Applied Mathematics and Mechanics (English Edition) ›› 1989, Vol. 10 ›› Issue (9): 853-866.

• 论文 • 上一篇    下一篇

CLIFFORD ALGEBRA,THEORY OF ITS FUNCTION AND THEIR APPLICATION TO MECHANICS

黄思训   

  1. Meteorological Institute of Air force, Nanjing
  • 收稿日期:1988-10-04 出版日期:1989-09-18 发布日期:1989-09-18
  • 基金资助:
    This is a comprehensive report at the Second National Symposium on Modern Mathematics and Mechanics;Project Supported by the Science Foundation of the Chinese Academy of Sciences

CLIFFORD ALGEBRA,THEORY OF ITS FUNCTION AND THEIR APPLICATION TO MECHANICS

Huang Si-xun   

  1. Meteorological Institute of Air force, Nanjing
  • Received:1988-10-04 Online:1989-09-18 Published:1989-09-18
  • Supported by:
    This is a comprehensive report at the Second National Symposium on Modern Mathematics and Mechanics;Project Supported by the Science Foundation of the Chinese Academy of Sciences

摘要: As is Wellknown 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-la 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.

Abstract: As is Wellknown 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-la 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.

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