Clifford algebra, theory of its function and their applicaton to mechanics

Abstract

As is well known, in both elastic mechanics and fluid 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 function and the analytic function, but 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 function 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.