• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.5
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• pp.1084-1094
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• 1993

An efficient method for determining forced responses of a general linear structural system in time domain using subtructure modes and Lagrange multipliers is presented. Compared with the conventional mode synthesis methods, the suggested method does not construct the equations of motion of the combined whole structure and thus the modal parameters of the whole structure are not required. Only modal parameters of each substructure and geometric compatibility conditions are needed. Both the loaded interface free-free modes and free interface modes can be employed as the modal bases of each substructure. Recurrence discrete-time state equations based upon state transition matrix are formulated for the transient analysis of a parameter-changing system. It is shown form numerical examples that the suggested method is very accurate and efficient to calculate transient responses compares with the direct numerical integration method.

• Bulletin of the Korean Space Science Society
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• 2010.04a
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• pp.28.1-28.1
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• 2010

이 연구에서는 기존 선형 상대운동방정식에 차등중력, 주위성의 이심율, J2 섭동 등의 비선형항을 추가하여 보다 정확한 상대운동방정식을 만든 후 섭동이론을 적용하여 위성편대 연료최적화 재배치 문제에 대한 근사 해석해를 구하고자 한다. 먼저, 비선형 섭동항을 테일러 급수를 이용하여 2차항까지 전개한 후, 이를 기존 선형상대운동방정식에 추가하여 새로운 비선형 상대운동방정식을 만든다. 이 때 사용된 선형상대운동방정식은 힐스 방정식으로 주위성의 궤도가 일반적인 타원이고 위성 간 상대거리가 충분히 가깝다고 가정한다. 최적화 조건으로부터 상태벡터와 라그랑지 곱수로 이루어진 연립 미분방정식이 만들어 지는데, 이 식은 힐스 방정식에 기인한 선형부분과 2차 비선형항에 기인한 섭동부분으로 나뉜다. 이 때, 이 연립미분방정식의 해는 선형부분의 해와 섭동으로 인한 변화량의 합으로 근사할 수 있으며 그 변화량은 섭동이론을 적용하여 얻을 수 있다. 이와 같이 얻어진 해는 여러 섭동의 비선형항을 2차까지 포함한 상대운동방정식을 사용했기 때문에, 기존 선형상대운동방정식을 사용하여 구한 최적해 보다 더 정확한 결과를 얻을 것이라 예상한다.

• 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.

• 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 Korean Institute of Communications and Information Sciences
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• v.38C no.2
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• pp.208-212
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• 2013

Due to the singularity of the within-class scatter, linear discriminant analysis (LDA) becomes ill-posed for small sample size (SSS) problems. An extension of LDA, the null space-based LDA (NLDA) provides good discriminant performances for SSS problems. In this paper, by applying the Lagrange technique, the procedure of transforming the problem of finding the feature extractor of NLDA into a linear equation problem is derived.

• The Journal of the Korea Contents Association
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• v.7 no.4
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• pp.234-240
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• 2007

The purpose of this paper was to architecture optimal model of the scooped swing in high bar. The scooped swing was modeled to the double pendulum and was simulated with the Lagrange's equation of motion. Lagrange's method based on a energy approaching method was implemented as a equation of motion. The subject was a national man-gymnast(age 18yrs, height 153 cut mass 48 kg) and the high bar of SPIETH company was used to measure the scooped swing. Qualisys system(six MCU-240 cameras, QTM software)was used to capture data for imaging analysis. The solution of a model and data processing were solved in Mathematica5.0. The results were as follows: First model value of maximum bar displacement was longer than experimental value, that is, 0.02 m. Second, both angular pattern of segment1(HAT) had a increasing curve but curve patterns had a different concave and convex me. Third the experimental value of maximum angular angle of segment2(total leg) had larger than model value, that is, $4^{\circ}$. Conclusively, model parameters were quasi-optimized to obtain a quasi-match between simulated and actual performances. It hopes to simulate a human model by means of integrating musculoskeletal and neuromuscular system in the future study.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.10
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• pp.1038-1044
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• 2009

In this study, vibrations of an electric motor are analyzed when the motor has the interaction between mechanical and electromagnetic behaviors. For this vibration analysis a 3-phase 8-pole brushless DC motor is selected. Vibrations of the motor are influenced by coupled electromechanical characteristics. The variation of air-gap induced by vibration has an influence on the inductance of the motor coil. To analyze dynamic characteristics of the rotor, we studied inductance by the variation of an air-gap. After obtaining the kinetic, potential and magnetic energies for the motor, the equations of motion are derived by using Lagrange's equation. By applying the Newmark time integration method to the equations, the dynamic responses for the displacements and currents are computed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1993.04a
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• pp.52-56
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• 1993

An efficient method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. The method is based upon the mode synthesis formulation procedure, but does not construct the equations of motion of the combined whole structure compared with the conventional methods. For modal bases of each linear substructure, either fixed or free interface modes can be employed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurate and efficient in calculating transient responses compared with the direct numerical integration method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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• pp.2457-2466
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• 1993

A simple method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. Although the method is based upon the mode synthesis formulation procedure, the equations of the combined whole structure are not constructed compared with the conventional methods. Lagrange multi-pliers are used to enforce the conditions of geometric compatibility between the substructure interfaces and they are treated as external forces on each substructure itself. Substructure eigenvalue problem is defined with the substructure interface free of fixed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurated and efficient in calculating transient responses compared with the direct numerical integration method.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2002.10a
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• pp.481-486
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• 2002

Automation of Field Robot has many advantages for efficiency and convenience. In this paper, mathematical equation of field robot is established and automation system is constructed. Hydraulic and Dynamic equation of field robot are constructed in this paper. Inputs of system are angle data from each link (boom, arm, bucket, swing) and pressure data from in, out port of each cylinder. Outputs of system are voltage into electo-proportional valve.