• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.33-46
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• 2023

Geodesic orbit spaces are homogeneous Finsler spaces whose geodesics are all orbits of one-parameter subgroups of isometries. Such Finsler spaces have vanishing S-curvature and hold the Bishop-Gromov volume comparison theorem. In this paper, we obtain a complete description of invariant (α₁, α₂)-metrics on spheres with vanishing S-curvature. Also, we give a description of invariant geodesic orbit (α₁, α₂)-metrics on spheres. We mainly show that a Sp(n + 1)-invariant (α₁, α2)-metric on S⁴ⁿ⁺³ = Sp(n + 1)/Sp(n) is geodesic orbit with respect to Sp(n + 1) if and only if it is Sp(n + 1)Sp(1)-invariant. As an interesting consequence, we find infinitely many Finsler spheres with vanishing S-curvature which are not geodesic orbit spaces.

• Bulletin of the Korean Chemical Society
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• v.18 no.9
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• pp.976-981
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• 1997

The magnetic susceptibilities of molybdenum ions with 4d1 electronic configuration in the octahedral crystal field were calculated on the basis of ligand field theory. The experimental magnetic susceptibilities for molybdenum ions, which are stabilized at the octahedral site in the perovskite lattice of Ba2ScMoⅤO6 and Sr2YMoⅤO6, were compared with the theoretical ones. We have tried to fit their temperature dependence of magnetic susceptibility with ligand field parameters, spin-orbit coupling constant ζSO, and orbital reduction parameter κ according to intermediate field coupling and strong field theory. Strong field coupling theory could not explain experimental curves without unrealistically large axial ligand field, since it ignores the mixing up between different state via spin-orbit interaction and ligand field. On the other hand, the intermediate field coupling theory could successfully reproduce experimental data in octahedral and trigonal ligand field. The fitting result demonstrates not only the fact that spin-orbit interaction is primarily responsible for the variation of magnetic behavior but also the fact that effective orbital overlap, enhanced by cubic crystal structure, reduces significantly orbital angular momentum as indicated by κ parameter.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.672-675
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• 1997

This paper presents the identification of rotor dynamic parameters. The solution of the system equation can be obtained using least square method. The sensitivity analysis is performed to extract optimized solution, which is considered to be insensitive to inherent measurement errors. The cosine and sine term of orbit shapes can be obtained by experiment the orbit analysis at a different speed after doing orbit analysis at an arbitrary selected speed. This values measured time domain used to search the stiffness and damping coefficients of rotor bearing.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.3
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• pp.112-119
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• 2003

This paper presents the identification of rotor dynamic parameters. The solution of the system equation can be obtained using least square method. The sensitivity analysis is performed to extract optimized solution, which is considered to be insensitive to inherent measurement errors. The cosine and sine term of orbit shapes can be obtain ed through the by experiment of the orbit analysis at a different speed after doing orbit analysis at an arbitrary selected speed. This values measured time domain are used to search the stiffness and damping coefficients of rotor bearing.

• Journal of Astronomy and Space Sciences
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• v.28 no.3
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• pp.183-192
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• 2011

The current study analyzes the effects of the scaling parameters of the batch unscented transformation on precision satellite orbit determination. Satellite laser ranging (SLR) data are used in the orbit determination algorithm, which consists of dynamics model, observation model and filtering algorithm composed of the batch unscented transformation. TOPEX/Poseidon SLR data are used by utilizing the normal point (NP) data observed from ground station. The filtering algorithm includes a repeated series of processes to determine the appropriate scaling parameters for the batch unscented transformation. To determine appropriate scaling parameters, general ranges of the scaling parameters of ${\alpha}$, ${\beta}$, k, $\lambda$ are established. Depending on the range settings, each parameter was assigned to the filtering algorithm at regular intervals. Appropriate scaling parameters are determined for observation data obtained from several observatories, by analyzing the relationship between tuning properties of the scaling parameters and estimated orbit precision. The orbit determination of satellite using the batch unscented transformation can achieve levels of accuracy within several tens of cm with the appropriate scaling parameters. The analyses in the present study give insights into the roles of scaling parameters in the batch unscented transformation method.

• Aerospace Engineering and Technology
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• v.11 no.2
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• pp.19-25
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• 2012

GEO-KOMPSAT2 shall provide higher quality of image than the COMS and uses star tracker instead of earth sensor, which requires precise onboard orbit information. This requires precise on-ground orbit determination. For COMS, orbit determination is performed using the ranging data obtained from tracking system located in DAEJON. For accurate orbit determination of GEO-KOMPSAT2, KARI is building a secondary tracking station in CHUUK Islands. In this paper, the achievable accuracy of table based onboard orbit parameter generator which interpolates orbit data obtained from on-ground orbit determination using tracking data collected from two ground stations. Two types of approaches have been applied; covariance analysis and numerical analysis. By combining two analysis results, total orbit error has been estimated.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.388-392
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• 1996

Orbit Determination is process of obtaining values of those parameter which completely specify the motion of an orbiting body through space, based on a set of observation of the body. For the narrow land of Korea, the ground tracking system has very limited time of operation. In this connection the use of GPS for orbit determination has advantage of full autonomy on the ground station. It would be more powerful economical method for near-earth satellites. Therfore we have better to pay attention to the research of satellites of orbit determination by use of GPS. So in this research, we studied themotion of the satellites with estimation using GPS. As a result, the result of computer simulation show that good convergence and indicated effective for real operation.

• Aerospace Engineering and Technology
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• v.8 no.2
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• pp.61-67
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• 2009

This paper proposes an on-board orbit data generation algorithm for geostationary satellites. The concept of the proposed algorithm is as follows. From the ground, the position and velocity deviations with respect to the assumed reference orbit are computed for 48 hours of time duration in 30 minutes interval, and the generated data are up-loaded to the satellite to be stored. From the table, three nearest data sets are selected to compute position and velocity deviation for asked epoch time by applying $2^{nd}$ order polynomial interpolation. The computed position and velocity deviation data are added to reference orbit to recover absolute orbit information. Here, the reference orbit is selected to be ideal geostationary orbit with a zero inclination and zero eccentricity. Thanks to very low computational burden, this algorithm allows us to generate orbit data at 1Hz or even higher. In order to support 48 hours autonomy, maximum 3K byte memory is required as orbit data storage. It is estimated that this additional memory requirement is acceptable for geostationary satellite application.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.87-90
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• 2005

The FORMOSAT-3/COSMIC mission is a micro satellite mission to deploy a constellation of six micro satellites at low Earth orbits. The final mission orbit is of an altitude of 750-800 lan. It is a collaborative Taiwan-USA science experiment. Each satellite consists of three science payloads in which the GPS occultation experiment (GOX) payload will collect the GPS signals for the studies of meteorology, climate, space weather, and geodesy. The GOX onboard FORMOSAT -3 is designed as a GPS receiver with 4 antennas. The fore and aft limb antennas are installed on the front and back sides, respectively, and as well as the two precise orbit determination (POD) antennas. The precise orbit information is needed for both the occultation inversion and geodetic research. However, the instrument associated errors, such as the antenna phase center offset and even the different cable delay due to the geometric configuration of fore- and aft-positions of the POD antennas produce error on the orbit. Thus, the focus of this study is to investigate the impact of POD antenna parameter on the determination of precise satellite orbit. Furthermore, the effect of the accuracy of the determined satellite orbit on the retrieved atmospheric and ionospheric parameters is also examined. The CHAMP data, the FORMOSAT-3 satellite and orbit parameters, the Bernese 5.0 software, and the occultation data processing system are used in this work. The results show that 8 cm error on the POD antenna phase center can result in ~8 cm bias on the determined orbit and subsequently cause 0.2 K deviation on the retrieved atmospheric temperature at altitudes above 10 lan.

• Journal of Mechanical Science and Technology
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• v.18 no.11
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• pp.1969-1977
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• 2004

To model and understand the physics of partial rub, a nonlinear rotor model is sought by applying a nonlinear parameter identification technique to the experimental data. The results show that the nonlinear terms of damping and stiffness should be included to model partial rotor rub. Especially, the impact and friction during the contact between rotor and stator are tried to explain with a nonlinear model on the basis of experimental data. The estimated nonlinear model shows good agreements between the numerical and the experimental results in its orbit. Also, the estimated nonlinear model could explain the backward whirling orbit and jump phenomenon, which are the typical phenomena of partial rub.