General Expressions Between Unit Vectors of Two Curvilinear Orthogonal Coordinate Systems

Concise expressions between unit vectors of curvilinear orthogonal coordinate systems and those of cartesian coordinate system were derived in terms of different analytical ideas. These expressions were expanded to more general relations between unit vectors of two curvilinear orthogonal coordinate systems. With the help of these expressions, relations between unit vectors of a curvilinear orthogonal coordinate system and those of cartesian coordinate system or another curvilinear orthogonal coordinate system can easily be obtained as long as the single value relations between these two coordinates are known. By means of the relations between curvilinear orthogonal coordinates provided by other authors, the transformation matrixes between unit vectors of curvilinear orthogonal coordinate systems and those of cartesian coordinate system or another curvilinear orthogonal coordinate system were given.