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Mei symmetry and Mei conserved quantity deduced directly from Mei symmetry for Appell equations in a dynamical system of the relative motion are investigated. The definition and the criterion of Mei symmetry of Appell equations in a dynamical system of the relative motion under the infinitesimal transformations of groups are given. The expressions of the determining equation of Mei symmetry of Appell equations and Mei conserved quantity deduced directly from Mei symmetry in a dynamical system of the relative motion are gained. An example is given to illustrate the application of the results.
[1] Appell P 1953 Traité de Mécanique Rationnelle Ⅱ (Paris:Gauthier-Villars) p335
[2] Mei F X. 2001 Chin. Phys. 10 177
[3] Li R J, QiaoY F, Meng J 2002 Acta Phys. Sin. 51 1 (in Chinese) [李仁杰、 乔永芬、 孟 军 2002 51 1]
[4] Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese)[罗绍凯 2002 51 712]
[5] Jia L Q, Zhang Y Y, Zheng S W 2007 J. Yunnan Univ. 29 589 (in Chinese)
[6] Jia L Q, Xie J F, Zheng S W 2008 Chin. Phys. B 17 17
[7] Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) p378 (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) 第378页]
[8] Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16 (in Chinese)[贾利群、 崔金超、 张耀宇、 罗绍凯 2009 58 16]
[9] Jia L Q, Cui J C, Luo S K, Yang X F 2009 Chin. Phys. Lett. 26 030303
[10] Cui J C, Jia L Q, Yang X F 2009 J. Henan Norm. Univ. (Natural Science) 37 70 (in Chinese) [崔金超、 贾利群、 杨新芳 2009 河南师范大学学报(自然科学版)37 70]
[11] Cui J C, Zhang Y Y, Yang X F, Jia L Q 2010 Chin. Phys. B 19 030304
[12] 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]
[13] Luo Y P, Fu J L 2010 Chin. Phys B 19 090303
[14] Jia L Q, Xie Y Y, 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] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) p172, 364, 422 (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)]p172, 364, 422
[16] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing:Beijing Institute of Technology Press) p228 (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) p228]
[17] Liu R W, Fu J L, Mei F X 1998 J. Beijing Inst. Technol. 7 221
[18] Chen X W, Wang M Q, Wang X M 2005 Commun. Theor. Phys. 43 577
[19] Mei F X, Liu D, Luo Y 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press) p295 (in Chinese)[梅凤翔、 刘 端、 罗 勇 1991 高等分析力学 (北京:北京理工大学出版社)第295页]
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[1] Appell P 1953 Traité de Mécanique Rationnelle Ⅱ (Paris:Gauthier-Villars) p335
[2] Mei F X. 2001 Chin. Phys. 10 177
[3] Li R J, QiaoY F, Meng J 2002 Acta Phys. Sin. 51 1 (in Chinese) [李仁杰、 乔永芬、 孟 军 2002 51 1]
[4] Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese)[罗绍凯 2002 51 712]
[5] Jia L Q, Zhang Y Y, Zheng S W 2007 J. Yunnan Univ. 29 589 (in Chinese)
[6] Jia L Q, Xie J F, Zheng S W 2008 Chin. Phys. B 17 17
[7] Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) p378 (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) 第378页]
[8] Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16 (in Chinese)[贾利群、 崔金超、 张耀宇、 罗绍凯 2009 58 16]
[9] Jia L Q, Cui J C, Luo S K, Yang X F 2009 Chin. Phys. Lett. 26 030303
[10] Cui J C, Jia L Q, Yang X F 2009 J. Henan Norm. Univ. (Natural Science) 37 70 (in Chinese) [崔金超、 贾利群、 杨新芳 2009 河南师范大学学报(自然科学版)37 70]
[11] Cui J C, Zhang Y Y, Yang X F, Jia L Q 2010 Chin. Phys. B 19 030304
[12] 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]
[13] Luo Y P, Fu J L 2010 Chin. Phys B 19 090303
[14] Jia L Q, Xie Y Y, 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] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) p172, 364, 422 (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)]p172, 364, 422
[16] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing:Beijing Institute of Technology Press) p228 (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) p228]
[17] Liu R W, Fu J L, Mei F X 1998 J. Beijing Inst. Technol. 7 221
[18] Chen X W, Wang M Q, Wang X M 2005 Commun. Theor. Phys. 43 577
[19] Mei F X, Liu D, Luo Y 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press) p295 (in Chinese)[梅凤翔、 刘 端、 罗 勇 1991 高等分析力学 (北京:北京理工大学出版社)第295页]
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