2006•Journal of Jianghan UniversityRequires access

Vector Transform of Spherical Coordinate Form of Navier-Stokes Equation

Chen Yong-guang

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Abstract

It is very complex to figure the spherical coordinate form of Navier-Stokes equation in fluid mechanics,so there are no solution process in many books and periodicals.Puts forward a simple method using the transitional matrix.Firstly transforms Cartesian coordinates of stress tensor,which in Navier-Stokes equation,to spherical coordinate,then does vector transform of spherical coordinate to Navier-Stokes equation.The results are the same comparing with the classical method.

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What this paper is about

It is very complex to figure the spherical coordinate form of Navier-Stokes equation in fluid mechanics,so there are no solution process in many books and periodicals.Puts forward a simple method using the transitional matrix.Firstly transforms Cartesian coordinates of stress tensor,which in Navier-Stokes equation,to spherical coordinate,then does vector transform of spherical coordinate to Navier-Stokes equation.The results are the same comparing with the classical method.

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Available abstract

It is very complex to figure the spherical coordinate form of Navier-Stokes equation in fluid mechanics,so there are no solution process in many books and periodicals.Puts forward a simple method using the transitional matrix.Firstly transforms Cartesian coordinates of stress tensor,which in Navier-Stokes equation,to spherical coordinate,then does vector transform of spherical coordinate to Navier-Stokes equation.The results are the same comparing with the classical method.

Key concepts: Cartesian coordinate system, Spherical coordinate system, Coordinate system, Mathematical analysis, Elliptic coordinate system, Vector spherical harmonics, Ellipsoidal coordinates, Mathematics

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