Clifford代数及其函数理论在力学上应用

众所周知,无论是弹性力学或流体力学,处理平面问题比处理空间问题要方便得多,其原因之一单复变函数尤其是解析函数有一整套完整的理论,而对空间问题来说就困难得多.本文首先介绍Clifford代数的一般理论,然后着重讨论三维空间上的Clifford代数,建立起三维空间中类似于解析函数的所谓正则函数.把平面问题的一些重要结果推广到三维或高维空间中去,这无疑是对弹性力学或流体力学有重要的意义.但由于Clifford代数是不可交换的代数.故把二维空间向三维推广时,许多地方仍存在着本质上的困难,故不能简单地平推一些结果.对存在的问题有待于以后深入研究.

Clifford Algebra,Theory of Its Function and Their Application to Mechanics

As is well known, in both elastic mechanics andfluid mechanics, the plane problems are more convenient than space problems.One of the causes is that there has been a complete theory about the complex Junction and the analytic junction, hut in space problems, the case is quite different.We have no effective method to deal with these problems.In this paper, we first introduces general theories of Clifford algebra.Then we emphatically explain Clifford algebra in three dimensions and establish theories of regular Junction in three dimensions analogically to analytic function in plane.Thus we extend some results of plane problem to three dimensions or high dimensions.Obviously, it is very important for elastic and fluid mechanics.But because Clifford algebra is not a commutative algebra, we can't simply extend the results of two dimensions to high dimensions.The left problems are yet to be found out.