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力学与实践 ›› 2017, Vol. 39 ›› Issue (4): 323-332.doi: 10.6052/1000-0879-17-181

• 专题综述 • 上一篇    下一篇

力学的几何化

武际可   

  1. 北京大学力学与工程科学系 100871
  • 收稿日期:2017-05-11 出版日期:2017-08-15 发布日期:2017-08-10
  • 通讯作者: 武际可,E-mail:wu_jike@sina.com E-mail:wu_jike@sina.com

GEOMETRIZATION OF MECHAINICS

WU Jike   

  1. Departmemt of Mechanics and Engineering sciences, Peking University, Beijing 100871, China
  • Received:2017-05-11 Online:2017-08-15 Published:2017-08-10

摘要:

本文介绍了力学发展过程中,力学理论系统的几何化.把力学的动力系统归结于黎曼几何、辛几何的几何课题,以及对偶概念、对称概念、变换和不变量概念在力学中的普遍应用.

关键词:

力学|几何化|对偶|黎曼几何|辛几何|变换|不变量

Abstract:

In the development of mechanics, the geometrization of theoretical systems of mechanics, is introduced. Dynaminc systems of mechanics reduced to Riemann geometry and Symplectic geometry are presented, the concepts of duel space, symmetry, transform, invariant, and there general applications in mechanics are introducd.

Key words:

mechanics|geometrization|duel space|Riemann geometry|Symplectic geometry|transformation|invariant

中图分类号: 

  • O302