Time Derivative of Unit Basis Vectors in Orthogonal Curvilinear Coordinate Systems

The transformation matrix in the unit basis vectors in deferent orthogonal curvilinear coordinate systems was unitary matrix in the complex field,and was orthogonal matrix in the real number field.The law of the unit basis vectors was deduced in the deferent orthogonal curvilinear coordinate systems.Then,the law of the time derivative of unit basis vectors was also deduced in orthogonal curvilinear coordinate systems,the unit basis vectors was chosen in the other orthogonal curvilinear coordinate systems as the unit constant vectors,and the pervasive formula was finally gotten.The time derivative of the unit basis vectors was discussed in their own coordinate systems,and the law of the first-other and the second-other time derivative of the unit basis vectors was respectively deduced in the spherical coordinate systems and the cylindrical coordinate systems.