力学的几何化

doi:10.6052/1000-0879-17-181

Abstract

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.

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O302

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WU Jike. GEOMETRIZATION OF MECHAINICS[J].Mechanics in Engineering, 2017, 39(4): 323-332.

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URL: http://lxsj.cstam.org.cn/EN/10.6052/1000-0879-17-181

http://lxsj.cstam.org.cn/EN/Y2017/V39/I4/323

References

1 阿诺尔德. 经典力学的数学方法 (第 4 版). 齐民友译. 北京:高等教育出版社, 2006
2 武际可. 谈谈对称. 科学网博文. http://blog.sciencenet.cn/blog-39472-781656.html
3 武际可. 从太极图说起——再谈对称. 科学网博文. http://blog.sciencenet.cn/blog-39472-786937.html
4 武际可, 黄克服. 微分几何及其在力学中的应用. 北京:北京大学出版社, 2011
5 武际可, 王敏中, 王炜. 弹性力学引论 (修订版). 北京:北京大学出版社, 2001
6 Olver PJ. Applications of Lie Groups to Differential Equations. New York:Springer-Verlag, 1990
7 Arnold VI, Khesin BA. Topological methods in Hydrodynamics//Applied Mathematical Sciences. New York:Springer-Verlag, 1998

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