Curve integral with path independent in orthogonal curvilinear coordinate system  

作　　者：YU Huai-min LUO Guang XIANG Yu-cui YUAN Meng YU Huai-min;罗光;XIANG Yu-cui;YUAN Meng

机构地区：[1]College of Physics and Electronic Engineering, Chongqing Normal University

出　　处：《Journal of Chongqing University》2018年第2期70-76,共7页重庆大学学报（英文版）

基　　金：Funded by the Natural Science Foundation Project of CQCSTC(No.cstc2012jj A50018);the Basic Research of Chongqing Municipal Education Commission(No.KJ120631);the Science Research Foundation Project of CQNU(No.16XYY31)

摘　　要：It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made.It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made.

关 键 词：CURVE integral ORTHOGONAL curvilinear COORDINATE system COORDINATE transformation green’s THEOREM STOKES FORMULA 

分 类 号：G64[文化科学—高等教育学]