• Journal of the Korean Physical Society
• /
• v.73 no.12
• /
• pp.1800-1807
• /
• 2018

In this paper, we study the gravitational perturbation of traversable wormhole spacetime, especially the Morris-Thorne wormhole spacetime, by using the linearized theory of gravity. We restrict our interest to the first order term and ignore the higher order terms. We assume that the perturbation is axisymmetric. We also assume that the time dependence follows the Fourier decomposition and the angular dependence is expressed in terms of the Legendre functions. As a result, we derive the gravitational perturbation equation of traversable wormhole in terms of a single linear second-order differential equation. As a consequence, we could analyze the unstability of the spacetime with the effective potentials. Furthermore, we consider the interaction between the external gravitational perturbation and the exotic matter, constituting traversable wormholes and its effect on the stability of traversable wormholes.

• Journal of the Korean Society for Precision Engineering
• /
• v.22 no.1
• /
• pp.89-96
• /
• 2005

This paper is concerned with a balancing motion formulation and control of the ZMP (Zero Moment Point) for a biped-walking robot that has a prismatic balancing weight or a revolute balancing weight. The dynamic stability equation of a walking robot which have a prismatic balancing weight is conditionally linear but a walking robot's stability equation with a revolute balancing weight is nonlinear. For a stable gait, stabilization equations of a biped-walking robot are modeled as non-homogeneous second order differential equations for each balancing weight type, and a trajectory of balancing weight can be directly calculated with the FDM (Finite Difference Method) solution of the linearized differential equation. In this paper, the 3dimensional graphic simulator is developed to get and calculate the desired ZMP and the actual ZMP. The operating program is developed for a real biped-walking robot IWRⅢ. Walking of 4 steps will be simulated and experimented with a real biped-walking robot. This balancing system will be applied to a biped humanoid robot, which consist legs and upper body, as a future work.

• 한국해양학회지
• /
• v.30 no.6
• /
• pp.543-549
• /
• 1995

The inverse method has been used to estimate a surface velocity field from sequential AVHRR/SST data. In the model, equation system was composed of heat equation and horizontal divergence minimization and the velocity field contained in the advective term of the heat equation, which was linearized in grid system, was estimated. A constraint was the minimization of horizontal divergence with weighting factor and introduced to compensate the null space(Menke, 1984) of the velocity solutions for the heat equation. The experiments were carried out to set up the range of weighting factor and the matrix equation was solved by SVD(Singular Value Decomposion). In the experiment, the scales of horizontal temperature gradient and divergence of synthetic velocity field were approximated to those of real field. The neglected diffusive effect and the horizontal variation of heat flux in the heat equation were regarded as random temperature errors. According to the result of experiments, the minimum of relative error was more desirable than the minimum of misfit as the criteria of setting up the weighting factor and the error of estimated velocity field became small when the weighting factor was order of $10^{-1}$

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.29 no.3
• /
• pp.237-244
• /
• 2016

This paper presents a nonlinear Moving Least Squares(MLS) difference method for material nonlinearity problem. The MLS difference method, which employs strong formulation involving the fast derivative approximation, discretizes governing partial differential equation based on a node model. However, the conventional MLS difference method cannot explicitly handle constitutive equation since it solves solid mechanics problems by using the Navier's equation that unifies unknowns into one variable, displacement. In this study, a double derivative approximation is devised to treat the constitutive equation of inelastic material in the framework of strong formulation; in fact, it manipulates the first order derivative approximation two times. The equilibrium equation described by the divergence of stress tensor is directly discretized and is linearized by the Newton method; as a result, an iterative procedure is developed to find convergent solution. Stresses and internal variables are calculated and updated by the return mapping algorithm. Effectiveness and stability of the iterative procedure is improved by using algorithmic tangent modulus. The consistency of the double derivative approximation was shown by the reproducing property test. Also, accuracy and stability of the procedure were verified by analyzing inelastic beam under incremental tensile loading.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.19 no.2
• /
• pp.608-616
• /
• 2018

If a general nonlinear system is linearized by the successive multiplication of the 1st and 2nd order systems, then there are four types of poles in this linearized system: the pole of the 1st order system and the equal poles, two distinct real poles, and complex conjugate pair of poles of the 2nd order system. Linear Quadratic (LQ) control is a method of designing a control law that minimizes the quadratic performance index. It has the advantage of ensuring the stability of the system and the pole placement of the root of the system by weighted matrix adjustment. LQ control by the weighted matrix can move the position of the pole of the system arbitrarily, but it is difficult to set the weighting matrix by the trial and error method. This problem can be solved using the characteristic equations of the Hamiltonian system, and if the control weighting matrix is a symmetric matrix of constants, it is possible to move several poles of the system to the desired closed loop poles by applying the control law repeatedly. The paper presents a method of calculating the state weighting matrix and the control law for moving the equal poles with Jordan blocks to two real poles using the characteristic equation of the Hamiltonian system. We express this characteristic equation with a state weighting matrix by means of a trigonometric function, and we derive the relation function (${\rho},\;{\theta}$) between the equal poles and the state weighting matrix under the condition that the two real poles are the roots of the characteristic equation. Then, we obtain the moving-range of the two real poles under the condition that the state weighting matrix becomes a positive semi-finite matrix. We calculate the state weighting matrix and the control law by substituting the two real roots selected in the moving-range into the relational function. As an example, we apply the proposed method to a simple example 3rd order system.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.8
• /
• pp.2113-2122
• /
• 1994

The 3-D FEM analysis for simulating the stamping operation of planar anisotropic sheet metals with arbitrarily-shaped tools is introduced. An implicit, incremental, updated Lagrangian formulation with a rigid-viscoplastic constitutive equation is employed. Contact and friction are considered through the mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of tool surfaces. The consistent full set of governing relations, comprising equilibrium equation and mesh-normal geometric constraints, is appropriately linearized. The linear triangular elements are used for depicting the formed sheet, based on membrane approximation. Barlat's non-quadratic anisotropic yield criterion(strain-rate potential) is employed, whose in-plane anisotropic properties are taken into account with anisotropic coefficients and non-quadratic function parameter. The planar anisotropic finite element formulation is tested with the numerical simulations of the stamping of an automotive hood inner panel and the drawing of a hemispherical punch. The in-plane anisotropic effects on the formability of both mild steel and aluminum alloy sheet metals are examined.

• The Transactions of the Korean Institute of Power Electronics
• /
• v.20 no.2
• /
• pp.175-181
• /
• 2015

In this study, a lithium polymer battery (LiPB) is simply expressed by a primary RC equivalent model. The PI state observer is designed in Matlab/Simulink. The non-linear relationship with the OCV-SOC is represented to be linearized with 0.1 pu intervals by using battery parameters obtained by constant-current pulse discharge. A state equation is configured based on battery parameters. The state equation, which applied Peukert's law, can estimate SOC more accurately. SOC estimation capability was analyzed by utilizing reduced Federal Test Procedure (FTP-72) current profile and using a bi-directional DC-DC converter at temperature ($25^{\circ}C$). The PI state observer, which is designed in this study, indicated a SOC estimation error rate of ${\pm}2%$ in any of the initial SOC states. The PI state observer confirms a strong SOC estimation performance despite disturbances, such as modeling errors and noise.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.15 no.2
• /
• pp.165-174
• /
• 2007

Variable displacement type piston pump uses various controllers for controlling more than one state quantity like pressure, flow, power, and so on. These controllers need the mathematical model closely expressing dynamic behavior of pump for analyzing the stability of control systems which usually use various kinds of state variables. This paper derives the nonlinear mathematical model for variable displacement type piston pump. This model consists of two 1st oder differential equations by the continuity equations and one 2nd oder differential equation by the motion equation. To simplify the model we obtain the linear state variable model by differentiating the three nonlinear equations. And we verify this linearized model by comparison of simulation with experimentation and analyze the stability for the flow/pressure control. Finally this paper suggests the design compensation to ensure the stability of the systems.

• Structural Engineering and Mechanics
• /
• v.72 no.5
• /
• pp.597-615
• /
• 2019

The paper studies the dispersion of the axisymmetric longitudinal wave propagating in the "hollow cylinder + surrounding medium" system with inhomogeneous initial stresses caused by the uniformly distributed radial compressional forces acting at infinity. Up to now in the world literature, there exist only a few investigations related to the wave dispersion in a hollow cylinder with inhomogeneous initial stresses. Therefore, this paper is one of the first attempts in this field in the sense of the development of investigations for the case where the cylinder is surrounded with an infinite medium. The three-dimensional linearized theory of elastic waves is used for describing the considered wave propagation problem and, for a solution to the corresponding mathematical problem, the discrete-analytical solution method is developed and employed. The corresponding dispersion equation is obtained and this equation is solved numerically and, as a result of this solution, the dispersion curves are constructed for the first and second modes. By analyzing these curves, the character of the influence of the inhomogeneous initial stresses on the dispersion curves is established. In particular, it is established that as a result of the inhomogeneity of the initial stresses both new dispersion curves and the "band gap" for the wave frequencies can appear.

• Journal of Astronomy and Space Sciences
• /
• v.11 no.2
• /
• pp.281-295
• /
• 1994

In this paper, the Variable Structure System(VSS) theory with new continuous switching dynamic equation is used to design an automatic controller for the active nutation damping in momentum bias stabilized spacecraft. In the application of VSS theory to a linearized multivariable system with the nutation damping systems, there exist some disadvantages such as how to determine the switching gains and how to reduce the chattering phenomina and reaching phase in input and state trajectories. To solve these drawbacks, this paper presents the continuous switching dynamic equation instead of the discontinuous switching logics to obtain the sliding mode. The new design approach is much simpler than the VSS theory. And there do not exist chattering phenomina in this method because the obtained control inputs are continuous. Simultaneously the reaching phase is reduced by a suitable choice of design factor.