引用本文:  YU Huaimin,LUO Guang,XIANG Yucui,YUAN Meng.[en_title][J].Journal of Chongqing University (English Edition),2018,17(2):70~76 
 YU Huaimin,LUO Guang,XIANG Yucui,YUAN Meng.Curve integral with path independent in orthogonal curvilinear coordinate system[J].Journal of Chongqing University (English Edition),2018,17(2):70~76 



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Curve integral with path independent in orthogonal curvilinear coordinate system 
YU Huaimin, LUO Guang, XIANG Yucui, YUAN Meng

College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 400047, P. R. China


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 twodimensional rectangular coordinate system and the condition is extended to arbitrary twodimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in threedimensional 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 threedimension orthogonal curvilinear coordinates. Lastly, the conclusions are made. 
关键词: curve integral orthogonal curvilinear coordinate system coordinate transformation green’s theorem stokes formula 
DOI：10.11835/j.issn.16718224.2018.02.005 
分类号: 
基金项目:Funded by the Natural Science Foundation Project of CQCSTC (No. cstc2012jjA50018), the Basic Research of Chongqing Municipal Education Commission (No. KJ120631), and the Science Research Foundation Project of CQNU (No. 16XYY31). 

Curve integral with path independent in orthogonal curvilinear coordinate system 
YU Huaimin, LUO Guang, XIANG Yucui, YUAN Meng

College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 400047, P. R. China

Abstract: 
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 twodimensional rectangular coordinate system and the condition is extended to arbitrary twodimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in threedimensional 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 threedimension orthogonal curvilinear coordinates. Lastly, the conclusions are made. 
Key words: curve integral orthogonal curvilinear coordinate system coordinate transformation green’s theorem stokes formula 



