Symmetry and conserved quantities of discrete generalized Birkhoffian system

doi:10.1088/1674-1056/19/12/124601

中国物理B ›› 2010, Vol. 19 ›› Issue (12): 124601-124601.doi: 10.1088/1674-1056/19/12/124601

Symmetry and conserved quantities of discrete generalized Birkhoffian system

张克军, 方建会, 李燕

College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China

收稿日期:2010-03-30 修回日期:2010-06-02 出版日期:2010-12-15 发布日期:2010-12-15
基金资助:
Project supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 09CX04018A).

Symmetry and conserved quantities of discrete generalized Birkhoffian system

Zhang Ke-Jun(张克军), Fang Jian-Hui(方建会)^†, and Li Yan(李燕)

College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China

Received:2010-03-30 Revised:2010-06-02 Online:2010-12-15 Published:2010-12-15
Supported by:
Project supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 09CX04018A).

摘要/Abstract

摘要： The Noether symmetry, the Mei symmetry and the conserved quantities of discrete generalized Birkhoffian system are studied in this paper. Using the difference discrete variational approach, the difference discrete variational principle of discrete generalized Birkhoffian system is derived. The discrete equations of motion of the system are established. The criterion of Noether symmetry and Mei symmetry of the system is given. The discrete Noether and Mei conserved quantities and the conditions for their existence are obtained. Finally, an example is given to show the applications of the results.

Abstract: The Noether symmetry, the Mei symmetry and the conserved quantities of discrete generalized Birkhoffian system are studied in this paper. Using the difference discrete variational approach, the difference discrete variational principle of discrete generalized Birkhoffian system is derived. The discrete equations of motion of the system are established. The criterion of Noether symmetry and Mei symmetry of the system is given. The discrete Noether and Mei conserved quantities and the conditions for their existence are obtained. Finally, an example is given to show the applications of the results.

Key words: discrete generalized Birkhoffian system, Noether symmetry, Mei symmetry, conserved quantity

中图分类号: (Variational and optimizational methods)

46.15.Cc

张克军, 方建会, 李燕. Symmetry and conserved quantities of discrete generalized Birkhoffian system[J]. 中国物理B, 2010, 19(12): 124601-124601.

Zhang Ke-Jun(张克军), Fang Jian-Hui(方建会), and Li Yan(李燕). Symmetry and conserved quantities of discrete generalized Birkhoffian system[J]. Chin. Phys. B, 2010, 19(12): 124601-124601.

参考文献 26

[1]	Noether A E 1918 Nachr. Akad. Wiss. Göttingen Math. Phys. 2 235
[2]	Lutzky M 1979 J. Phys. A: Math. Gen. 12 973
[3]	Mei F X 2000 J. Beijing Inst. Tech. 9 120
[4]	Mei F X 2001 Chin. Phys. 10 177
[5]	Zhang H B and Chen L Q 2005 J. Phys. Soc. Jpn. 74 905
[6]	Fang J H, Peng Y and Liao Y P 2005 Acta Phys. Sin. 54 496 (in Chinese)
[7]	Qiao Y F and Zhao S H 2006 Acta Phys. Sin. 55 499 (in Chinese)
[8]	Liu H J, Fu J L and Tang Y F 2007 Chin. Phys. 16 599
[9]	Luo S K 2007 Chin. Phys. 16 3182
[10]	Xie J F, Gang T Q and Mei F X 2008 Chin. Phys. B 17 390
[11]	Jia L Q, Xie J F and Luo S K 2008 Chin. Phys. B 17 1560
[12]	Mei F X, Xie J F and Gang T Q 2008 Commun. Theor. Phys. 49 1413
[13]	Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese)
[14]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)
[15]	Luo S K and Zhang Y F 2008 Advances in the Study of Dynamics of Constrained System (Beijing: Science Press) (in Chinese)
[16]	Zhang H B, Chen L Q and Liu R W 2005 Chin. Phys. 14 238
[17]	Zhang H B, Chen L Q, Gu S L and Liu C Z 2007 Chin. Phys. 16 582
[18]	Fu J L, Dai G D, Salvador J and Tang Y F 2007 Chin. Phys. 16 570
[19]	Shi S Y, Fu J L and Chen L Q 2008 Chin. Phys. B 17 385
[20]	Shi S Y, Chen L Q and Fu J L 2008 Commun. Theor. Phys. 50 607
[21]	Lu K, Fang J H, Zhang M J and Wang P 2009 Acta Phys. Sin. 58 7421 (in Chinese)
[22]	Guo H Y, Li Y Q, Wu K and Wang S K 2002 Commun. Theor. Phys. 37 1
[23]	Guo H Y, Li Y Q, Wu K and Wang S K 2002 Commun. Theor. Phys. 37 129
[24]	Guo H Y, Li Y Q, Wu K and Wang S K 2002 Commun. Theor. Phys. 37 257
[25]	Guo H Y and Wu K 2003 J. Math. Phys. 44 5978
[26]	Luo X D, Guo H Y, Li Y Q and Wu K 2004 Commun. Theor. Phys. 42 443

Symmetry and conserved quantities of discrete generalized Birkhoffian system

Symmetry and conserved quantities of discrete generalized Birkhoffian system

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 26

相关文章 2

Metrics

本文评价

推荐阅读 0

[1]	Haiqin Wang(王海钦), and Xinpeng Xu(徐新鹏). Variational approximation methods for long-range force transmission in biopolymer gels[J]. 中国物理B, 2022, 31(10): 104602-104602.
[2]	S Chakraverty,Laxmi Behera. Buckling analysis of nanobeams with exponentially varying stiffness by differential quadrature method[J]. 中国物理B, 2017, 26(7): 74602-074602.