계산결과가 정확하다는 사실이 입증되었다. 연구결과 Euler매개변수를 회전좌표로 사용할 경우 특이 경우(singular case)가 발 생하지 않으며, 이 방법은 역동력학 해석용 다목적 전산프로그램 개발에 광범위하게 응용될 수 있음이 밝혀졌다.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.4
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• pp.2370-2378
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• 2015

This paper proposes an algorithm using Lagrange interpolation method to realize trajectory planning for torque minimization of robot manipulators. For the algorithm, position constraints of robot manipulators should be given and the stability of robot manipulators should be satisfied. In order to avoid Runge's phenomenon, we set up time interpolation points using Chebyshev interpolation points. After that, we found suitable angle which corresponds to the points and then we got trajectories of joint's angle, velocity, acceleration using Lagrange interpolation method. We selected performance index for torque consumption optimization of robot manipulator. The method went through repetitive computation process to have minimum value of the performance index by calculated trajectory. Through the process, we could get optimized trajectory to minimize torque and performance index and guarantee safety of the motion for manipulator performance.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.4
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• pp.37-41
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• 2021

This paper presents a study to implement a touch screen capable of real-time response processing in a low-end embedded system. This was done by introducing an algorithm using an interpolation method to represent real-time response characteristics when a touch input is performed. In this experiment, we applied a linear interpolation algorithm that estimates random data by deriving a first-order polynomial from 2-point data. We also applied a Lagrange interpolation algorithm that estimates random data by deriving a quadratic polynomial from 3-point data. As a result of the experiment, it was found that the Lagrange interpolation method was more complicated than the linear interpolation method, and the processing speed was slow, so the text was not smooth. When using the linear interpolation method, it was confirmed that the speed displayed on a screen is 2.4 times faster than when using the Lagrange interpolation method. For real-time response characteristics, it was confirmed that smaller size of the executable file of the algorithm is more advantageous than the superiority of the algorithm itself. In conclusion, in order to secure real-time response characteristics in a low-end embedded system, it was confirmed that a relatively simple linear interpolation algorithm performs touch operations with better real-time response characteristics than the Lagrange interpolation method.

• The KIPS Transactions:PartA
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• v.14A no.4
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• pp.191-196
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• 2007

In the field of computer graphics, Navier-Stokes equations would be used for realistic simulations of smokes and currents. However, implementations derived from these equations are hard to achieve for real-time simulations, mainly due to its massive and complex calculations. Thus, there have been various attempts to approximate these equations for real-time simulation of smokes and others. When the advection terms of the equations are approximated by the Semi-Lagrange methods, the fluid density can be rapidly reduced and small-scale vorticity phenomena are easy to be missed, mainly due to the numerical losses over time. In this paper, we propose an improved numerical method to approximately calculate the advection terms, and thus eliminate these problems. To calculate the advection terms, our method starts to set critical regions around the target grid points. Then, among the grid points in a specific critical region, we search for a grid point which will be advected to the target grid point, and use the velocity of this grid point as its advection vector. This method would reduce the numerical losses in the calculation of densities and vorticity phenomena, and finally can implement more realistic smoke simulations. We also improve the overall efficiency of vector calculations and related operations through GPU-based implementation techniques, and thus finally achieve the real-time simulation.

• Journal of the Korean Data and Information Science Society
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• v.12 no.2
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• pp.95-102
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• 2001

최적의 SVM 가중치를 선택하는 방법 중에서 메모리와 속도의 문제를 해결하는 방법 중 하나가 커널애더트론 방법(Kernel Adatron, KA)이다. 본 연구에서는 KA방법을 제곱무감각손실함수까지 확장을 한 알고리즘을 개발한다. 그리고 추정해야 될 라그랑제 배수(Lagrange multiplier)의 수를 반으로 줄이는 알고리즘을 제시한다. 그리고 제시된 알고리즘의 효율성을 여러 모의실험을 통해서 입증한다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.6
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• pp.1852-1860
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• 1991

A shape design sensitivity of the elastic deformation due to a change of traction boundary condition is presented. The solution of governing equations for a linear elasticity problem is obtained by finite element method and the traction boundary is defined by design variables. The performance functional to be considered involves both the domain and boundary integral. Variations of geometry can be defined as design velocity. Using material derivative concept and adjoint equations, the design sensitivity is derived by Lagrange multiplier method. For a given geometry of a structure, the change of traction boundary is described by the tangential component of the design velocity only. The final result for the shape design sensitivity is formulated as the boundary integral form, the integrand is defined by tangential component of design velocity and first order derivatives of parameters. Numerical implementation of design sensitivity is discussed and is compared with the difference of the actual values.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2006.05a
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• pp.253-256
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• 2006

A numerical study for spray flow of fuel and oxidizer droplets in the combustion chamber has been conducted prior to the analysis of spray combustion of the liquid rocket engine. As the spray combustion model, DSF model and Euler-Lagrange scheme have been used. While the coupling effects of the droplets between gas phase and evaporated vapor have been calculated using PSIC model, SIMPLER algorithm and QUICK scheme have been used as numerical schemes. As the results, the calculations have shown velocity and temperature distribution in combustion chamber as well as mole fraction of fuel and oxidizer.

• Journal of Korea Water Resources Association
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• v.35 no.6
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• pp.779-786
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• 2002

A boundary element method with a Lagrangian approach and B-spline technique is employed to investigate characteristics of solitary waves attacking on beach slopes. By comparing numerical solutions with available laboratory measurements, it is shown that the maximum run-up heights of the present model are more agreeable than those of the existing numerical model. Variations of run-up heights and velocity vectors for different slopes are also described. Characteristics of hydrodynamic pressure acting beach slopes are investigated in detail.