• 대한수학회논문집
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• 제16권1호
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• pp.153-161
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• 2001

In the course of working on the preconditioning $C^1$ polynomial spline collocation method, one has to deal with the exponential decay of $C^1$ Lagrange polynomial splines. In this paper we show the exponential decay of $C^1$ Lagrange polynomial splines using the Chebyshev-Gauss points as the local data points.

• Journal of Astronomy and Space Sciences
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• 제38권2호
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• pp.145-155
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• 2021

In this work, preliminary launch opportunities from NARO Space Center to the Sun-Earth Lagrange point are analyzed. Among five different Sun-Earth Lagrange points, L1 and L2 points are selected as suitable candidates for, respectively, solar and astrophysics missions. With high fidelity dynamics models, the L1 and L2 point targeting problem is formulated regarding the location of NARO Space Center and relevant Target Interface Point (TIP) for each different launch date is derived including launch injection energy per unit mass (C3), Right ascension of the injection orbit Apoapsis Vector (RAV) and Declination of the injection orbit Apoapsis Vector (DAV). Potential launch periods to achieve L1 and L2 transfer trajectory are also investigated regarding coasting characteristics from NARO Space Center. The magnitude of the Lagrange Orbit Insertion (LOI) burn, as well as the Orbit Maintenance (OM) maneuver to maintain more than one year of mission orbit around the Lagrange points, is also derived as an example. Even the current work has been made under many assumptions as there are no specific mission goals currently defined yet, so results from the current work could be a good starting point to extend diversities of future Korean deep-space missions.

• 한국정보통신학회논문지
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• 제8권3호
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• pp.702-707
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• 2004

본 논문은 CCD 카메라와 거리 센서를 사용하여 컨테이너의 자세 측정에 관하여 연구하였다. 특히 특징점을 추출하고 영상의 잡음을 줄이는 방법에 대하여 중점적으로 기술하였다. 가우시안 및 랜덤 노이즈를 제거하기 위하여 Euler-Lagrange 방정식을 소개하였으며 PDE(Partial Differential Equation)를 기초로 한 Euler-Lagrange 방정식을 풀기 위하여 ADI(Alternating Direction Implicit)방법을 적용하였다. 그리고 스프레더와 컨테이너의 특징점을 추출하기 위해서 기존의 황금 분할법과 이분 분할법을 이용한 방법은 지역적 최대 및 최소 값의 경우 정확한 해를 구할 수 없어서 k차 곡률 알고리즘을 이용하였다. 제안된 알고리즘은 영상의 전처리과정에서 잡음제거에 효과적이며 카메라와 거리센서를 이용한 제안 시스템은 기존시스템의 구조적 변경 없이 사용가능하기 때문에 비용이 저렴한 장점이 있다.

• Journal of Astronomy and Space Sciences
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• 제20권4호
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• pp.313-318
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• 2003

A communications satellite system placed in three-Lagrange points, $L_3$, $L_4$ and $L_5$, of the restricted three-body problem in Earth-Moon system is proposed in this paper. LEO satellite constellation has been another choice of communications system. The proposed system which is alternatives of limited geostationary orbit resources, has some weak points such as long distance from the Earth, relatively expensive launch cost, long delay time, more required power, and so on. It has good points like less efforts (fuel) for station keeping, less eclipses, etc. This system has limitations for applications to provide commercial services but it is still some attractive points.

• 대한토목학회논문집
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• 제41권4호
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• pp.331-340
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• 2021

본 논문은 비예측 극한하중인 폭발하중에 노출된 RC building 구조물의 폭발손상평가를 위한 수치해석적 연구이다. 수치해석의 효율성 및 정확성을 높이기 위해, 폭발하중에 대한 정의, 유체-구조 연성을 위한 Euler-Lagrange 커플링 기법 적용, 그리고 고변형률 속도가 고려된 콘크리트 및 강재 재료구성모델이 제안된다. 특히 효율적인 폭발하중 정의를 위해, Euler-FCT 기법을 통하여 TNT 질량에 따른 시간별 압력하중 데이터가 확보되고, 이는 RC building 구조물 총 7 지점의 폭발위치에 적용되며, ANSYS-AUTODYN 솔버에 연결되어 수치 시뮬레이션이 수행된다. 해석결과, TNT 질량 및 폭발 위치에 따라 손상 차이가 발생하였으며, 먼저 TNT 질량 20 kg 일 경우 3 곳의 폭발손상 지점에서 주부재 중 슬래브에서만 중간 및 가벼운 손상이 발생되었고, TNT 질량 100 kg 일 경우 5 곳의 폭발손상 지점 중 3 곳은 슬래브 및 보 부재에서 중간 손상이 발생되었으며, 2 곳은 슬래브에서 심각한 손상이 발생되었다.

• 한국산학기술학회논문지
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• 제16권4호
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• pp.2370-2378
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• 2015

본 논문에서는 로봇 매니퓰레이터의 토크 최소화를 위한 궤적계획을 위해 라그랑지 보간법을 이용한 Algorithm을 제안하였다. 이를 위해 로봇 매니퓰레이터의 위치에 대한 구속조건이 주어지고 안정성이 보장되어야 한다. 라그랑지 보간법의 Runge's 현상을 회피하기 위해 Chebyshev 보간점을 이용하여 시간 보간점을 설정하였고, 이에 대응하는 최적각도를 찾아내어 라그랑지 보간법을 이용한 매끄러운 관절의 각도, 속도, 가속도 궤적을 얻을 수 있다. 로봇 매니퓰레이터의 토크 소비 최적화를 위한 성능지표를 선정하였으며, 계산된 궤적을 통해 이 성능지표가 최소값을 가지도록 반복 계산하는 과정을 거친다. 이를 통해, 토크와 성능지표를 최소화 시키는 최적의 궤적을 얻을 수 있으며, 로봇 매니퓰레이터가 작업을 수행하기 위한 움직임의 안전성을 보장한다.

• 소음진동
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• 제5권4호
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• pp.503-514
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• 1995

In the case of performing experimental modal analysis(EMA) and finite- element analysis(EFA) for a whole structure of automotive body that is composed of many complex parts, a trouble may arise from the calculation time, the capacity of memory in computers and the experimental conditions, etc. In this paper, for the vibrational analysis of automotive body model, the efficient modal synthesis method by means of dividing the whole structure into two parts and performing EMA and FEA for each part is studied. In addition, the method based on Lagrange interpolation is proposed for approximating rotational degrees-of-freedom information and linking FEA with EMA. In result, by measuring translational degrees-of-freedom information of only few points and adopting only few modes, the linking method based on Lagrange interpolation turned out to be efficient and accurate in the low frequency range.

• 충청수학회지
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• 제29권2호
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• pp.267-281
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• 2016

In this paper, we consider multi-degree reduction of $B{\acute{e}}zier$ curves with continuity of any (r, s) order with respect to $L_2$ norm. With help of matrix theory about generalized inverses we can use Lagrange multipliers to obtain the degree reduction matrix in a very simple form as well as the degree reduced control points. Also error analysis comparing with the least squares degree reduction without constraints is given. The advantage of our method is that the relationship between the optimal multi-degree reductions with and without constraints of continuity can be derived explicitly.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.2246-2251
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• 2003

This paper proposes shape design of frame structures for vibration suppression and weight reduction. The $H_{\infty}$ norm of the transfer function from disturbance sources to the output points where vibration should be suppressed, is adopted as the performance index to represent the magnitude of vibration transfer. The design parameters are the node positions of the frame structure, on which constraints are imposed so that the structure achieves given tasks. For computation of Pareto optimal solutions to the two-objective design problem, a number of linear combinations of the $H_{\infty}$ norm and the total weight of the structure are considered and minimized. For minimization of the scalared objective function, a Lagrange function is defined by the objective function and the imposed constraints on the design parameters. The solution for which the Lagrange function satisfies the Karush-Kuhn-Tucker condition, is searched by the sequential quadratic programming (SQP) method. Numerical examples are presented to demonstrate the effectiveness of the proposed design method.

• International Journal of Aeronautical and Space Sciences
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• 제15권2호
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• pp.183-189
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• 2014

Pseudo-spectral method typically converges at an exponential rate. However, it requires a special set of fixed collocation points (CPs) to get highly accurate formulas for partial integration and differentiation. In this study, computational nodes for defining the discrete variables of states and controls are built independently of the CPs. The state and control variables at each CP, which are required to transcribe an NOCP into the corresponding NLP, are interpolated, using those variables allocated at each node. Additionally, Lagrange interpolation and spline interpolation are investigated, to provide a guideline for selecting a favorable interpolation method. The proposed techniques are applied to the solution of an NOCP using equally spaced nodes, and the computed results are compared to those using the standard PS approach, to validate the usefulness of the proposed methods.