河南科学
河南科學
하남과학
HENAN SCIENCE
2015年
7期
1081-1086
,共6页
罗秀华%张光照%邢家省
囉秀華%張光照%邢傢省
라수화%장광조%형가성
正交曲线坐标网%测地曲率%Liouville公式%高斯曲率%Brioschi公式
正交麯線坐標網%測地麯率%Liouville公式%高斯麯率%Brioschi公式
정교곡선좌표망%측지곡솔%Liouville공식%고사곡솔%Brioschi공식
coordinate grid of the orthogonal curve%geodesic curvature%Liouville formula%Gaussian curvature%Brioschi formula
考虑曲面正交网下曲线的测地曲率的计算公式的推导问题，运用向量的表示，给出了直接推导过程。简化了高斯曲率是内蕴量的Brioschi公式的推导方法；在正交曲线坐标网下，指明了高斯曲率简化公式的推导来源与测地曲率的关系。
攷慮麯麵正交網下麯線的測地麯率的計算公式的推導問題，運用嚮量的錶示，給齣瞭直接推導過程。簡化瞭高斯麯率是內蘊量的Brioschi公式的推導方法；在正交麯線坐標網下，指明瞭高斯麯率簡化公式的推導來源與測地麯率的關繫。
고필곡면정교망하곡선적측지곡솔적계산공식적추도문제，운용향량적표시，급출료직접추도과정。간화료고사곡솔시내온량적Brioschi공식적추도방법；재정교곡선좌표망하，지명료고사곡솔간화공식적추도래원여측지곡솔적관계。
The derivation of calculation formula of geodesic curvature on surface orthogonal net is discussed in this paper. The direct derivation is obtained by means of vector representation. The derivation of Brioschi formula with Gaussian curvature as the intrinsic quantities is simplified. The relationship between the derivation of the simplified formula of Gaussian curvature and the geodesic curvature is demonstrated in the coordinate grid of the orthogonal curve.
