相对运动完整系统Appell方程Mei对称性的共形不变性与守恒量

张芳; 张耀宇; 薛喜昌; 贾利群

doi:10.7498/aps.64.134501

摘要

研究相对运动完整系统Appell方程Mei对称性的共形不变性与守恒量. 引入无限小单参数变换群及其生成元向量, 给出相对运动完整系统Appell方程的Mei对称性和共形不变性的定义, 导出系统Mei对称性的共形不变性确定方程, 重点讨论系统共形不变性和Mei对称性的关系, 然后借助规范函数满足的结构方程导出系统Mei对称性导致的Mei守恒量表达式, 最后举例说明结果的应用.

关键词:

For a holonomic system in relative motion, the conformal invariance and the conserved quantity of Mei symmetry with Appell equations are investigated. First, by using the infinitesimal one-parameter transformation group and the infinitesimal generator vector, the definitions of Mei symmetry and the conformal invariance with Appell equations in a holonomic system in relative motion are given, and the determining equations of the conformal invariance of Mei symmetry for the system are derived. Relationship between the conformal invariance and Mei symmetry for the system is mainly studied. Then, by means of the structural equation which the gauge function satisfies, the expression of Mei conserved quantity deduced from Mei symmetry for the system is obtained. Finally, an example is given to illustrate the application of the result.

Keywords:

作者及机构信息

1.
平顶山学院电气信息工程学院, 平顶山 467002;

2.
江南大学理学院, 无锡 214122

基金项目: 国家自然科学基金(批准号:11142014)资助的课题.

Authors and contacts

1.
College of Electric and Information Engineering, Pingdingshan University, Pingdingshan 467002, China;

2.
School of Science, Jiangnan University, Wuxi 214122, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11142014).

参考文献

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[2]	Han Y L, Wang X X, Zhang, M L, Jia L Q 2013 Nonlinear Dyn. 71 401
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[4]	Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Acta Phys. Sin. 62 110201 (in Chinese) [韩月林, 王肖肖, 张美玲, 贾利群 2013 物理学报 62 110201]
[5]	Chen X W, Li Y M, Zhao Y H 2005 Phys. Lett. A 337 274
[6]	Luo S K, Li L 2013 Nonlinear Dyn. 73 639
[7]	Luo S K, Li L 2013 Nonlinear Dyn. 73 339
[8]	Luo S K, Li Z J, Peng W, Li L 2013 Acta Mech. 224 71
[9]	Luo S K, Li Z J, Li L 2012 Acta Mech. 223 2621
[10]	Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
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[19]	Wang X X, Sun X T, Zhang M L, Xie Y L, Jia L Q 2011 Chin. Phys. B 20 124501
[20]	Fang J H, Zhang B, Zhang W W, Xu R L 2012 Chin. Phys. B 21 050202
[21]	Zhang B, Fang J H, Zhang W W 2012 Chin. Phys. B 21 070208
[22]	Xia L L, Cai J L 2010 Chin. Phys. B 19 040302
[23]	Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica. 47 63
[24]	Huang W L, Cai J L 2012 Acta Mech. 223 433
[25]	Cai J L 2012 Nonlinear Dyn. 69 487
[26]	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]
[27]	Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems( Beijing: Science Press) (in Chinese) [梅凤翔 1999 李群和李代数对约束力学系统的应用(北京: 科学学出版社)]
[28]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (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)]
[29]	Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Journal of Yunnan University (Natural Sciences Edition) 34 664 (in Chinese) [张美玲, 王肖肖, 韩月林, 贾利群 2012 云南大学学报 34 664]
[30]	Chen X W, Zhao Y H, Li Y M 2009 Chin. Phys. B 18 3139
[31]	Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin. Phys. B 21 100203
[32]	Xie Y L, Jia L Q, Luo S K 2011 Chin. Phys. B 20 010203

施引文献

[1]	Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807
[2]	Han Y L, Wang X X, Zhang, M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[3]	Jia L Q, Sun X T, Zhang M L, Zhang Y Y, Han Y L 2014 Acta Phys. Sin. 63 010201 (in Chinese) [贾利群, 孙现亭, 张美玲, 张耀宇, 韩月林 2014 物理学报 63 010201]
[4]	Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Acta Phys. Sin. 62 110201 (in Chinese) [韩月林, 王肖肖, 张美玲, 贾利群 2013 物理学报 62 110201]
[5]	Chen X W, Li Y M, Zhao Y H 2005 Phys. Lett. A 337 274
[6]	Luo S K, Li L 2013 Nonlinear Dyn. 73 639
[7]	Luo S K, Li L 2013 Nonlinear Dyn. 73 339
[8]	Luo S K, Li Z J, Peng W, Li L 2013 Acta Mech. 224 71
[9]	Luo S K, Li Z J, Li L 2012 Acta Mech. 223 2621
[10]	Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[11]	Wang X X, Han YL, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[12]	Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 73 357
[13]	Han Y L, Wang X X, Zhang M L, Jia L Q 2014 Journal of Mechanics. 30 21
[14]	Wang P, Fang J H, Wang X M 2009 Chin. Phys. B 18 1312
[15]	Fang J H 2010 Chin. Phys. B 19 040301
[16]	Cui J C, Han Y L, Jia L Q 2012 Chin. Phys. B 21 080201
[17]	Jia L Q, Xie Y L, Zhang Y Y, Yang X F 2010 Chin. Phys. B 19 110301
[18]	Jia L Q, Zhang M L, Wang X X, Han Y L 2012 Chin. Phys. B 21 070204
[19]	Wang X X, Sun X T, Zhang M L, Xie Y L, Jia L Q 2011 Chin. Phys. B 20 124501
[20]	Fang J H, Zhang B, Zhang W W, Xu R L 2012 Chin. Phys. B 21 050202
[21]	Zhang B, Fang J H, Zhang W W 2012 Chin. Phys. B 21 070208
[22]	Xia L L, Cai J L 2010 Chin. Phys. B 19 040302
[23]	Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica. 47 63
[24]	Huang W L, Cai J L 2012 Acta Mech. 223 433
[25]	Cai J L 2012 Nonlinear Dyn. 69 487
[26]	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]
[27]	Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems( Beijing: Science Press) (in Chinese) [梅凤翔 1999 李群和李代数对约束力学系统的应用(北京: 科学学出版社)]
[28]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (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)]
[29]	Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Journal of Yunnan University (Natural Sciences Edition) 34 664 (in Chinese) [张美玲, 王肖肖, 韩月林, 贾利群 2012 云南大学学报 34 664]
[30]	Chen X W, Zhao Y H, Li Y M 2009 Chin. Phys. B 18 3139
[31]	Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin. Phys. B 21 100203
[32]	Xie Y L, Jia L Q, Luo S K 2011 Chin. Phys. B 20 010203

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