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 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.
基金项目
Funded by the Natural Science Foundation Project of CQCSTC(cstc2012jjA50018)
Basic Research of ChongqingMunicipal Education Commission(KJ120631)
theScience Research Foundation Project of CQNU(16XYY31)
NETL
NSTL
维普
万方数据