• 한국수학사학회지
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• 제19권1호
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• pp.33-42
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• 2006

본 논문은 조합론 분야에서 매우 중요하게 다루는 조합대상들의 동형문제에 관한 이론적 배경의 연구와 아울러 역사적 배경을 고찰해본다. 또한, 유한체에서 케일리대상들의 동형사상 문제에 대한 부분적인 결과를 소개한다.

• Current Optics and Photonics
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• 제8권3호
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• pp.300-306
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• 2024

To solve the nozzle swing angle non-contact measurement problem, we present a nozzle pose estimation algorithm involving weighted measurement uncertainty based on rotation parameters. Firstly, the instantaneous axis of the rocket nozzle is constructed and used to model the pivot point and the nozzle coordinate system. Then, the rotation matrix and translation vector are parameterized by Cayley-Gibbs-Rodriguez parameters, and the novel object space collinearity error equation involving weighted measurement uncertainty of feature points is constructed. The nozzle pose is obtained at this step by the Gröbner basis method. Finally, the swing angle is calculated based on the conversion relationship between the nozzle static coordinate system and the nozzle dynamic coordinate system. Experimental results prove the high accuracy and robustness of the proposed method. In the space of 1.5 m × 1.5 m × 1.5 m, the maximum angle error of nozzle swing is 0.103°.