• Title, Summary, Keyword: the Euler Lagrange equation.

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Derivation of Extended Mild-Slope Equation Using Euler-Lagrange Equation (Euler-Lagrange 식을 사용한 확장형 완경사방정식 유도)

  • Lee, Changhoon;Kim, Kyu-Han
    • 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.

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The Container Pose Measurement Using Computer Vision (컴퓨터 비젼을 이용한 컨테이너 자세 측정)

  • 주기세
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.8 no.3
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    • pp.702-707
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    • 2004
  • This article is concerned with container pose estimation using CCD a camera and a range sensor. In particular, the issues of characteristic point extraction and image noise reduction are described. The Euler-Lagrange equation for gaussian and random noise reduction is introduced. The alternating direction implicit(ADI) method for solving Euler-Lagrange equation based on partial differential equation(PDE) is applied. The vertex points as characteristic points of a container and a spreader are founded using k order curvature calculation algorithm since the golden and the bisection section algorithm can't solve the local minimum and maximum problems. The proposed algorithm in image preprocess is effective in image denoise. Furthermore, this proposed system using a camera and a range sensor is very low price since the previous system can be used without reconstruction.

GENERALIZED STABILITY OF EULER-LAGRANGE TYPE QUADRATIC MAPPINGS

  • Jun, Kil-Woung;Oh, Jeong-Ha
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.4
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    • pp.535-542
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    • 2007
  • In this paper, we investigate the generalized Hyers-Ulam{Rasssias stability of the following Euler-Lagrange type quadratic functional equation $$f(ax+by+cz)+f(ax+by-cz)+f(ax-by+cz)+f(ax-by-cz)=4a^2f(x)+4b^2f(y)+4c^2f(z)$$.

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A CELL BOUNDARY ELEMENT METHOD FOR A FLUX CONTROL PROBLEM

  • Jeon, Youngmok;Lee, Hyung-Chun
    • Journal of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.81-93
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    • 2013
  • We consider a distributed optimal flux control problem: finding the potential of which gradient approximates the target vector field under an elliptic constraint. Introducing the Lagrange multiplier and a change of variables the Euler-Lagrange equation turns into a coupled equation of an elliptic equation and a reaction diffusion equation. The change of variables reduces iteration steps dramatically when the Gauss-Seidel iteration is considered as a solution method. For the elliptic equation solver we consider the Cell Boundary Element (CBE) method, which is the finite element type flux preserving methods.

Dynamic response of concrete gravity dams using different water modelling approaches: westergaard, lagrange and euler

  • Altunisik, A.C.;Sesli, H.
    • Computers and Concrete
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    • v.16 no.3
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    • pp.429-448
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    • 2015
  • The dams are huge structures storing a large amount of water and failures of them cause especially irreparable loss of lives during the earthquakes. They are named as a group of structures subjected to fluid-structure interaction. So, the response of the fluid and its hydrodynamic pressures on the dam should be reflected more accurately in the structural analyses to determine the real behavior as soon as possible. Different mathematical and analytical modelling approaches can be used to calculate the water hydrodynamic pressure effect on the dam body. In this paper, it is aimed to determine the dynamic response of concrete gravity dams using different water modelling approaches such as Westergaard, Lagrange and Euler. For this purpose, Sariyar concrete gravity dam located on the Sakarya River, which is 120km to the northeast of Ankara, is selected as a case study. Firstly, the main principals and basic formulation of all approaches are given. After, the finite element models of the dam are constituted considering dam-reservoir-foundation interaction using ANSYS software. To determine the structural response of the dam, the linear transient analyses are performed using 1992 Erzincan earthquake ground motion record. In the analyses, element matrices are computed using the Gauss numerical integration technique. The Newmark method is used in the solution of the equation of motions. Rayleigh damping is considered. At the end of the analyses, dynamic characteristics, maximum displacements, maximum-minimum principal stresses and maximum-minimum principal strains are attained and compared with each other for Westergaard, Lagrange and Euler approaches.

APPROXIMATE EULER-LAGRANGE-JENSEN TYPE ADDITIVE MAPPING IN MULTI-BANACH SPACES: A FIXED POINT APPROACH

  • Moradlou, Fridoun
    • Communications of the Korean Mathematical Society
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    • v.28 no.2
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    • pp.319-333
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    • 2013
  • Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces: $${\sum_{1{\leq}i_<j{\leq}n}}\;f(\frac{r_ix_i+r_jx_j}{k})=\frac{n-1}{k}{\sum_{i=1}^n}r_if(x_i)$$.

Hamilton제s Principle for the Free Surface Waves of Finite Depth (유한수심 자유표면파 문제에 적용된 해밀톤원리)

  • 김도영
    • Journal of Ocean Engineering and Technology
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    • v.10 no.3
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    • pp.96-104
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    • 1996
  • Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

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A study on dynamic motion equations for a robot manipulator (로보트 팔의 제어를 위한 Dynamics 방정식들에 관한 연구)

  • 김승배;오세정;박인갑;김형래
    • 제어로봇시스템학회:학술대회논문집
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    • pp.52-57
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    • 1987
  • In this paper, it is dealt with the dynamic motion equations for a robot arm. Four kinds of the dynamic equations which are the Lagrange-Euler equations, the Recursive L-E equations, the Newton-Euler equations and the improved N-E equation are derived on robot PUMA 600. Finally the algorithms on these equations are programmed using PASCAL. and are compared with each other. As the results, it is found that the improved N-E equations has the most fastest execution time among the equations and can be used in real time processing.

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