• Communications of the Korean Mathematical Society
• /
• v.24 no.3
• /
• pp.451-458
• /
• 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
• /
• v.15 no.2
• /
• pp.437-447
• /
• 1998

Orbit error analysis was performed for the GPS navigation solutions and ground station tracking data of the KOMPSAT (Korea Multi-Purpose SATellite), which will be launched in 1999 for cartography of Korean peninsula as main mission. A least square method was used for the orbit determination and prediction error simulation including tracking data noises and dynamic modeling errors. It was found that a short-term periodic orbit determination error was caused by the tracking data noise and dominant orbit prediction error was caused by solar flux uncertainty.

• Journal of Positioning, Navigation, and Timing
• /
• v.6 no.2
• /
• pp.71-78
• /
• 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.

• Journal of computational fluids engineering
• /
• v.20 no.4
• /
• pp.58-62
• /
• 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.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.35 no.1
• /
• pp.55-62
• /
• 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.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.3 no.1
• /
• pp.113-120
• /
• 1999

In this paper, chaotic signals of a Chua's oscillator are effectively controlled to low periodic signal(1-periodic signal, 2-periodic signal, etc) or equilibrium point using the linear state feedback technique. The proposed linear state feedback technique has characteristics, that any solution of the Chua's oscillator can be a goal of the control(fixed point, periodic orbit, etc). The controller has a very simple structure, which does not require adjusting system parameters.

• Journal of Astronomy and Space Sciences
• /
• v.10 no.1
• /
• pp.17-27
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.1
• /
• pp.149-157
• /
• 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
• /
• v.10 no.2
• /
• pp.173-177
• /
• 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.

• The Pure and Applied Mathematics
• /
• v.6 no.2
• /
• pp.67-77
• /
• 1999

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