• 대한수학회논문집
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• 제24권3호
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• pp.451-458
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• 2009

The set of root classes plays a crucial role in the Nielsen root theory. Extending Brown et al.'s work on the set of root classes of iterates of maps, we rearrange it into the reduced orbit set and show that under suitable hypotheses, any reduced orbit has the full depth property as in the Nielsen type theory of periodic orbits.

• Journal of Astronomy and Space Sciences
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• 제15권2호
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• pp.437-447
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• 1998

한반도의 지도 제작을 주임무로 1999년에 발사될 다목적 실용위성의 궤도 오차를 GPS 항행 해와 지상 안테나의 추적 데이터를 이용하여 분석하였다. 측정 데이터의 잡음과 모델 링의 오차를 고려하여 최소 자승 방법으로 궤도 결정과 예측 오차를 시뮬레이션 하였다. 측정 데이터의 잡음은 단기간 오차의 주 요인이 되며, 태양 플럭스의 불확실성으로 인한 오차가 궤도 예측 오차에 가장 크게 작용함을 알 수 있었다.

• Journal of Positioning, Navigation, and Timing
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• 제6권2호
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• pp.71-78
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• 2017

The sidereal day of a Global Positioning System (GPS) satellite was intended to equal one half of a sidereal day of the Earth. However, the sidereal day of GPS satellites has become unequal to one half of a sidereal day of the Earth. This is fundamentally caused by the non-sphericity of the Earth and the gravity of the Moon. The difference between sidereal days of GPS satellites and the Earth is known as a sidereal shift. The details surrounding sidereal shifts and their origins have yet to be fully understood. We calculated the periodicity of sidereal shifts for GPS satellites using broadcast ephemeris data. To conduct a periodic analysis of the sidereal shift, we employ the Lomb-Scargle periodogram method. It shows that the orbit periods of GPS satellites have small-amplitude perturbations with a 13.6-day period. In addition, we compare the GPS satellite orbit periods with the periodicity of geomagnetic indices and the solar wind parameters to identify the cause of the perturbations. Our results suggest that the solar wind stream might also affect the 13.6-day period of the sidereal shifts.

• 한국전산유체공학회지
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• 제20권4호
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• pp.58-62
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• 2015

Recent studies on wall-bounded shear flow have emphasized the significance of the stable manifold of simple nonlinear invariant solutions to the Navier-Stokes equation in the formation of the boundary between the laminar and turbulent regions in state space. In this paper we present newly discovered homoclinic orbits of the Kawahara and Kida(2001) periodic solution in plane Couette flow. We show that as the Reynolds number decreases a pair of homoclinic orbits move closer to each other until they disappear to exhibit homoclinic tangency.

• 한국측량학회지
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• 제35권1호
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• pp.55-62
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• 2017

The SRP (Solar Radiation Pressure) model has always been an issue in the dynamic GPS (Global Positioning System) orbit determination. The widely used CODE (Center for Orbit Determination in Europe) model and its variants have nine parameters to estimate the solar radiation pressure from the Sun and to absorb the remaining forces. However, these parameters show a very high correlation with each other and, therefore, only several of them are estimated at most of the IGS (International GNSS Service) analysis centers. In this study, we attempted to numerically verify the correlation between the parameters. For this purpose, a bi-directional, multi-step numerical integrator was developed. The correlation between the SRP parameters was analyzed in terms of post-fit residuals of the orbit. The integrated orbit was fitted to the IGS final orbit as external observations. On top of the parametric analysis of the SRP parameters, we also verified the capabilities of orbit prediction at later time epochs. As a secondary criterion for orbit quality, the positional discontinuity of the daily arcs was also analyzed. The resulting post-fit RMSE (Root-Mean-Squared Error) shows a level of 4.8 mm on average and there is no significant difference between block types. Since the once-per-revolution parameters in the Y-axis are highly correlated with those in the B-axis, the periodic terms in the D- and Y-axis are constrained to zero in order to resolve the correlations. The 6-hr predicted orbit based on the previous day yields about 3 cm or less compared to the IGS final orbit for a week, and reaches up to 6 cm for 24 hours (except for one day). The mean positional discontinuity at the boundary of two 1-day arcs is on the level of 1.4 cm for all non-eclipsing satellites. The developed orbit integrator shows a high performance in statistics of RMSE and positional discontinuity, as well as the separations of the dynamic parameters. In further research, additional verification of the reference frame for the estimated orbit using SLR is necessary to confirm the consistency of the orbit frames.

• 한국정보통신학회논문지
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• 제3권1호
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• pp.113-120
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• 1999

Chua 발진기의 카오스 신호를 선형 상태 피드백 제어 이론을 적용하여 평형점, 1주기, 2주기의 신호로 제어하는 방법을 제안하였다. 제안한 선형 상태 피드백 이득 값을 리아프노프 함수를 이용하여 Chua 오실레이터가 나타내는 모든 카오스 현상을 제어할 수 있도록 파라미터 부호의 조합에 의해 4가지로 분류하였다. 본 논문의 상태 피드백 제어 기법은 시스템의 카오스 상태에서 얻고자 하는 상태(평형점, 주기 신호등)로 효율적으로 제어 가능하고, 매우 간단한 구조로 파라미터의 변화 없이 최소의 입력으로 가능케 하였다.

• Journal of Astronomy and Space Sciences
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• 제10권1호
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• pp.17-27
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• 1993

The orbit characteristics and perturbation effects of an artificial satellite with critical inclination have been studied. The critical inclination problem in artificial satellite theory is treated as Ideal Resonance Problem(IRP). The KITSAT-1 satellite launched by Arian 42P at Guiana in August 11, 1992 has orbital inclination close to the critical value cos-1(1/√5). In that case, there is a singularity in some perturbation terms and perigee of the orbit is fixed because d$\omega$/dt is theoretically equal to zero. But actually the long periodic behaviour in argument of perigee, $\omega$ shows a small oscillation. The causes of the oscillation and the relativistic effect in IRP have been studied and applied to the KITSAT-1. The geo-potential perturbation terms which are seperated inclination terms have been obtained using Algebraic manipulation. Also luni-solar disturbing funtion based on the relative position of the sun, moon, and satellite has been obtained. Phase portraits are used to depict the change of eccentricity and grgument of perigee. The variations of each orbital elements have been obtained in case of the KITSAT-1.

• 대한수학회보
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• 제52권1호
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• pp.149-157
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• 2015

We show that $C^1$-generically, the shadowable chain component of a $C^1$-vector field containing a hyperbolic periodic orbit is hyperbolic if it is locally maximal.

• Korean Journal of Mathematics
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• 제10권2호
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• pp.173-177
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• 2002

The purpose of this paper is to study and characterize the flows of characteristic 0. It is shown that the homomorphic image of distal flow of characteristic 0 is a distal flow of characteristic 0. It is also shown that the closure of every orbit in a 0-graphic flow is regular minimal.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제6권2호
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• pp.67-77
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• 1999

In this paper we study periodic orbit of some planar control systems and investigate phase portraits of the FSs.