• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.379-385
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• 2021

We consider the local uniqueness of a catenoid under the condition for the Gaussian curvature analogous to Bianchi surfaces. More precisely, if a nonplanar minimal surface in ℝ³ has the Gaussian curvature $K={\frac{1}{(U(u)+V(v))^2}}$ for any functions U(u) and V (v) with respect to a line of curvature coordinate system (u, v), then it is part of a catenoid. To do this, we use the relation between a conformal line of curvature coordinate system and a Chebyshev coordinate system.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.52.2-52
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• 2002

In this paper we consider an approach to a formal linearization for time-variant nonlinear systems. A time-variant nonlinear sysetm is assumed to be described by a time-variant nonlinear differential equation. For this system, we introduce a coordinate transformation function which is composed of the Chebyshev polynomials. Using Chebyshev expansion to the state variable and Laguerre expansion to the time variable, the time-variant nonlinear sysetm is transformed into the time-variant linear one with respect to the above transformation function. As an application, we synthesize a time-variant nonlinear observer. Numerical experiments are included to demonstrate the validity of...

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.47 no.3
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• pp.220-227
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• 2019

The satellites in orbit use a sun reference vector from solar model based the ephemeris. To get the ephemeris, we use DE-Series, an ephemeris developed by the Jet Propulsion Laboratory (JPL), or the reference vector generation formula proposed by Vallado. The DE-Series provides the numerical coefficients of Chebyshev polynomials, which have the advantage of high precision, but there is a computational burden on the satellite. The Vallado's method has low accuracy, although the sun vector can be easily obtained through the sun vector generation equation. In this paper, we have developed a program to provide the Chebyshev polynomial coefficients to obtain the sun position coordinates in the inertial coordinate system. The proposed method can improve the accuracy compared to the conventional method and can be used for high - performance, high - precision nano satellite missions.