• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.1
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• pp.31-38
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• 2008

This paper deals with the nonlinear optimal control approach to helicopter maneuver problems using the indirect method. We apply a penalty function to the integral deviation from a prescribed trajectory to convert the system optimality to an unconstrained optimal control problem. The resultant two-point boundary value problem has been solved by using a multiple-shooting method. This paper focuses on the model selection strategies to resolve the problem of numerical instability and high wait time when a high fidelity model with rotor dynamics is applied. Four different types of helicopter models are identified, two of which are linear models with or without rotor models, as well as two models which include the nonlinear mathematical model for rotor in its formulation. The relative computation time and the number of function calls for each model are compared in order to provide a guideline for the selection of helicopter model.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.7
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• pp.647-654
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• 2007

A Discrete continuation Method/homotopy approaches are studied for energy/fuel optimal low thrust Earth escape trajectory by solving a two point boundary value problem(TPBVP). Recently, maneuvers using low thrust propulsion system have been identified as emerging technologies. The low thruster is considered as the main actuator for orbit maneuvers. The cost function consists of a energy/fuel consumption function, and constraints are position and velocity vectors at the terminal escape point. Solving the minimum energy/fuel problem directly is not an easy task, so we adopt the homotopy analysis. Using a solution of the minimum energy, which is solved by discrete continuation method, we obtain the solution of the minimum fuel problem.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.491-505
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• 2010

A computational analysis of the nonlinear free vibration of corrugated annular plates with shallow sinusoidal corrugations under uniformly static ambient temperature is examined. The governing equations based on Hamilton's principle and nonlinear bending theory of thin shallow shell are established for a corrugated plate with a concentric rigid mass at the center and rotational springs at the outer edges. A simple harmonic function in time is assumed and the time variable is eliminated from partial differential governing equations using the Kantorovich averaging procedure. The resulting ordinary equations, which form a nonlinear two-point boundary value problem in spatial variable, are then solved numerically by shooting method, and the temperature-dependent characteristic relations of frequency vs. amplitude for nonlinear vibration of heated corrugated annular plates are obtained. Several numerical results are presented in both tabular and graphical forms, which demonstrate the accuracy of present method and illustrate the amplitude frequency dependence for the plate under such parameters as ambient temperature, plate geometry, rigid mass and elastic constrain.

• School Mathematics
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• v.17 no.2
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• pp.241-255
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• 2015

The purpose of this study is to analyze teachers' understanding on generating random number in Monte Carlo simulation and to provide educational implications in school practice. The results showed that the 70% of the teachers selected wrong ideas from three types for random-number as strategies for problem solving a probability problem and also they make some errors to justify their opinion. The first kind of the errors was that the probability of a point or boundary was equal to the value of the probability density function in the continuous probability distribution. The second kind of the errors was that the teachers failed to recognize that the sample space has been changed by conditional probability. The third kind of the errors was that when two random variables X, Y are independence of each other, then only, joint probability distribution is satisfied $P(X=x,\;Y=y)=p(X=x){\times}P(Y=y{\mid}X=x)$.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.1
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• pp.22-30
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• 2008

This paper deals with the nonlinear optimal control approach to helicopter maneuver problems using the indirect method. We apply a penalty function to the deviation from a prescribed trajectory to convert the system optimality to an unconstrained optimal control problem. The resultant two-point boundary value problem has been solved by using the multiple-shooting method. This paper focuses on the effect of the number of shooting nodes and initialization methods on the numerical solution in order to define the minimum number of shooting nodes required for numerical convergence and to provide a method increasing convergence radius of the indirect method. The results of this study can provide an approach to improve numerical stability and convergence of the indirect method when we solve the optimal control problems of an inherently unstable helicopter system.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.8 no.3
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• pp.437-450
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• 1996

A set of stability equations is formulated for natural convection flows adjacent to a vertical isothermal surface melting in cold pure water. It takes account of the nonparallelism of the base flows. The melting rate is regarded as a blowing velocity at the ice surface. The numerical solutions of the linear stability equations which constitute a two-point boundary value problem are accurately obtained for various values of the density extremum parameter $R=(T_m-T_{\infty})/(T_0-T_{\infty})$ in the range $0.3{\leq}R{\leq}0.6$, by using a computer code COLNEW. The blowing effects on the base flow becomes more significant as ambient temperature ($T_{\infty}$) increases to $T_{\infty}=10^{\circ}C$. The maximum decrease of heat transfer rate is about 6.4 percent. The stability results show that the melting at surface causes the critical Grashof number $G^*$ and the maximum frequency of disturbances to decrease. In comparision with the results for the conventional parallel flow model, the nonparallel flow model has a higher critical Grashof number but has lower amplification rates of disturbances than does the parallel flow model. The spatial amplification contours exhibit that the selective frequency $B_0$ of the nonparallel flow model is higher than that of the parallel flow model and that the effects of melting are rather small. The present study also indicates that the selective frequency $B_0$ can be easily predicted by the value of the frequency parameter $B^*$ at $G^*$, which comes from the neutral stability results of the nonparallel flow model.

• Economic and Environmental Geology
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• v.29 no.3
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• pp.335-343
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• 1996

The dipole-dipol electrical resistivity survey was conducted to investigate the probable contamination of the Han river by leachate from the near-by Nanjido Landfill. The survey line of 3 km was set along the unpaved road toward the Han river. For the convenience of the field work, the survey line was divided into four segments. The complete two-dimensional resistivity section was constructed by connecting the inversion result of each segment. Gravity survey was also carried out along the profile parallel to the resistivity line. Near surface resistivity generally appeared to be of very low value in most part of the survey area and the boundary between the alluvium layer and underlying basement rocks is well discriminated on the resistivity section. These results agree well with those of the preceding Schlumberger depth sounding made at adjacent area by Lee and fun (1995). The variation of thickness of the alluvium layer delineated by gravity anomaly profile also correlates well with the result of the resistivity survey on the qualitative basis. The problem of contamination by leachate from the Nanjido Landfill, where various waste materials have been dumped without any proper treatment facilities, has been remains unsolved yet. Therefore, we present the most probable passages of leachate flow based on the survey results and have briefly discussed about measure for contamination control. Considering the thickness of alluvium and the possible existence of fractured zone, the middle point between 1st and 2nd landfill and the midst of 1st landfill are the most hazardous regions to make leachates flow into the Han river. Since large amounts of leachates are observed from the test wells located on the lines extending from the border between the 1st and 2nd landfill and the middle of the lst landfill, contamination protection barriers are strongly recommended near these regions.

• Membrane Journal
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• v.16 no.4
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• pp.252-258
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• 2006

A numerical analysis was performed for a separation process of carbon dioxide from a flue gas stream using polyethersulfone hollow fiber membranes. Countercurrent flow governing equations were regarded to be two point boundary-value problem and the nonlinear ordinary differential equation were simultaneously solved using the finite- difference method. A computer program was developed using the Compaq Visual Fortran 6.6 software. The carbon dioxide permeate driving force and the fred gas residence time at the inside of membrane were found to be very important factors affecting the permeation characteristics of carbon dioxide. The carbon dioxide concentration in the permeate and the flow rate of the permeate were found to be slightly larger by a few percent with a countercurrent flow analysis than those with a cocurrent flow analysis.