基于新矩阵变量下的测地线方程

Geodesic Equation Based on New Matrix Variable

利用Levi-Civita联络定义了一个新变量矩阵函数,将测地线方程问题转换成了线性动力系统问题,极大地简化了测地线方程,得到了具有普遍性的唯一动力学解以及性质,间接地求得了测地线曲线的非线性坐标解。

A new variable matrix function is defined by Levi-Civita connection.The geodesic equation problem is transformed into a linear dynamic system problem.The geodesic equation is greatly simplified,the dynamic solution and properties are obtained,and the related problems of the matrix composed of new variables are discussed.