Conformal invariance and conserved quantities of a general holonomic system with variable mass

doi:10.1088/1674-1056/19/4/040302

Abstract Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied. The definition and the determining equation of conformal invariance for a general holonomic system with variable mass are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition under which the conformal invariance would be the Lie symmetry of the system under an infinitesimal one-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.

Keywords: variable mass conformal invariance conformal factor conserved quantity

Received: 18 August 2008
Revised: 07 September 2009
Accepted manuscript online:

PACS:	45.20.Jj	(Lagrangian and Hamiltonian mechanics)
	02.20.Sv	(Lie algebras of Lie groups)

Fund: Project supported by the Key Disciplines' Building Foundation of Henan Institute of Education，the Natural Science Foundation of Education Bureau of Henan Province, China (Grant No.~2009A140003) and the Young Core Instructor from Henan Institute of Educati

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Xia Li-Li(夏丽莉) and Cai Jian-Le(蔡建乐) Conformal invariance and conserved quantities of a general holonomic system with variable mass 2010 Chin. Phys. B 19 040302

[1]	Noether A E 1918 Math. Phys. KI II 235
[2]	Lutzky M 1979 J. Phys. A: Math. Gen. 12 973
[3]	Mei F X 2000 J. Beijing Inst. Technol. 9 120
[4]	Mei F X 2001 Chin. Phys. 10 177
[5]	Luo S K and Cai J L 2003 Chin. Phys. 12 357
[6]	Lou Z M 2006 Chin. Phys. 15 891
[7]	Mei F X 2003 Acta Phys. Sin. 52 1048 (in Chinese)
[8]	Luo S K, Chen X W and Guo Y X 2007 Chin. Phys. 16 3176
[9]	Mei F X 2000 Acta Phys. Sin. 49 1207 (in Chinese)
[10]	Luo S K, Guo Y X and Chen X W 2001 Acta Phys. Sin. 50 2053 (in Chinese)
[11]	Fang J H, Ding N and Wang P 2007 Chin. Phys. 16 887
[12]	Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese)
[13]	Xia L L and Li Y C 2007 Commun. Theor. Phys. (Beijing, China) 48 23
[14]	Xia L L, Li Y C, Wang J and Hou Q B 2006 Acta Phys. Sin. 55 4995 (in Chinese)
[15]	Zhao Y Y and Mei F X 1999 Symmetries and Invariants of Mechanical Systems (Beijing: Science Press) (in Chinese)
[16]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Techanology Press) (in Chinese)
[17]	Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese)
[18]	Galiullin A S, Gafarov G G, Malaishka R P and Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow: UFN) (in Russian)
[19]	Cai J L, Luo S K and Mei F X 2008 Chin. Phys. B 17] 3170
[20]	Cai J L 2009 Acta Phys. Sin. 59 22 (in Chinese)
[21]	Liu C, Mei F X and Guo Y X 2009 Chin. Phys. B 18 395
[22]	Fu J L 2008 Chin. Phys. Lett. 25 2413
[23]	Cai J L 2008 Chin. Phys. Lett. 25 1523

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Conformal invariance and conserved quantities of a general holonomic system with variable mass

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