摘要Conformal invariance and conserved quantities of general holonomic systems are studied. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators are described. The definition of conformal invariance and determining equation for the system are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition, that conformal invariance of the system would be Lie symmetry, is obtained under the infinitesimal one-parameter transformation group. The corresponding conserved quantity is derived with the aid of a structure equation. Lastly, an example is given to demonstrate the application of the result.
Abstract：Conformal invariance and conserved quantities of general holonomic systems are studied. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators are described. The definition of conformal invariance and determining equation for the system are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition, that conformal invariance of the system would be Lie symmetry, is obtained under the infinitesimal one-parameter transformation group. The corresponding conserved quantity is derived with the aid of a structure equation. Lastly, an example is given to demonstrate the application of the result.
CAI Jian-Le. Conformal Invariance and Conserved Quantities of General Holonomic Systems[J]. 中国物理快报, 2008, 25(5): 1523-1526.
CAI Jian-Le. Conformal Invariance and Conserved Quantities of General Holonomic Systems. Chin. Phys. Lett., 2008, 25(5): 1523-1526.
[1] Noether A E 1918 Nachr. Akad. Math. 2 235 [2] Djukie D S and Vujanovie B D 1975 Acta Mech. 2317 [3] Mei F X 1999 Applications of Lie Groups and Lie Algebrasto Constrained Mechanical Systems (Beijing: Science) (in Chinese) [4] Zhao Y Y and Mei F X 1999 Symmetries and Invariantsof Mechanical Systems (Beijing: Science) (in Chinese) [5] Mei F X 2000 J. Beijing Inst. Tech. 9 120(in Chinese) [6] Mei F X 2001 Chin. Phys. 10 177 [7] Mei F X and Chen X W 2001 J. Beijing Inst. Tech. 10 138 (in Chinese) [8] Luo S K 2003 Acta Phys. Sin. 52 2941 (in Chinese) [9] Fang J H 2003 Commun. Theor. Phys. 40 269 [10] Mei F X 2004 Symmetries and Conserved Quantities ofConstrained Mechanical Systems (Beijing: Beijing Institute ofTechnology) (in Chinese) [11] Luo S K 2002 Chin. Phys. Lett. 19 449 [12] Luo S K 2003 Chin. Phys. lett. 20 597 [13] Luo S K 2003 Acta Phys. Sin. 52 1 (in Chinese) [14] Zhang Y 2005 Acta Phys. Sin. 54 2980 (in Chinese) [15] Mei F X 2004 J. Dynamics and Control 2 28 (in Chinese) [16] Xu X J and Mei F X 2005 Acta Phys. Sin. 545521 (in Chinese) [17] Zhang Y 2005 Acta Phys. Sin. 54 4488(in Chinese) [18] Fang J H and Li H 2004 Acta Phys. Sin. 53 2807(in Chinese) [19] Zheng S W, Xie J F and Jia L Q 2006 Chin. Phys. Lett. 23 2924 [20] Zheng S W, Xie J F and Zhang Q H 2007 Chin. Phys. Lett. 24 2164 [21] Zhang Y 2007 Acta Phys. Sin. 56 3054 (in Chinese) [22] He G and Mei F X 2007 J. Beijing Inst. Tech. 27565 (in Chinese) [23] Jing H X, Li Y C and Xia L L 2007 Acta Phys. Sin. 56 3043 (in Chinese) [24] 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)
2008, Vol. 25 
