完整系统Appell方程Mei对称性的共形不变性与守恒量

韩月林; 孙现亭; 张耀宇; 贾利群

doi:10.7498/aps.62.160201

摘要

研究完整系统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, 定义完整系统动力学方程的Mei对称性和共形不变性, 给出该系统Mei对称性共形不变性的确定方程. 利用规范函数满足的结构方程导出系统相应的Mei守恒量. 举例说明结果的应用.

关键词:

For a holonomic system, the conformal invariance and conserved quantity of Mei symmetry for Appell equations are studied. Firstly, by the infinitesimal one-parameter transformation group and the infinitesimal generator vector, we define Mei symmetry and conformal invariance of differential equations of motion for holonomic system, and the determining equation of Mei symmetry and conformal invariance for holonomic system are given. Then, taking advantage of a structure equation that gauge function satisfies, the system corresponding Mei conserved quantity is derived. Finally, an example is given to illustrate the application of the result.

Keywords:

作者及机构信息

1.
江南大学理学院, 无锡 214122;

2.
平顶山学院电气信息工程学院, 平顶山 467002

基金项目: 国家自然科学基金 (批准号: 11142014)和江苏省普通高校研究生科研创新计划 (批准号: CXLX12_0720)资助的课题.

Authors and contacts

1.
School of Science, Jiangnan University, Wuxi 214122, China;

2.
School of Electric and Information Engineering, Pingdingshan University, Pingdingshan 467002, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11142014) and the Scientific Research and Innovation Plan for College Graduates of Jiangsu Province, China (Grant No. CXLX12_0720).

参考文献

[1]	Lutzky M 1979 J. Phys. A Math. Gen. 12 973
[2]	Noether A E 1918 Nachr. Akad. Math. 2 235
[3]	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)]
[4]	Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow: UFN) (in Russian)
[5]	Zhang Y, Xue Y 2009 Chin. Q. Mech. 30 216 (in Chinese) [张毅, 薛纭2009力学季刊 30 216]
[6]	Cai J L, Shi S S, Fang H J 2012 Meccanica 47 63
[7]	Chen X W, Zhao Y H, Li Y M 2009 Chin. Phys. B 18 3139
[8]	Cai J L, Shi S S 2012 Acta Phys. Sin. 61 030201 (in Chinese) [蔡建乐, 史生水2012 61 030201]
[9]	Appell P 1953 Traité de Mécanique Rationnelle II (Paris: Gauthier-Villars) p335
[10]	Xue W X 1987 Acta Mech. Sin. 19 156
[11]	Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese) [罗绍凯2002 51 712]
[12]	Cui J C, Zhang Y Y, Yang X F, Jia L Q 2010 Chin. Phys. B 19 030304
[13]	Li Y C, Xia L L, Wang X M, Liu X W 2010 Acta Phys. Sin. 59 3639 (in Chinese) [李元成, 夏丽莉, 王小明, 刘晓巍2010 59 3639]
[14]	Jia L Q, Xie Y L, Zhang Y Y, Cui J C, Yang X F 2010 Acta Phys. Sin. 59 7552 (in Chinese) [贾利群, 解银丽, 张耀宇, 崔金超, 杨新芳2010 59 7552]
[15]	Yang X F, Sun X T, Wang X X, Zhang M L, Jia L Q 2011 Acta Phys. Sin. 60 111101 (in Chinese) [杨新芳, 孙现亭, 王肖肖, 张美玲, 贾利群2011 60 111101]
[16]	Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[17]	Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press)
[18]	Mei F X, Chen X W 2000 Chin. Phys. 9 721
[19]	Luo S K 2004 Chin. Phys. 13 2182
[20]	Cai J L 2008 Chin. Phys. Lett. 25 1523
[21]	Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔2008 57 5369]
[22]	Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170
[23]	Zhang Y, Mei F X 2004 Acta Phys. Sin. 53 2419 (in Chinese) [张毅, 梅凤翔2004 53 2419]
[24]	Luo S K, Zhang Y F 2008 Progress of Dynamics of Constrained Systems (Beijing: Science Press) (in Chinese) [罗绍凯, 张永发 2008 约束系统动力学研究进展 (北京: 科学出版社)]
[25]	Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese) [方建会2009 58 3617]
[26]	Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐2009 58 22]
[27]	Cai J L 2009 Acta Phys. Pol. A 115 854
[28]	Xie Y L, Jia L Q 2010 Chin. Phys. Lett. 27 120201
[29]	Zheng S W, Xie J F, Chen X W 2010 Acta Phys. Sin. 59 5209 (in Chinese) [郑世旺, 解佳芳, 陈向炜 2010 59 5209]
[30]	Jia L Q, Sun X T, Zhang M L, Wang X X, Xie Y L 2011 Acta Phys. Sin. 60 084501 (in Chinese) [贾利群, 孙现亭, 张美玲, 王肖肖, 解银丽2011 60 084501]
[31]	Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 60 060201]
[32]	Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[33]	Cai J L 2012 Nonlinear Dyn. 69 487
[34]	Mei F X 2001 Chin. Phys. 10 177
[35]	Jia L Q, Zhang Y Y, Cui J C 2009 Journal of Yunnan University 31 52 (in Chinese) [贾利群, 张耀宇, 崔金超2009云南大学学报 31 52]

施引文献

[1]	Lutzky M 1979 J. Phys. A Math. Gen. 12 973
[2]	Noether A E 1918 Nachr. Akad. Math. 2 235
[3]	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)]
[4]	Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow: UFN) (in Russian)
[5]	Zhang Y, Xue Y 2009 Chin. Q. Mech. 30 216 (in Chinese) [张毅, 薛纭2009力学季刊 30 216]
[6]	Cai J L, Shi S S, Fang H J 2012 Meccanica 47 63
[7]	Chen X W, Zhao Y H, Li Y M 2009 Chin. Phys. B 18 3139
[8]	Cai J L, Shi S S 2012 Acta Phys. Sin. 61 030201 (in Chinese) [蔡建乐, 史生水2012 61 030201]
[9]	Appell P 1953 Traité de Mécanique Rationnelle II (Paris: Gauthier-Villars) p335
[10]	Xue W X 1987 Acta Mech. Sin. 19 156
[11]	Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese) [罗绍凯2002 51 712]
[12]	Cui J C, Zhang Y Y, Yang X F, Jia L Q 2010 Chin. Phys. B 19 030304
[13]	Li Y C, Xia L L, Wang X M, Liu X W 2010 Acta Phys. Sin. 59 3639 (in Chinese) [李元成, 夏丽莉, 王小明, 刘晓巍2010 59 3639]
[14]	Jia L Q, Xie Y L, Zhang Y Y, Cui J C, Yang X F 2010 Acta Phys. Sin. 59 7552 (in Chinese) [贾利群, 解银丽, 张耀宇, 崔金超, 杨新芳2010 59 7552]
[15]	Yang X F, Sun X T, Wang X X, Zhang M L, Jia L Q 2011 Acta Phys. Sin. 60 111101 (in Chinese) [杨新芳, 孙现亭, 王肖肖, 张美玲, 贾利群2011 60 111101]
[16]	Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[17]	Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press)
[18]	Mei F X, Chen X W 2000 Chin. Phys. 9 721
[19]	Luo S K 2004 Chin. Phys. 13 2182
[20]	Cai J L 2008 Chin. Phys. Lett. 25 1523
[21]	Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔2008 57 5369]
[22]	Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170
[23]	Zhang Y, Mei F X 2004 Acta Phys. Sin. 53 2419 (in Chinese) [张毅, 梅凤翔2004 53 2419]
[24]	Luo S K, Zhang Y F 2008 Progress of Dynamics of Constrained Systems (Beijing: Science Press) (in Chinese) [罗绍凯, 张永发 2008 约束系统动力学研究进展 (北京: 科学出版社)]
[25]	Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese) [方建会2009 58 3617]
[26]	Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐2009 58 22]
[27]	Cai J L 2009 Acta Phys. Pol. A 115 854
[28]	Xie Y L, Jia L Q 2010 Chin. Phys. Lett. 27 120201
[29]	Zheng S W, Xie J F, Chen X W 2010 Acta Phys. Sin. 59 5209 (in Chinese) [郑世旺, 解佳芳, 陈向炜 2010 59 5209]
[30]	Jia L Q, Sun X T, Zhang M L, Wang X X, Xie Y L 2011 Acta Phys. Sin. 60 084501 (in Chinese) [贾利群, 孙现亭, 张美玲, 王肖肖, 解银丽2011 60 084501]
[31]	Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 60 060201]
[32]	Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[33]	Cai J L 2012 Nonlinear Dyn. 69 487
[34]	Mei F X 2001 Chin. Phys. 10 177
[35]	Jia L Q, Zhang Y Y, Cui J C 2009 Journal of Yunnan University 31 52 (in Chinese) [贾利群, 张耀宇, 崔金超2009云南大学学报 31 52]

[1]	孙现亭, 张耀宇, 薛喜昌, 贾利群. 增加附加项后广义Hamilton系统的形式不变性与Mei守恒量. , 2015, 64(6): 064502. doi: 10.7498/aps.64.064502
[2]	张芳, 张耀宇, 薛喜昌, 贾利群. 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. , 2015, 64(13): 134501. doi: 10.7498/aps.64.134501
[3]	刘洪伟. 广义Hamilton系统的共形不变性与Mei守恒量. , 2014, 63(5): 050201. doi: 10.7498/aps.63.050201
[4]	张芳, 李伟, 张耀宇, 薛喜昌, 贾利群. 变质量Chetaev型非完整系统Appell方程Mei对称性的共形不变性与守恒量. , 2014, 63(16): 164501. doi: 10.7498/aps.63.164501
[5]	孙现亭, 张耀宇, 张芳, 贾利群. 完整系统Appell方程Lie对称性的共形不变性与Hojman守恒量. , 2014, 63(14): 140201. doi: 10.7498/aps.63.140201
[6]	王肖肖, 张美玲, 韩月林, 贾利群. Chetaev型非完整约束相对运动动力学系统Nielsen方程的Mei对称性和Mei守恒量. , 2012, 61(20): 200203. doi: 10.7498/aps.61.200203
[7]	孙现亭, 韩月林, 王肖肖, 张美玲, 贾利群. 完整系统Appell方程Mei对称性的一种新的守恒量. , 2012, 61(20): 200204. doi: 10.7498/aps.61.200204
[8]	蔡建乐, 史生水. Chetaev型非完整系统Mei对称性的共形不变性与守恒量. , 2012, 61(3): 030201. doi: 10.7498/aps.61.030201
[9]	刘洪伟, 李玲飞, 杨士通. Kepler方程的共形不变性、Mei对称性与守恒量. , 2012, 61(20): 200202. doi: 10.7498/aps.61.200202
[10]	姜文安, 罗绍凯. 广义Hamilton系统的Mei对称性导致的Mei守恒量. , 2011, 60(6): 060201. doi: 10.7498/aps.60.060201
[11]	杨新芳, 孙现亭, 王肖肖, 张美玲, 贾利群. 变质量Chetaev型非完整系统Appell方程的Mei对称性和Mei守恒量. , 2011, 60(11): 111101. doi: 10.7498/aps.60.111101
[12]	贾利群, 解银丽, 罗绍凯. 相对运动动力学系统Appell方程Mei对称性导致的Mei守恒量. , 2011, 60(4): 040201. doi: 10.7498/aps.60.040201
[13]	贾利群, 张耀宇, 杨新芳, 崔金超, 解银丽. Lagrange系统Mei对称性的Ⅲ型结构方程和Ⅲ型Mei守恒量. , 2010, 59(5): 2939-2941. doi: 10.7498/aps.59.2939
[14]	李元成, 夏丽莉, 王小明, 刘晓巍. 完整系统Appell方程的Lie-Mei对称性与守恒量. , 2010, 59(6): 3639-3642. doi: 10.7498/aps.59.3639
[15]	贾利群, 解银丽, 张耀宇, 崔金超, 杨新芳. Appell方程Mei对称性导致的一种新型守恒量. , 2010, 59(11): 7552-7555. doi: 10.7498/aps.59.7552
[16]	贾利群, 崔金超, 张耀宇, 罗绍凯. Chetaev型约束力学系统Appell方程的Lie对称性与守恒量. , 2009, 58(1): 16-21. doi: 10.7498/aps.58.16
[17]	贾利群, 崔金超, 罗绍凯, 张耀宇. 事件空间中单面非Chetaev型非完整系统Nielsen方程的Mei对称性与Mei守恒量. , 2009, 58(4): 2141-2146. doi: 10.7498/aps.58.2141
[18]	蔡建乐. 一般完整系统Mei对称性的共形不变性与守恒量. , 2009, 58(1): 22-27. doi: 10.7498/aps.58.22
[19]	贾利群, 罗绍凯, 张耀宇. 非完整系统Nielsen方程的Mei对称性与Mei守恒量. , 2008, 57(4): 2006-2010. doi: 10.7498/aps.57.2006
[20]	贾利群, 郑世旺, 张耀宇. 事件空间中非Chetaev型非完整系统的Mei对称性与Mei守恒量. , 2007, 56(10): 5575-5579. doi: 10.7498/aps.56.5575

计量

文章访问数: 6411
PDF下载量: 820
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板