完整系统Appell方程Mei对称性的一种新的守恒量

孙现亭; 韩月林; 王肖肖; 张美玲; 贾利群

doi:10.7498/aps.61.200204

摘要

研究完整系统Appell方程Mei对称性的一种新的守恒量.在群的无限小变换下, 由完整系统Appell方程Mei对称性的定义和判据,得到用Appell函数表示的完整系统Appell方程Mei对称性的一种新的结构方程和新的守恒量.最后,举例说明结果的应用.

关键词:

A type of new conserved quantity of Mei symmetry for Appell equations in a holonomic system is investigated. Based on the definition and criterion of Mei symmetry for Appell equations in a holonomic system, a type of new structural equation and new conserved quantity of Mei symmetry for Appell equations in a holonomic system expressed by Appell function under the infinitesimal transformations of groups are obtained. An example is given to illustrate the application of the results.

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, 61178032)资助的课题.

Authors and contacts

1.
School 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 Nos. 11142014, 61178032).

参考文献

[1]	Noether A E 1918 Nachr. Akad. Wiss. Göttingen. Math. Phys. Kl 235
[2]	Lutzky M D 1979 Phys. A Math. Gen. 12 973
[3]	Vujanović B A 1986 Acta Mech. 65 63
[4]	Hojman S A 1992 Phys. A Math. Gen. 25 291
[5]	Mei F X 1999 Application of Lie Groups and Lie Algebra to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese) [梅凤翔 1999 李群和李群代数约束力学系统的的应用(北京:科学出版社)]
[6]	Mei F X 2000 Beijing Inst. Technol. 9 120 (in Chinese) [梅凤翔 2000 北京理工大学学报 9 120]
[7]	Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔 2008 57 5369]
[8]	Cai J L 2008 Chin. Phys. Lett. 25 1523
[9]	Ge W K 2008 Acta Phys. Sin. 57 6714 (in Chinese) [葛伟宽 2008 57 6714]
[10]	Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170
[11]	Chen X W, Zhao Y H, Liu C 2009 Acta Phys. Sin. 58 5150 (in Chinese) [陈向炜, 赵永红, 刘畅 2009 58 5150]
[12]	Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[13]	Zhang Y 2009 Chin. Phys. B 18 4636
[14]	Cai J L 2010 Chin. J. Phys. 48 728
[15]	Zheng S W, Xie J F, Chen W C 2008 Chin. Phys. Lett. 25 809
[16]	Wu H B, Mei F X 2010 Chin. Phys. B 19 030303
[17]	Fang J H 2010 Chin. Phys. B 19 040301
[18]	Mei F X, Wu H B 2010 Chin. Phys. B 19 050301
[19]	Li Y C, Wang X M, Xia L L 2010 Acta Phys. Sin. 59 2935 (in Chinese) [李元成, 王小明, 夏丽莉 2010 59 2935]
[20]	Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[21]	Xie Y L, Jia L Q, Yang X F 2011 Acta Phys. Sin. 60 030201 (in Chinese) [解银丽, 贾利群, 杨新芳 2011 60 030201]
[22]	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]
[23]	Jiang W A, Li L, Li Z J, Luo S K 2012 Nonlinear Dynam. 67 075
[24]	Jiang W A, Luo S K 2012 Nonlinear Dynam. 67 475
[25]	Mei F X 2001 Chin. Phys. 10 177
[26]	Li R J, Qiao Y F, Meng J 2002 Acta Phys. Sin. 51 1 (in Chinese) [李仁杰, 乔永芬, 孟军 2002 51 1]
[27]	Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese) [罗绍凯 2002 51 712]
[28]	Jia L Q, Xie J F, Zheng S W 2008 Chin. Phys. B 17 17

施引文献

[1]	Noether A E 1918 Nachr. Akad. Wiss. Göttingen. Math. Phys. Kl 235
[2]	Lutzky M D 1979 Phys. A Math. Gen. 12 973
[3]	Vujanović B A 1986 Acta Mech. 65 63
[4]	Hojman S A 1992 Phys. A Math. Gen. 25 291
[5]	Mei F X 1999 Application of Lie Groups and Lie Algebra to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese) [梅凤翔 1999 李群和李群代数约束力学系统的的应用(北京:科学出版社)]
[6]	Mei F X 2000 Beijing Inst. Technol. 9 120 (in Chinese) [梅凤翔 2000 北京理工大学学报 9 120]
[7]	Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔 2008 57 5369]
[8]	Cai J L 2008 Chin. Phys. Lett. 25 1523
[9]	Ge W K 2008 Acta Phys. Sin. 57 6714 (in Chinese) [葛伟宽 2008 57 6714]
[10]	Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170
[11]	Chen X W, Zhao Y H, Liu C 2009 Acta Phys. Sin. 58 5150 (in Chinese) [陈向炜, 赵永红, 刘畅 2009 58 5150]
[12]	Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[13]	Zhang Y 2009 Chin. Phys. B 18 4636
[14]	Cai J L 2010 Chin. J. Phys. 48 728
[15]	Zheng S W, Xie J F, Chen W C 2008 Chin. Phys. Lett. 25 809
[16]	Wu H B, Mei F X 2010 Chin. Phys. B 19 030303
[17]	Fang J H 2010 Chin. Phys. B 19 040301
[18]	Mei F X, Wu H B 2010 Chin. Phys. B 19 050301
[19]	Li Y C, Wang X M, Xia L L 2010 Acta Phys. Sin. 59 2935 (in Chinese) [李元成, 王小明, 夏丽莉 2010 59 2935]
[20]	Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[21]	Xie Y L, Jia L Q, Yang X F 2011 Acta Phys. Sin. 60 030201 (in Chinese) [解银丽, 贾利群, 杨新芳 2011 60 030201]
[22]	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]
[23]	Jiang W A, Li L, Li Z J, Luo S K 2012 Nonlinear Dynam. 67 075
[24]	Jiang W A, Luo S K 2012 Nonlinear Dynam. 67 475
[25]	Mei F X 2001 Chin. Phys. 10 177
[26]	Li R J, Qiao Y F, Meng J 2002 Acta Phys. Sin. 51 1 (in Chinese) [李仁杰, 乔永芬, 孟军 2002 51 1]
[27]	Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese) [罗绍凯 2002 51 712]
[28]	Jia L Q, Xie J F, Zheng S W 2008 Chin. Phys. B 17 17

[1]	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
[2]	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
[3]	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
[4]	韩月林, 孙现亭, 张耀宇, 贾利群. 完整系统Appell方程Mei对称性的共形不变性与守恒量. , 2013, 62(16): 160201. doi: 10.7498/aps.62.160201
[5]	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
[6]	贾利群, 孙现亭, 张美玲, 王肖肖, 解银丽. Nielsen方程Mei对称性导致的一种新型守恒量. , 2011, 60(8): 084501. doi: 10.7498/aps.60.084501
[7]	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
[8]	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
[9]	郑世旺, 解加芳, 陈向炜, 杜雪莲. 完整系统Tzénoff方程的Mei对称性直接导致的另一种守恒量. , 2010, 59(8): 5209-5212. doi: 10.7498/aps.59.5209
[10]	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
[11]	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
[12]	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
[13]	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
[14]	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
[15]	葛伟宽. 一类动力学方程的Mei对称性. , 2007, 56(1): 1-4. doi: 10.7498/aps.56.1
[16]	方建会, 丁宁, 王鹏. Hamilton系统Mei对称性的一种新守恒量. , 2007, 56(6): 3039-3042. doi: 10.7498/aps.56.3039
[17]	郑世旺, 贾利群. 非完整系统Tzénoff方程的Mei对称性和守恒量. , 2007, 56(2): 661-665. doi: 10.7498/aps.56.661
[18]	顾书龙, 张宏彬. Emden方程的Mei对称性、Lie对称性和Noether对称性. , 2006, 55(11): 5594-5597. doi: 10.7498/aps.55.5594
[19]	张毅, 葛伟宽. 相对论性力学系统的Mei对称性导致的新守恒律. , 2005, 54(4): 1464-1467. doi: 10.7498/aps.54.1464
[20]	顾书龙, 张宏彬. Vacco动力学方程的Mei对称性、Lie对称性和Noether对称性. , 2005, 54(9): 3983-3986. doi: 10.7498/aps.54.3983

计量

文章访问数: 6787
PDF下载量: 634
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