• Transactions of the Korean Society of Automotive Engineers
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• v.21 no.2
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• pp.122-130
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• 2013

Rail geometries such as cant, grade and curvature can be easily represented by means of a track coordinate system. In this analysis, in order to derive a dynamic and constraint equation of a wheelset, the track coordinate system is used as an intermediate stage. Dynamic and constraint equations of railway vehicle bodies except the wheelset are written in the Cartesian coordinate system as a conventional method. Therefore, whole dynamic equations of a railway vehicle are derived by combining wheelset dynamic equations and dynamic equations of railway vehicle bodies. Constraint equations and constraint Jacobians are newly derived for the track coordinate system. A process for numerical analysis is suggested for the derived dynamic and constraint equations of a railway vehicle. The proposed dynamic analysis of a railway vehicle is validated by comparison against results obtained from VI-RAIL analysis.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.52-57
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• 1987

In this paper, it is dealt with the dynamic motion equations for a robot arm. Four kinds of the dynamic equations which are the Lagrange-Euler equations, the Recursive L-E equations, the Newton-Euler equations and the improved N-E equation are derived on robot PUMA 600. Finally the algorithms on these equations are programmed using PASCAL. and are compared with each other. As the results, it is found that the improved N-E equations has the most fastest execution time among the equations and can be used in real time processing.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.869-878
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• 2013

We study boundedness of solutions of dynamic equations on time scales by using Lyapunov-type functions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.994-999
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• 2002

The Pendulum Automatic Dynamic Balancer is a device to reduce the unbalanced mass of rotors. For the analysis of dynamic stability and behavior, the nonlinear equations of motion for a system including the Pendulum Balancer are derived with respect to polar coordinate by Lagrange's equations. And the perturbation method is applied to find the equilibrium positions and to obtain the linear variation equations. Based on the linearized equations, the dynamic stability of the system around the equilibrium positions is investigated by the eigenvalue problem. Furthermore, in order to confirm the stability, the time responses for the system are computed from the nonlinear equations of motion.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.10
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• pp.4733-4738
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• 2013

This paper proposes a method to obtain the dynamic equilibrium configuration of a constrained mechanical system by using multibody dynamic analysis. Dynamic equilibrium equations with independent coordinates are derived from the time-dependent constraint equations and dynamic equations of a multibody system. The Newton-Raphson method is used to find numerical solutions for nonlinear algebraic equations that are composed of the dynamic equilibrium and constraint equations. The proposed method is applied to obtain the dynamic equilibrium configuration of a speed governor, and the results are verified on the basis of the results from conventional dynamic analysis. Furthermore, vertical displacements at equilibrium configuration, which varied with the rotational velocity of the speed governor, are calculated, and design parameter analysis of the equilibrium configuration is presented.

• Structural Engineering and Mechanics
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• v.13 no.3
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• pp.329-343
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• 2002

In this research, the dynamic stability of an orthotropic elastic conical shell, with elasticity moduli and density varying in the thickness direction, subject to a uniform external pressure which is a power function of time, has been studied. After giving the fundamental relations, the dynamic stability and compatibility equations of a nonhomogeneous elastic orthotropic conical shell, subject to a uniform external pressure, have been derived. Applying Galerkin's method, these equations have been transformed to a pair of time dependent differential equations with variable coefficients. These differential equations are solved using the method given by Sachenkov and Baktieva (1978). Thus, general formulas have been obtained for the dynamic and static critical external pressures and the pertinent wave numbers, critical time, critical pressure impulse and dynamic factor. Finally, carrying out some computations, the effects of the nonhomogeneity, the loading speed, the variation of the semi-vertex angle and the power of time in the external pressure expression on the critical parameters have been studied.

• Steel and Composite Structures
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• v.15 no.1
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• pp.57-79
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• 2013

This paper studies the dynamic instability of laminated composite plates under thermal and arbitrary in-plane periodic loads using first-order shear deformation plate theory. The governing partial differential equations of motion are established by a perturbation technique. Then, the Galerkin method is applied to reduce the partial differential equations to ordinary differential equations. Based on Bolotin's method, the system equations of Mathieu-type are formulated and used to determine dynamic instability regions of laminated plates in the thermal environment. The effects of temperature, layer number, modulus ratio and load parameters on the dynamic instability of laminated plates are investigated. The results reveal that static and dynamic load, layer number, modulus ratio and uniform temperature rise have a significant influence on the thermal dynamic behavior of laminated plates.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.299-312
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• 2008

In this paper, we establish some oscillation criteria for nonautonomous second order neutral delay dynamic equations $(x(t){\pm}r(t)x({\tau}(t)))^{{\Delta}{\Delta}}+H(t,\;x(h_1(t)),\;x^{\Delta}(h_2(t)))=0$ on a time scale ${\mathbb{T}}$. Oscillatory behavior of such equations is not studied before. This is a first paper concerning these equations. The results are not only can be applied on neutral differential equations when ${\mathbb{T}}={\mathbb{R}}$, neutral delay difference equations when ${\mathbb{T}}={\mathbb{N}}$ and for neutral delay q-difference equations when ${\mathbb{T}}=q^{\mathbb{N}}$ for q>1, but also improved most previous results. Finally, we give some examples to illustrate our main results. These examples arc [lot discussed before and there is no previous theorems determine the oscillatory behavior of such equations.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.396.2-396
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• 2002

Dynamic stability and behavior are analyzed fur Pendulum Automatic Dynamic Balancer which is a device to reduce an unbalanced mass of rotors. The nonlinear equations of motion for a system including a Pendulum Balancer are derived with respect to polar coordinate by Lagrange's equations. The perturbation method is applied to find the equilibrium positions and to obtain the linear variation equations. Based on linearized equations, the dynamic stability of the system around the equilibrium positions is investigated by the eigenvalue problem. (omitted)

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.425-438
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• 2007

In this paper, we establish some new oscillation criteria for a second-order delay dynamic equation $$u^{{\Delta}{\Delta}}(t)+p(t)u(\tau(t))=0$$ on a time scale $\mathbb{T}$. The results can be applied on differential equations when $\mathbb{T}=\mathbb{R}$, delay difference equations when $\mathbb{T}=\mathbb{N}$ and for delay $q$-difference equations when $\mathbb{T}=q^{\mathbb{N}}$ for q > 1.