• 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 A
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• v.20 no.1
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• pp.35-43
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• 1996

A computer program for automatic deriving the symbolic equations of motion for robots using the programming language MATHEMATICA has been developed. The program, developed based on the Lagrange formalism, is applicable to the closed chain robots as well as the open chain robots. The closed chains are virtually cut open, and the kinematics and dynamics of the virtual open chain robot are analyzed. The constraints are applied to the virtually cut joints. As a result, the spatial closed chain robot can be considered as a tree structured open chain robot with kinematic constraints. The topology of tree structured open chain robot is described by a FATHER array. The FATHER array of a link indicates the link that is connected in the direction of base link. The constraints are represented by Lagrange multipliers. The parallel robot, DELTA, having three-dimensional closed chains is modeled and simulated to illustrate the approach.

• Korean Journal of Optics and Photonics
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• v.12 no.2
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• pp.109-114
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• 2001

Optical system has some optical and mechanical constraints. The constraints should be preserved in optimization of optical system. For the purpose, the constraints are combined with the merit function by using Lagrange's undetermined multipliers. We propose an active optimization control by using the fact that the errors of constraints are corrected with higher priority than the other errors of the merit function. In this control, the errors which have large contribution to the merit function are converted into constraints. At that time, if the errors are corrected at once, the optimization will be unstable because of their non-linearity. Hence we introduce a target rate which represents a fraction of error to be corrected, and the errors are corrected progressively. An optimization program was developed on the bases of the proposed active control, and applied to design a photographic lens system. By using the active control, we could get better results compared with conventional damped least squares method. ethod.

• Structural Engineering and Mechanics
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• v.2 no.4
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• pp.313-326
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• 1994

Some structures under the action of some specific loads can be treated as consisting of rigid and deformable parts. The paper presents a way to include rigid elements into a finite element model accounting for geometrical and material nonlinearities. Lagrange multipliers technique is used to derive equations of motion for the coupled deformable-rigid system. Solution algorithm based on the elimination of the Lagrangian multipliers and dependent kinematic unknowns at the element level is described. A follow-up paper(Rojek and Kleiber 1993) complements the discussion by giving details of the computer implementation and presenting some realistic test examples.

• Journal of the Korean Operations Research and Management Science Society
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• v.15 no.1
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• pp.99-115
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• 1990

This paper is concerned with the unit commitment problem in an electric power system with both thermal and pumped-storage hydroelectric units. This is a mixed integer programming problem and the Lagrangean relaxation method is used. We show that the relaxed problem decomposes into two kinds of subproblems : a shortest-path problem for each thermal unit and a minimum cost flow problem for each pumped-storage hydroelectric unit. A method of obtaining an incumbenet solution from the solution of a relaxed problem is presented. The Lagrangean multipliers are updated using both subgradient and incremental cost. The algorithm is applied to a real Korean power generation system and its computational results are reported and compaired with other works.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.595-601
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• 2003

In this paper we propose an on line training method for classification based on least squares support vector machine. Proposed method enables the computation cost to be reduced and the training to be peformed incrementally, With the incremental formulation of an inverse matrix in optimization problem, current information and new input data can be used for building the new inverse matrix for the estimation of the optimal bias and Lagrange multipliers, so the large scale matrix inversion operation can be avoided. Numerical examples are included which indicate the performance of proposed algorithm.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1375-1381
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• 2007

In this paper, we propose a linear modeling and identical PD controller design scheme for the three-pole hybrid-type AMB recently developed in the laboratory, which consists of three permanent magnets, providing bias flux, three Hall diodes, measuring rotor displacements, and ring type permanent magnet bearing, stabilizing in axial and tilting directions. Along the three physical coordinates formed by three poles, we introduce the redundant coordinate system and three identical decoupled controllers to construct linear model. The experiments are also carried out in order to verify the effectiveness of proposed controller in stabilizing the transient and steady state response of rotor.

• The Journal of the Acoustical Society of Korea
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• v.15 no.2
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• pp.33-39
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• 1996

A theoretical study of the forced vibration response of a cantilevered beam with non-linear dry friction damping is analyzed by various slip displacements and force levels for the position coordinates of spring-mass-damper and external exciting force. A component mode analysis is carried out based on the constraint conditions and Lagrange multipliers to treat physical systems with non-linear damping. The analysis has shown that the basic phenomena observed for a simply supported beam with a dry friction damper attached are also observed for cantilevered beam.

• Journal of the Korea institute for structural maintenance and inspection
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• v.1 no.1
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• pp.113-124
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• 1997

Based on the recent developments of the reliability-based structural analysis and design as well as the extending knowledge on the probabilistic characteristics of load and resistances, the probability based design criteria have been successfully developed for many standards. Since the probabilistic characteristics depend highly on the local load and resistances, it is recognized to develop the design criterion compatible with domestic requirements. The existing optimum design methods, which are generally based on the structural theory and certain engineering exprience, do not realistically consider the uncertainties of load and resistances and the basic reliability concepts. This study is directed to propose a optimum design based Expected Total Cost Minimization on two-way slab system which could possibly replace optimum design based traditional provisions of the current code, based on the AFOSM reliablity theory.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.17-24
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• 2004

This paper established the dynamic model of a flexible Timoshenko beam with geometrical nonlinearities subject to large overall motions by using the finite element method. The equations of motion are derived by using Hamilton principle based on expressing the kinetic and potential energies of the flexible beam in terms of generalized coordinates. The nonlinear constraint equations are adjoined to the system equations of motion by using Lagrange multipliers.