[1] Birkhoff G D 1927 Dynamical Systems (Providence: AMS
College Publisher)

[2] Santilli R M 1978 Foundations of Theoretical
Mechanics I (New York: Springer)

[3] Santilli R M 1983 Foundations of Theoretical
Mechanics I$\!$I (New York: Springer)

[4] Mei F X, Shi R C, Zhang Y F and Wu H B 1996 Dynamics
of Birkhoff Systems (Beijing: Beijing Institute of Technology) (in
Chinese)

[5] Zhang H B 2001 Acta Phys. Sin. 50 1837 (in
Chinese)

[6] Guo Y X, Luo S K and Shang M 2001 Rep. Math. Phys.
47 313

[7] Luo S K, Lu Y B, Zhou Q, Wang Y D and Ou Y S 2002
Acta Phys. Sin. 51 1913 (in Chinese)

[8] Shang M, Guo Y X and Mei F X 2007 Chin. Phys.
16 292

[9] Ge W K and Mei F X 2007 Acta Phys. Sin. 56
2476 (in Chinese)

[10] Mei F X, Gang T Q and Xie J F 2006 Chin. Phys.
15 1678

[11] Fu J L, Chen L Q, Luo S K, Chen X W and Wang X M 2001
Acta Phys. Sin. 50 2289 (in Chinese)

[12] Zhang Y 2008 Acta Phys. Sin. 57 5374 (in
Chinese)

[13]Gu S L and Zhang H B 2004 Chin. Phys. 13 979

[14]Ding N, Fang J H and Chen X X 2008 Chin. Phys. B
17 1967

[15]Chen X W, Zhang R C and Mei F X 2000 Acta Mech. Sin.
16 282

[16]Chen X W and Mei F X 2000 Mech. Res. Commun.
27 365

[17]Chen X W 2002 Chin. Phys. 11 441

[18]Li Y M 2008 J. Henan Normal University 36 52
(in Chinese)

[19] Mei F X 1993 Sci. Chin. A 36 1456

[20] Mei F X, Zhang Y F and He G 2007 J. Beijing
Institute of Technology 27 1035 (in Chinese)

[21] Mei F X, Xie J F and Gang T Q 2008 Acta Phys. Sin.
57 4649 (in Chinese)

[22] Mei F X and Cai J L 2008 Acta Phys. Sin. 57
4657 (in Chinese)

[23] Ge W K and Mei F X 2009 Acta Phys. Sin. 58
699 (in Chinese)

[24] Mei F X, Xie J F and Gang T Q 2008 Acta Mech. Sin.
24 583

[25] Guo Y X 2001 Chin. Phys. 10 181

[26] Mei F X, Zhang Y F and Shang M 1999 Mech. Res.
Commun. 26 7

[27] Luo S K 2003 Commun. Theor. Phys. 40 265

[28] Ibragimov N H 1999 Elementary Lie Group Analysis and
Ordinary Differential Equations (London: Wiley)

[29] Borner H G and Davidson W F 1978 Phys. Rev. Lett.
40 167

[30] Fuchs J C 1991 J. Math. Phys. 32 1703

[31] Aguirre M and Krause J 1988 J. Math. Phys. 29
9

[32] Ibragimov N H 1996 CRC Handbook of Lie Group
Analysis of Differential Equations (New York: CRC) vol 3

[33] Kruskal M 1962 J. Math. Phys. 3 806

[34] Djukic D J S 1981 Int. J. Nonlinear Mech. 16
489

[35] Fu J L and Chen L Q 2004 Phys. Lett. A 324 95

[36] Hu J H 1999 SIAM J. Appl. Math. 59 322

[37] Zhao Y Y and Mei F X 1996 Acta Mech. Sin. 28
207 (in Chinese).

[38] Chen X W, Li Y M and Zhao Y H 2005 Phys. Lett. A
337 274

[39] Ostrovsky V N and Prudov N V 1995 J. Phys. B
20 4435