Derivation of Calculation Formula of Geodesic Curvature Under the Coordinate Grid of the Orthogonal Curve
XING Jiasheng;BAI Lu;GAO Jianquan;School of Mathematics and Systems Science,Beihang University;LMIB of the Ministry of Education;Pingdingshan Institute of Education;
The derivation method of calculation formula of curve geodesic curvature on the curved surface was considered in the paper. Based on the coordinate grid of the orthogonal curve,the parametric equation form of the calculation formula of geodesic curvature on the surface was put forward,and thus a derivation method of Liouville formula to calculate the geodesic curvature was obtained. Taking good use of the orthogonal condition of curvilinear coordinate grid,a direct method for deriving the Liouville formula was introduced,which can figure out the internal links of these two derivation methods. Under the common parametric coordinate grid of curved surface,the form of differential equation set that parameter equation of geodesic curve meets was put forward directly,with which the geodesic curve differential equation set under coordinate grid of the orthogonal curve was derived.