相空间中相对运动完整力学系统的共形不变性与守恒量
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摘要
研究了相空间中相对运动完整力学系统的共形不变性与守恒量.给出了该系统共形不变性的定义,并推导出相空间中相对运动完整力学系统的运动微分方程具有共形不变性并且是Lie对称性的充分必要条件.利用规范函数满足的结构方程导出该系统相应的守恒量,并给出应用算例.
Conformal invariance and conserved quantity of relative motion holonomic dynamical system in phase space are studied. The definition of conformal invariance of relative motion holonomic dynamical system in phase space is provided.The necessary and sufficient conditions that conformal invariance of the system would be Lie symmetry are deduced.By use of a structure equation that the gauge function satisfies, the corresponding conserved quantity of the system is derived. Finally an illustrative example is given to verify the results.
Conformal invariance and conserved quantity of relative motion holonomic dynamical system in phase space are studied. The definition of conformal invariance of relative motion holonomic dynamical system in phase space is provided.The necessary and sufficient conditions that conformal invariance of the system would be Lie symmetry are deduced.By use of a structure equation that the gauge function satisfies, the corresponding conserved quantity of the system is derived. Finally an illustrative example is given to verify the results.
引文
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[12]Han Y L,Wang X X,Zhang M L,Jia L Q 2013 Nonlinear Dyn.71 401
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[20]Jia L Q,Wang X X,Zhang M L,Han Y L 2012 Nonlinear Dyn.69 1807
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[25]Chen R,Xu X J 2012 Acta Phys.Sin.61 021102(in Chinese)[陈蓉,许学军2012物理学报61 021102]
[26]Chen X W,Zhao Y H,Li Y M 2009 Chin.Phys.B 183139
[27]Cai J L,Shi S S,Fang H J,Xu J 2012 Mechanica 47 63
[28]Huang W L,Cai J L 2012 Acta Mech.223 433
[29]Cai J L 2012 Nonlinear Dyn.69 487
[30]Wang T Z,Sun X T,Han Y L 2013 Acta Phys.Sin.62231101(in Chinese)[王廷志,孙现亭,韩月林2013物理学报62 231101]
[31]Cai J L,Luo S K,Mei F X 2008 Chin.Phys.B 17 3170
[32]Fang J H,Zhang P Y 2004 Acta Phys.Sin.53 4041(in Chinese)[方建会,张鹏玉2004物理学报53 4041]
[33]Fang J H,Zhang B,Zhang W W,Xu R L 2012 Chin.Phys.B 21 050202
[2]Djukic D S,Vujanovi B D 1975 Acta Mech.23 17
[3]Lutzky M 1979 J.Phys.A:Math.Gen.12 973
[4]Hojman S A 1992 J.Phys.A:Math.Gen.25 L291
[5]Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems(Beijing:Beijing Institute of Technology Press)p43(in Chinese)[梅凤翔2004约束力学系统的对称性与守恒量(北京:北京理工大学出版社)第43页]
[6]Galiullin A S,Gafarov G G,Malaishka R P,Khwan A M 1997 Analytical Dynamics of Helmholtz Birkhoff and Nambu Systems(Moscow:UFN)p183(in Russian)
[7]Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems(Beijing:Science Press)p366(in Chinese)[梅凤翔1999李群和李代数对约束力学系统的应用(北京:科学出版社)第366页]
[8]Zhang M L,Wang X X,Han Y L,Jia L Q 2012 Chin.Phys.B 21 100203
[9]Wang X X,Han Y L,Zhang M L,Jia L Q 2013 Chin.Phys.B 22 020201
[10]Luo S K,Li Z J,Li L 2012 Acta Mech.223 2621
[11]Li Z J,Luo S K 2012 Nonlinear Dyn.70 1117
[12]Han Y L,Wang X X,Zhang M L,Jia L Q 2013 Nonlinear Dyn.71 401
[13]Han Y L,Wang X X,Zhang M L,Jia L Q 2013 Nonlinear Dyn.73 357
[14]Lou Z M,Mei F X,Chen Z D 2012 Acta Phys.Sin.61110204(in Chinese)[楼智美,梅凤翔,陈子栋2012物理学报61 110204]
[15]Xu C,Li Y C 2013 Acta Phys.Sin.62 171101(in Chinese)[徐超,李元成2013物理学报62 171101]
[16]Yang X F,Sun X T,Wang X X,Zhang M L,Jia L Q2011 Acta Phys.Sin.60 111101(in Chinese)[杨新芳,孙现亭,王肖肖,张美玲,贾利群2011物理学报60 111101]
[17]Wang X X,Zhang M L,Han Y L,Jia L Q 2012 Acta Phys.Sin.61 200203(in Chinese)[王肖肖,张美玲,韩月林,贾利群2012物理学报61 200203]
[18]Sun X T,Han Y L,Wang X X,Zhang M L,Jia L Q2012 Acta Phys.Sin.61 200204(in Chinese)[孙现亭,韩月林,王肖肖,张美玲,贾利群2012物理学报61 200204]
[19]Zhang M L,Wang X X,Han Y L,Jia L Q 2012 Chin.Phys.B 21 100203
[20]Jia L Q,Wang X X,Zhang M L,Han Y L 2012 Nonlinear Dyn.69 1807
[21]Zhang Y,Xue Y 2009 Chin.Q.Mech.30 216(in Chinese)[张毅,薛纭2009力学季刊30 216]
[22]Cai J L 2009 Acta Phys.Sin.58 22(in Chinese)[蔡建乐2009物理学报58 22]
[23]Han Y L,Sun X T,Zhang Y Y,Jia L Q 2013 Acta Phys.Sin.62 160201(in Chinese)[韩月林,孙现亭,张耀宇,贾利群2013物理学报62 160201]
[24]Chen X W,Zhao Y H,Liu C 2009 Acta Phys.Sin.585150(in Chinese)[陈向炜,赵永红,刘畅2009物理学报58 5150]
[25]Chen R,Xu X J 2012 Acta Phys.Sin.61 021102(in Chinese)[陈蓉,许学军2012物理学报61 021102]
[26]Chen X W,Zhao Y H,Li Y M 2009 Chin.Phys.B 183139
[27]Cai J L,Shi S S,Fang H J,Xu J 2012 Mechanica 47 63
[28]Huang W L,Cai J L 2012 Acta Mech.223 433
[29]Cai J L 2012 Nonlinear Dyn.69 487
[30]Wang T Z,Sun X T,Han Y L 2013 Acta Phys.Sin.62231101(in Chinese)[王廷志,孙现亭,韩月林2013物理学报62 231101]
[31]Cai J L,Luo S K,Mei F X 2008 Chin.Phys.B 17 3170
[32]Fang J H,Zhang P Y 2004 Acta Phys.Sin.53 4041(in Chinese)[方建会,张鹏玉2004物理学报53 4041]
[33]Fang J H,Zhang B,Zhang W W,Xu R L 2012 Chin.Phys.B 21 050202