• Title/Summary/Keyword: Lagrange-stable

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Chain Recurrences on Conservative Dynamics

  • Choy, Jaeyoo;Chu, Hahng-Yun
    • Kyungpook Mathematical Journal
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    • v.54 no.2
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    • pp.165-171
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    • 2014
  • Let M be a manifold with a volume form ${\omega}$ and $f:M{\rightarrow}M$ be a diffeomorphism of class 𝒞$^1$ that preserves ${\omega}$. We prove that if M is almost bounded for the diffeomorphism f, then M is chain recurrent. Moreover, we get that Lagrange stable volume-preserving manifolds are also chain recurrent.

A Comparative Study of the Incompressibility Constraint on the Rigid Plastic Finite Element Method (강소성 유한요소법에서 비압축성조건의 비교 연구)

  • 이상재;조종래;배원병
    • Transactions of Materials Processing
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    • v.8 no.1
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    • pp.47-56
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    • 1999
  • The governing functional in plastic deformation has to satisfy the incompressibility constraint. This incompressibility constraint imposed on velocity fields can be removed by introducing either Lagrange multiplier or the penalty constant into the functional. In this study, two-dimensional rigid plastic FEM programs using these schemes were developed. These two programs and DEFORM were applied in a cylinder upsetting and a closed die forging to compare the values of load, local mean stress and volume loss. As the results, the program using Lagrange multiplier obtained a more exact and stable solution, but it took more computational time than the program using the penalty constant. Therefore, according to user's need, one of these two programs can be chosen to simulate a metal forming processes.

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A New Penalty Parameter Update Rule in the Augmented Lagrange Multiplier Method for Dynamic Response Optimization

  • Kim, Min-Soo;Choi, Dong-Hoon
    • Journal of Mechanical Science and Technology
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    • v.14 no.10
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    • pp.1122-1130
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    • 2000
  • Based on the value of the Lagrange multiplier and the degree of constraint activeness, a new update rule is proposed for penalty parameters of the ALM method. The theoretical exposition of this suggested update rule is presented by using the algorithmic interpretation and the geometric interpretation of the augmented Lagrangian. This interpretation shows that the penalty parameters can effect the performance of the ALM method. Also, it offers a lower limit on the penalty parameters that makes the augmented Lagrangian to be bounded. This lower limit forms the backbone of the proposed update rule. To investigate the numerical performance of the update rule, it is embedded in our ALM based dynamic response optimizer, and the optimizer is applied to solve six typical dynamic response optimization problems. Our optimization results are compared with those obtained by employing three conventional update rules used in the literature, which shows that the suggested update rule is more efficient and more stable than the conventional ones.

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An Efficient Unified Method to Compute Voltage Collapse Point (전압붕괴 임계점 계산을 위한 효율적 통합법)

  • Nam, Hae-Gon;Kim, Dong-Jun;Song, Chung-Gi;Mun, Yeong-Hwan;Kim, Tae-Gyun;Lee, Hyo-Sang
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.48 no.8
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    • pp.951-957
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    • 1999
  • The saddle node bifurcation (SNB) and the distance voltage instability are valuable information in power system planning and operation. This paper presents a new efficient, robust and unified strategy to compute the SNB by the combined use of the continuation power flow (CPF), Point of Collapse (PoC) method, and the method of a pair of multiple load flow solutions (PMLFS) with Lagrange interpolation utilizing only their advantages: the approximate nose curves and critical loading are determined fast by Lagrange-interpolating two stable and two unstable solutions obtained by using the robust CPF and PMLFS; the exact SNB is computed by the quadratically converging PoC method. The proposed method has been tested on Klos-Kerner 11-bus, New England 30-bus, IEEE 118-bus and KEPCO 791-bus systems. The method is found to be so efficient that computation time for determining the SNB of the KEPCO 791-bus system is 17.82 sec by a notebook PC with 300 MHz Pentium processor.

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A Study on Control of Stable Grasping Motion for Finger Robot (손가락 로봇의 안정 파지 운동 제어에 관한 연구)

  • Choi, Jong-Hwan
    • Journal of Advanced Marine Engineering and Technology
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    • v.30 no.3
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    • pp.428-437
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    • 2006
  • This paper attempts to derive and analyze the dynamic system of grasping a rigid object by means of two multi-degrees-of-freedom robot flngers with soft and deformable tips. It is shown firstly that a set of differential equation describing dynamics system of the manipulators and object together with geometric constraint of tight area-contacts is formulated by Lagrange's equation. It is shown secondly that the problems of controlling both the forces of pressing object and the rotation angle of the object under the geometric constraints are discussed. In this paper. the control method for dynamic stable grasping and enhancing dexterity in manipulating things is proposed. It is illustrated by computer simulation that the control system gives the performance improvement in the dynamic stable grasping of the dual fingers robot with soft tips.

A Study on Stable Grasping Motion Control of Dual-Finger (듀얼-핑거의 안정적 파지 운동 제어에 관한 연구)

  • Um Hyuk;Choi Jong-Hwan;Kim Seung-Soo;Han Hyun-Yong;Yang Soon-Yong;Lee Jin-Gul
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.14 no.4
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    • pp.81-88
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    • 2005
  • This paper attempts to derive the dynamic model of handling tasks in finger robot which grasps stable and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraint of tight area-contacts is formulated by Lagrange's equation. Secondly, the roblems of controlling both the forces of pressing object and the rotation angle of the object under the geometric constraints are discussed. The effect of geometric constraints of area-contacts between the link's end-effector and the object is analyzed and the model based on the differential-algebraic equations is presented. In this paper, the control method for dynamic stable grasping and enhancing dexterity in manipulating things is proposed. It is illustrated by computer simulation and the experiment that the control system gives the performance improvement in the dynamic stable grasping and nimble manipulating of the dual fingers robot with soft tips.

Adaptive Data Association for Multi-Target Tracking using Relaxation

  • Lee, Yang-Weon;Hong Jeong
    • Journal of Electrical Engineering and information Science
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    • v.3 no.2
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    • pp.267-273
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    • 1998
  • This paper introduces an adaptive algorithm determining the measurement-track association problem in multi-target tracking(MTT). We model the target and measurement relationships with mean field theory and then define a MAP estimate for the optimal association. Based on this model, we introduce an energy function defined over the measurement space, that incorporates the natural constraints for target tracking. To find the minimizer of the energy function, we derived a new adaptive algorithm by introducing the Lagrange multipliers and local dual theory. Through the experiments, we show that this algorithm is stable and works well in general environments. Also the advantages of the new algorithm over other algorithms are discussed.

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A NONEXISTENCE THEOREM FOR STABLE EXPONENTIALLY HARMONIC MAPS

  • Koh, Sung-Eun
    • Bulletin of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.211-214
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    • 1995
  • Let M and N be compact Riemannian manifolds and $f : M \to N$ be a smooth map. Following J. Eells, f is exponentially harmonic if it represents a critical point of the exponential energy integral $$ E(f) = \int_{M} exp(\left\$\mid$ df \right\$\mid$^2) dM $$ where $(\left\ df $\mid$\right\$\mid$^2$ is the energy density defined as $\sum_{i=1}^{m} \left\$\mid$ df(e_i) \right\$\mid$^2$, m = dimM, for orthonormal frame $e_i$ of M. The Euler- Lagrange equation of the exponential energy functional E can be written $$ exp(\left\$\mid$ df \right\$\mid$^2)(\tau(f) + df(\nabla\left\$\mid$ df \right\$\mid$^2)) = 0 $$ where $\tau(f)$ is the tension field along f. Hence, if the energy density is constant, every harmonic map is exponentially harmonic and vice versa.

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Research of Stable Grasping for Handling Tasks in Field Robot

  • Park, Kyung-Taek;Kim, Sung-Su;Yang, Soon-Yong;Lee, Byung-Rong;Ahn, Kyoung-Kwan;Han, Hyun-Yong
    • 제어로봇시스템학회:학술대회논문집
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    • 2001.10a
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    • pp.132.6-132
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    • 2001
  • This paper aims to derive a mathematical model of the dynamics of handling tasks in field robot which stable grasping and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraint of tight area-contacts is formulated by Lagrange equation. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of area-contacts of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Thirdly, simulation results are shown and the effects of geometric constraints of area-contact is discussed.

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Landing Dynamic and Key Parameter Estimations of a Landing Mechanism to Asteroid with Soft Surface

  • Zhao, Zhijun;Zhao, JingDong;Liu, Hong
    • International Journal of Aeronautical and Space Sciences
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    • v.14 no.3
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    • pp.237-246
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    • 2013
  • It is of great significance to utilize a landing mechanism to explore an asteroid. A landing mechanism named ALISE (Asteroid Landing and In Situ Exploring) for asteroid with soft surface is presented. The landing dynamic in the first turning stage, which represents the landing performance of the landing mechanism, is built by a Lagrange equation. Three key parameters can be found influencing the landing performance: the retro-rocket thrust T, damping element damping $c_1$, and cardan element damping $c_2$. In this paper, the retro-rocket thrust T is solved with considering that the landing mechanism has no overturning in extreme landing conditions. The damping element damping c1 is solved by a simplified dynamic model. After solving the parameters T and $c_1$, the cardan element damping $c_2$ is calculated using the landing dynamic model, which is built by Lagrange equation. The validities of these three key parameters are tested by simulation. The results show a stable landing, when landing with the three estimated parameters T, $c_1$, and $c_2$. Therefore, the landing dynamic model and methods to estimate key parameters are reasonable, and are useful for guiding the design of the landing mechanism.