• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.397-406
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• 1997

In this paper we introduce GESS method and show that dynamics of the system ｙ＇=A(s,t,y) ｙ is more faithfully approxi-mated by GESS method that by Euler method. Numerical experiments are given for the comparison of GESS method with Euler method.

• Computational Structural Engineering
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• v.9 no.3
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• pp.187-197
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• 1996

An explicit direct time integration method based solution algorithm is presented to predict dynamic buckling response of Euler column. On the basis of large deflection beam theory, a plane frame finite element is formulated and implemented into the solution algorithm. The element formulation takes into account geometrical nonlinearity and overall buckling of steel structural frames. The solution algorithm employs the central difference method. Using the computer program developed by the author, dynamic instability behavior of Euler column under impact loading is investigated by considering the time variation of load, load magnitude, and load duration. The free vibration of Euler column caused by a short duration impact load is also studied. The validity and efficiency of the present formulation and solution algorithm are verified through illustrative numerical examples.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2003.05a
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• pp.163-167
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• 2003

A novel method for 3-dimensional dynamic analysis of marine slender structure gas been developed by using Euler parameters. The Euler parameter rotation, which is being widely used in aerospace vehicle dynamics and multi-body dynamics, has been applied to elastic structure analysis. Large deformation of flexible slender structures is described by means of Euler parameters. Euler parameter method is implemented effectively in incremental-iterative algorithm for 3D dynamic analysis. The normalization constraint of Euler parameters is efficiently satisfied by means of a sequential updating method.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.31-40
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• 1992

We introduce the generalized Runge-Kutta methods with the exponentially dominant order .omega. in [3], and the convergence theorems of the generalized explicit Euler method are derived in [4]. In this paper we will study the convergence of the generalized implicit Euler method.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.1081-1098
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• 2006

Mathematical analysis is made on a mesh free method for the compressible Euler equations. In particular, the Moving Least Square Reproducing Kernel (MLSRK) method is employed for space approximation. With the backward-Euler method used for time discretization, existence of discrete solution and it's $L^2-error$ estimate are obtained under a regularity assumption of the continuous solution. The result of numerical experiment made on the biconvex airfoil is presented.

• Transactions of the Korean Society of Automotive Engineers
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• v.4 no.4
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• pp.9-17
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• 1996

This paper develops a sequential updating method of the Euler parameter generalized coordinates for the machine kinematics and dynamics, The Newton's method is slightly modified so as to utilize the Jacobian matrix with respect to the virtual rotation instead of this with repect to the Euler parameters. An intermediate variable is introduced and the modified Newton's method solves for the variable first. Relational equation of the intermediate variable is then solved for the Euler parameters. The solution process is carried out efficiently by symoblic inversion of the relational equation of the intermediate variable and the iteration equation of the Euler parameter normalization constraint. The proposed method is applied to a kinematic and dynamic analysis with the Generalized Coordinate Partitioning method. Covergence analysis is performed to guarantee the local convergence of the proposed method. To demonstrate the validity and practicalism of the proposed method, kinematic analysis of a motion base system and dynamic analysis of a vehicle are carried out.

• 한국전산유체공학회:학술대회논문집
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• 2007.04a
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• pp.116-119
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• 2007

In this study the unsteady aerodynamic analysis of a hovering helicopter rotor is performed. For the accurate flow field analysis Euler equations and the free wake method are coupled. The Euler equations are solved to find the pressure distribution around the rotor, and free wake method is used to give the boundary condition for the solution of Euler equations. Also, vortex strength and wake motion after the rotor are simulated by the free wake method. The accuracy of the present method is compared with the source sink model. The present method is applied to the hovering Caradonna-Tung rotor and compared with experimental results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.43-50
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• 2014

In this paper we discussed Euler-Maruyama method for stochastic differential equations with jump diffusion. We give a convergence result for Euler-Maruyama where the coefficients of the stochastic differential equation are locally Lipschitz and the pth moments of the exact and numerical solution are bounded for some p > 2.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.12
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• pp.1044-1050
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• 2001

This paper presents firstly the method of Euler angle matching designing the transfer alignment using the attitude matching. In this method, the observation directly uses Euler angle difference between MINS and SINS so it needs to describe the rotation vector error to the Euler angle error. The rotation vector error related to the Euler angle error is derive from the direction cosine matrix error equation. The feasibility of the Kalman filter designed for the transfer alignment by Euler angle matching is analyzed by the alignment error results with respect to the roll angle the pitch angle, and the yaw angle matching.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.545-555
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• 2004

Ever since the time of Euler, the so-called Euler sums have been evaluated in many different ways. We give here a proof of the classical Euler sum by following Lewin's method. We also consider some related formulas involving Euler sums, which are evaluatable from some known definite integrals.