Conserved Quantities and Conformal Mechanico-Electrical Systems
FU Jing-Li1, WANG Xian-Jun2, XIE Feng-Ping1
1Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 3100182Department of Physics, Henan Institute of Education, Zhengzhou 450014
Conserved Quantities and Conformal Mechanico-Electrical Systems
FU Jing-Li1, WANG Xian-Jun2, XIE Feng-Ping1
1Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 3100182Department of Physics, Henan Institute of Education, Zhengzhou 450014
摘要The conformal mechanico-electrical systems are presented by infinitesimal point transformations of time and generalized coordinates. The necessary and sufficient conditions that the conformal mechanico-electrical systems possess Lie symmetry are given. The Noether conserved quantities of the conformal mechanico-electrical systems are obtained from Lie symmetries.
Abstract:The conformal mechanico-electrical systems are presented by infinitesimal point transformations of time and generalized coordinates. The necessary and sufficient conditions that the conformal mechanico-electrical systems possess Lie symmetry are given. The Noether conserved quantities of the conformal mechanico-electrical systems are obtained from Lie symmetries.
[1] Olver P 1993 Applications of Lie Groups to DifferentialEquations (New York: Springer) [2] Ovisiannikov L V 1982 Group Analysis of Difference Equations(New York: Academic) [3] Ibragimov N H 1985 Transformation Groups Applied toMathematical Physics (Boston: Reidel) [4] Bluman G W and Kumei S 1989 Symmetries of DifferentialEquations (Berlin: Springer) [5] Hydon P 1999 Symmetry Methods for Ordinary DifferentialEquations (Cambridge: Cambridge University Press) [6] Mei F X 1999 Applications of Lie Group and Lie algebra toConstraint Mechanical Systems (Beijing: Science) (in Chinese) [7] Noether A E 1918 Nachr, Akad. Wiss. Gottingen Math.Phys. KI I$\!$I 235 [8] Lutzky M 1979 Phys. Lett. A 72 86 [9] Lutzky M 1995 J. Phys. A 28 637 [10] Mei F X 2000 J. Beijing Institute of Technology 9 120 [11] Mei F X 2001 Chin. Phys. 10 177 [12] Guo Y X, Jiang L Y and Yu Y 2001 Chin. Phys. 10 181 [13] Zhang Y and Mei F X 2003 Chin. Phys. 12 1058 [14] Chen X W, Liu C M and Li Y M 2006 Chin. Phys. 15 470 [15] Fang J H,Liao Y P, Ding N and Wang P 2006 Chin. Phys. 15 2792 [16] Zhang H B, Chen L Q, Gu S L and Liu C Z 2007 Chin. Phys. 16 582 [17] Liu R W,Zhang H B and Chen L Q 2006 Chin. Phys. 15 249 [18] Zheng S W, Xie J F and Zhang Q H 2007 Chin. Phys. Lett. 24 2164 [19] Zhao W J, Weng Y Q and Fu J L 2007 Chin. Phys. Lett. 24 2773 [20] Fu J L and Chen L Q 2003 Phys. Lett. A 317 255 [21] Galiullin A S et al 1997 Analytical Dynamics of Helmholtz,Birkhoff and Nambu Systems (Moscow: UFN) p 183 (in Russian) [22] McLachlan R and Perlmutter M 2001 J. Geom. Phys. 39 276 [23] Liu C, Mei F X and Guo Y X 2008 Chin. Phys. (in press)