正交曲线坐标系中单位基矢对时间的导数  

Time Derivative of Unit Basis Vectors in Orthogonal Curvilinear Coordinate Systems

作　　者：孙树生[1] 成泰民[1] 

机构地区：[1]沈阳化工大学数理系,辽宁沈阳110142

出　　处：《沈阳化工大学学报》2010年第2期175-177,191,共4页Journal of Shenyang University of Chemical Technology

基　　金：国家自然科学基金项目(10647138);辽宁省教育厅科学研究项目(20060667)

摘　　要：不同正交曲线坐标系的单位基矢之间的变化矩阵是复数域的幺正矩阵,在实数域是正交矩阵.由此,推导出不同正交曲线坐标系的单位基矢之间的变化规律,进而推导出正交曲线坐标系的单位基矢对本身坐标的求导和对时间的求导规律.再将中间过程的另一正交曲线坐标系的单位基矢选取为单位常矢量,得出普适公式.最后以球坐标系与柱坐标系的单位基矢的本身空间坐标求导为例进行讨论,分别得出球坐标系与柱坐标系中单位基矢对时间的一阶、二阶导数的变化规律.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.

关 键 词：正交曲线坐标系 幺正算符 单位基矢 

分 类 号：O411.1[理学—理论物理]