• Title/Summary/Keyword: the Euler Lagrange equation.

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Design on the Controller of Flexible Robot using Sliding Sector Control (슬라이딩 섹터 제어를 이용한 유연한 로봇 팔에 대한 제어기 설계)

  • Han, Jong-Kil;Bae, Sung-Hwan;Yang, Keun-Ho
    • The Journal of the Korea institute of electronic communication sciences
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    • v.5 no.5
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    • pp.541-546
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    • 2010
  • When a flexible arm is rotated by a motor about an joint axis, transverse vibration may occur. The motor torque should be controlled in such a way that the moter rotates by a specified angle, while simultaneously stabilizing vibration of the flexible arm so that it is arrested at the end of rotation. In this paper, the dynamic model of flexible robot arm is modeled by using Bernoulli-Euler beam theory and Lagrange equation. Nonlinear control with hysteresis deadzone using the sliding sector theory with continued input function in the sector is proposed.

Deterministic Nonlinear Control of Two-Link Flexible Arm (2관절 유연한 로봇 팔에 대한 비선형 제어)

  • Han, Jong-Kil;Son, Yong-Su
    • The Journal of the Korea institute of electronic communication sciences
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    • v.4 no.3
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    • pp.236-242
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    • 2009
  • When two-link flexible arm is rotated about an joint axis, transverse vibration may occur. In this paper, vibration dynamics of flexible robot arm is modeled by using Bernoulli-Euler beam theory and Lagrange equation. Using the fact that matrix $\dot{D}$-2C is skew symmetric, new controllers which have a simplified structure with less computational burden is proposed. Lyapunov stability theory is applied to achieve a stable deterministic nonlinear controller for the regulation of joint angle.

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THE TENSION FIELD OF THE ENERGY FUNCTIONAL ON RIEMANNIAN SUBMERSION

  • Choi, Boo-Yong
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.2
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    • pp.239-245
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    • 2011
  • In this paper, we will study the tension field of the function related to a Riemannain submersion ${\pi}\;:\;N{\rightarrow}M$ with totally geodesic fibres. In case that the Riemannain submersion ${\pi}\;:\;N{\rightarrow}M$ particularly has a smooth map $f\;:\;M{\rightarrow}N$ which happens to be a section, we will show that tension field ${\tau}(f)$ of the energy functional can be decomposed into the horizontal and vertical parts.

MEDICAL IMAGE ANALYSIS USING HIGH ANGULAR RESOLUTION DIFFUSION IMAGING OF SIXTH ORDER TENSOR

  • K.S. DEEPAK;S.T. AVEESH
    • Journal of applied mathematics & informatics
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    • v.41 no.3
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    • pp.603-613
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    • 2023
  • In this paper, the concept of geodesic centered tractography is explored for diffusion tensor imaging (DTI). In DTI, where geodesics has been tracked and the inverse of the fourth-order diffusion tensor is inured to determine the diversity. Specifically, we investigated geodesic tractography technique for High Angular Resolution Diffusion Imaging (HARDI). Riemannian geometry can be extended to a direction-dependent metric using Finsler geometry. Euler Lagrange geodesic calculations have been derived by Finsler geometry, which is expressed as HARDI in sixth order tensor.

Transient Response Analysis of Locally Nonlinear Structures Using Substructure-Based State Equations (부분구조의 상태방정식을 이용한 국부 비선형계의 과도응답해석)

  • 김형근;박윤식
    • 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.

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A New Dynamic Analysis of 6-3 Stewart Platform Manipulator (6-3 스튜워트 플랫폼 운동장치의 운동방정식 해석)

  • Kim, Nak-In;Lee, Chong-Won
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.25 no.11
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    • pp.1820-1828
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    • 2001
  • The dynamics of the 6-3 Stewart platform manipulator (SPM) is newly derived based on the kinematic relations particularly developed fur the SPM. The essence of the analysis is to deal with three subsystems of the SPM, each consisting of the command and feedback line links associated with two joined neighboring actuators. The dynamics of the command and feedback line links are first formulated using Lagrange and Newton-Euler method and then combined to derive the dynamic equations of motion fur the SPM. The derived nonlinear equations of motion are so computationally effective that it can be easily applied to real-time high-speed tracking control of 6-3 SPM.

Vibration Analysis of Stiffened Plates having a Resiliently Mounted or Concentrated Mass (탄성지지부가물(彈性支持附加物) 또는 집중질량(集中質量)을 갖는 보강판(補剛板)의 진동해석(振動解析))

  • S.Y.,Han;K.C.,Kim
    • Bulletin of the Society of Naval Architects of Korea
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    • v.23 no.1
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    • pp.23-32
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    • 1986
  • By virtue of an application of the receptance method, simplified formulae to calculate natural frequencies of stiffened plates having a resiliently mounted or concentrated mass are obtained. Some numerical results are compared with those based on Lagrange's equation of motion and with experimental results. For the problem formulation the stiffened plate is reduced to an equivalent orthotropic plate, a resiliently mounted mass to a spring-mass system, and mode shapes of the plate are assumed with comparison functions consisting of Euler beam functions. The proposed formulae give results in good conformity to both numerical results based on Lagrange's equation of motion and experimental results for in-phase modes of the coupled system. For out-of-phase modes the conformity is assured only in case that the natural frequency of the attached system is less than a half of that the stiffened plate. It is also found that a resiliently mounted mass having its own natural frequency of about two or more times that of the stiffened plate can be reduced to a concentrated mass with assurance of a few percent error in the frequency.

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Dynamic Characteristics and Stability of an Infrared Search and Track (적외선 탐색 및 추적장비의 동적 특성 및 안정화)

  • Choi, Jong-Ho;Park, Yong-Chan;Lee, Joo-Hyoung;Choi, Young-Soo
    • Journal of the Korea Institute of Military Science and Technology
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    • v.11 no.2
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    • pp.116-124
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    • 2008
  • Current paper investigates the dynamic behavior and stability of an infrared search and track subjected to external disturbance having gimbal structure with three rotating axes keeping constant angular velocity in the azimuth direction. Euler-Lagrange equation is applied to derive the coupled nonlinear dynamic equation of motion of infrared search and track and the characteristics of dynamic coupling are investigated. Two equilibrium points with small variations from the nonlinear coupling system are derived and the specific condition from which a coupled equation can be three independent equations is derived. Finally, to examine the stability of system, Lyapunov direct method was used and system stability and stability boundaries are investigated.

A Study on Dynamic Behavior of Cantilever Pipe Conveying Fluid with Crack and Moving mass (II)-Focused on the Frequency Change- (크랙과 이동질량을 가진 유체유동 외팔 파이프의 동특성에 관한 연구(II)-진동수 변화를 중심으로-)

  • Son, In-Soo;Yoon, Han-Ik
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.14 no.12
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    • pp.1304-1313
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    • 2004
  • In this paper a dynamic behavior of a cracked cantilever pipe conveying fluid with the moving mass is presented. It has the results focused on the frequency change. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. When the velocity of the moving mass is constant, the influences of the crack severity, the position of the crack, the moving mass, and the coupling of these factors on the frequencies of the cantilever pipe are depicted.

Dynamic Behavior of Rotating Cantilever Pipe Conveying Fluid with Moving mass (이동질량을 가진 유체유동 회전 외팔 파이프의 동특성)

  • Son, In-Soo;Yoon, Han-Ik
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.05a
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    • pp.308-311
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    • 2005
  • In this paper, we studied about the effects of the rotating cantilever pipe conveying fluid with a moving mass. The influences of a rotating angular velocity, the velocity of fluid flow and moving mass on the dynamic behavior of a cantilever pipe have been studied by the numerical method. The equation of motion is derived by using the Lagrange's equation. The cantilever pipe is modeled by the Euler-Bemoulli hew theory. When the velocity of a moving mass is constant, the lateral tip-displacement of a cantilever pipe is proportional to the moving mass and the angular velocity. In the steady state, the lateral tip-displacement of a cantilever pipe is more sensitive to the velocity of fluid than the angular velocity, and the axial deflection of a cantilever, pipe is more sensitive to the effect of a angular velocity.

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