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Curve integral with path independent in orthogonal curvilinear coordinate system

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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.

curve integralorthogonal curvilinear coordinate systemcoordinate transformationgreen’s theoremstokes formula

YU Huai-min、LUO Guang、XIANG Yu-cui、YUAN Meng

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

Funded by the Natural Science Foundation Project of CQCSTCBasic Research of ChongqingMunicipal Education CommissiontheScience Research Foundation Project of CQNU

cstc2012jjA50018KJ12063116XYY31

2018

10.11835/j.issn.1671-8224.2018.02.05

重庆大学学报(英文版)
重庆大学

重庆大学学报(英文版)

影响因子：0.02
ISSN：1671-8224
年,卷(期)：2018.17(2)
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