Stability for manifolds of equilibrium states of generalized Birkhoff system

doi:10.1088/1674-1056/19/8/080302

Abstract Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized Birkhoffian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.

Keywords: generalized Birkhoff system manifold of equilibrium states stability

Received: 23 November 2009
Revised: 15 December 2009
Accepted manuscript online:

PACS:	02.40.Sf	(Manifolds and cell complexes)
	02.30.Jr	(Partial differential equations)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10772025, 10932002 and 10972127), the Natural Science Foundation of Henan Province, China (Grant No. 102300410144), and the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics, China.

Cite this article:

Li Yan-Min(李彦敏) and Mei Feng-Xiang(梅凤翔) Stability for manifolds of equilibrium states of generalized Birkhoff system 2010 Chin. Phys. B 19 080302

[1]	Santilli R M 1978 Foundations of Theoretical Mechanics I (New York: Springer-Verlag)
[2]	Santilli R M 1983 Foundations of Theoretical Mechanics II (New York: Springer-Verlag)
[3]	Mei F X, Shi R C, Zhang Y F and Wu H B 1996 Dynamics of Birkhoff Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)
[4]	Zhang H B 2001 Acta Phys. Sin. 50 1837 (in Chinese)
[5]	Guo Y X, Luo S K and Shang M 2001 Rep. Math. Phys. 47 313
[6]	Luo S K, Lu Y B, Zhou Q, Wang Y D and Ou Y S 2002 Acta Phys. Sin. 51 1913 (in Chinese)
[7]	Shang M, Guo Y X and Mei F X 2007 Chin. Phys. 16 292
[8]	Ge W K and Mei F X 2007 Acta Phys. Sin. 56 2476 (in Chinese)
[9]	Mei F X, Gang T Q and Xie J F 2006 Chin. Phys. 15 1678
[10]	Fu J L, Chen L Q, Luo S K, Chen X W and Wang X M 2001 Acta Phys. Sin. 50 2289 (in Chinese)
[11]	Zhang Y 2008 Acta Phys. Sin. 57 5374 (in Chinese)
[12]	Gu S L and Zhang H B 2004 Chin. Phys. 13 979
[13]	Ding N, Fang J H and Chen X X 2008 Chin. Phys. B 17 1967
[14]	Chen X W, Zhang R C and Mei F X 2000 Acta Mech. Sin. 16 282
[15]	Chen X W and Mei F X 2000 Mechanics Research Communications 27 365
[16]	Chen X W 2002 Chin. Phys. 11 441
[17]	Li Y M 2008 J. Henan Normal University 36 52 (in Chinese)
[18]	Mei F X 1993 Sci. Chin. Ser. A 36 1456
[19]	Mei F X, Zhang Y F and He G 2007 J. Beijing Institute of Technology 27 1035 (in Chinese)
[2]	Mei F X, Xie J F and Gang T Q 2008 Acta Phys. Sin. 57 4649 (in Chinese)
[21]	Mei F X and Cai J L 2008 Acta Phys. Sin. 57 4657 (in Chinese)
[22]	Ge W K and Mei F X 2009 Acta Phys. Sin. 58 699 (in Chinese)
[23]	Mei F X, Xie J F and Gang T Q 2008 Acta Mech. Sin. 24 583
[24]	Mei F X 1993 Chin. Sci. Bull. 38 311
[25]	Mei F X 1996 J. Beijing Institute of Technology 16 245 (in Chinese)
[26]	Shi R C, Mei F X and Zhu H P 1994 Mechanics Research Communications 21 269
[27]	Fu J L, Chen L Q, Lu Y and Luo S K 2003 Chin. Phys. 12 351
[28]	Fu J L, Chen L Q, Xue Y and Luo S K 2002 Acta Phys. Sin. 51 2683 (in Chinese)
[29]	Fu J L, Chen L Q, Xue Y and Luo S K 2003 Acta Phys. Sin. 52 256 (in Chinese)

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