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Another kind of conserved quantity deduced from Mei symmetry of Tzénoff equations for holonomic systems is studied. The expression of this conserved quantity and the determining equation to induce this conserved quantity are presented. The results indicate that this new method is easier to find conserved quantities than methods reported previously. Finally, application of this new result is presented by a practical example.
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Keywords:
- holonomic systems /
- Tzénoff equations /
- Mei symmetry /
- conserved quantity
[1] Noether A E 1918 Nachr. Akad. Wiss. Gttingen. Math. Phys. KI II 235
[2] Liu D 1991 Sci. Chin 34 419
[3] Li Z P 1993 Classical and Quantum Dynamics of Constrained Systems and Their Symmetrical Properties (Beijing:Beijing Polytechnic University Press) (in Chinese) [李子平1993 经典和量子约束系统及其对称性质(北京: 北京工业大学出版社)]
[4] Chen X W,Li Y M 2003 Chin. Phys. 12 936
[5] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems(Beijing: Science Press) p90 (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90页]
[6] Luo S K 2007 Chin. Phys. 16 3182
[7] Lou Z M 2007 Acta Phys. Sin. 56 2475 (in Chinese) [楼智美 2007 56 2475]
[8] Chen X W,Liu C M,Li Y M 2006 Chin. Phys. 15 470
[9] Luo S K, Jia L Q,Cai J L 2005 Commun. Theor. Phys. 43 193
[10] 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)]
[11] Fu J L,Chen L Q,Xie F P 2004 Chin. Phys. 13 1611
[12] Xia L L,Li Y C,Wang X J 2009 Acta Phys. Sin.58 28 (in Chinese) [夏丽莉、李元成、王显军 2009 58 28]
[13] Liu C,Liu S X,Mei F X,Guo Y X 2008 Acta Phys. Sin.57 6709 (in Chinese) [刘 畅、刘世兴、梅凤翔、郭永新 2008 57 6709]
[14] Zhang H B, Chen L Q,Gu S L 2004 Commun. Theor. Phys. 42 321
[15] Zhang Y 2007 Acta Phys. Sin.56 3054 (in Chinese) [张 毅 2007 56 3054]
[16] Fang J H,Ding N,Wang P 2007 Chin. Phys. 16 887
[17] Mei F X 2000 J. Beijing Inst. Technol. 9 120
[18] Jia L Q,Luo S K,Zhang Y Y 2008 Acta Phys . Sin. 57 2006 (in Chinese) [贾利群、罗绍凯、张耀宇 2008 57 2006]
[19] Zhang Y,Mei F X 2003 Chin. Phys. 12 936
[20] Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese) [方建会 2009 58 3617]
[21] Mei F X 2001 Chin. Phys. 10 177
[22] Zheng S W, Jia L Q,Yu H S 2006 Chin. Phys. 15 1399
[23] Ge W K 2008 Acta Phys. Sin. 57 6714 (in Chinese) [葛伟宽 2008 57 6714]
[24] Yang X F, Jia L Q 2010 Chin. Phys.B. 19 30305
[25] Xu X J, Qin M C, Mei F X 2005 Chin. Phys. 14 1287
[26] Li Y C, Xia L L,Wang X M 2009 Acta Phys. Sin. 58 6732 (in Chinese) [李元成、夏丽莉、王小明2009 58 6732]
[27] Mei F X,Wu H B 2009 Acta Phys . Sin. 58 5916 (in Chinese) [梅凤翔、吴惠彬2009 58 5916]
[28] Wu H B,Mei F X 2010 Chin. Phys.B 19 3
[29] Zhang Y 2009 Acta Phys. Sin. 58 7447 (in Chinese) [张 毅 2009 58 7447] 〖30] Zheng S W,Jia L Q 2007 Acta Phys. Sin. 56 661 (in Chinese)[郑世旺、贾利群 2007 56 661]
[30] Zheng S W,Xie J F,Jia L Q 2006 Chin. Phys. Lett. 23 2924
[31] Zheng S W,Xie J F,Jia L Q 2007 Commun. Theor. Phys. 48 43
[32] Zheng S W,Xie J F,Zhang Q H 2007 Chin. Phys. Lett. 24 2164
[33] Zheng S W,Xie J F,Chen W C 2008 Chin. Phys. Lett. 25 809
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[1] Noether A E 1918 Nachr. Akad. Wiss. Gttingen. Math. Phys. KI II 235
[2] Liu D 1991 Sci. Chin 34 419
[3] Li Z P 1993 Classical and Quantum Dynamics of Constrained Systems and Their Symmetrical Properties (Beijing:Beijing Polytechnic University Press) (in Chinese) [李子平1993 经典和量子约束系统及其对称性质(北京: 北京工业大学出版社)]
[4] Chen X W,Li Y M 2003 Chin. Phys. 12 936
[5] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems(Beijing: Science Press) p90 (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90页]
[6] Luo S K 2007 Chin. Phys. 16 3182
[7] Lou Z M 2007 Acta Phys. Sin. 56 2475 (in Chinese) [楼智美 2007 56 2475]
[8] Chen X W,Liu C M,Li Y M 2006 Chin. Phys. 15 470
[9] Luo S K, Jia L Q,Cai J L 2005 Commun. Theor. Phys. 43 193
[10] 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)]
[11] Fu J L,Chen L Q,Xie F P 2004 Chin. Phys. 13 1611
[12] Xia L L,Li Y C,Wang X J 2009 Acta Phys. Sin.58 28 (in Chinese) [夏丽莉、李元成、王显军 2009 58 28]
[13] Liu C,Liu S X,Mei F X,Guo Y X 2008 Acta Phys. Sin.57 6709 (in Chinese) [刘 畅、刘世兴、梅凤翔、郭永新 2008 57 6709]
[14] Zhang H B, Chen L Q,Gu S L 2004 Commun. Theor. Phys. 42 321
[15] Zhang Y 2007 Acta Phys. Sin.56 3054 (in Chinese) [张 毅 2007 56 3054]
[16] Fang J H,Ding N,Wang P 2007 Chin. Phys. 16 887
[17] Mei F X 2000 J. Beijing Inst. Technol. 9 120
[18] Jia L Q,Luo S K,Zhang Y Y 2008 Acta Phys . Sin. 57 2006 (in Chinese) [贾利群、罗绍凯、张耀宇 2008 57 2006]
[19] Zhang Y,Mei F X 2003 Chin. Phys. 12 936
[20] Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese) [方建会 2009 58 3617]
[21] Mei F X 2001 Chin. Phys. 10 177
[22] Zheng S W, Jia L Q,Yu H S 2006 Chin. Phys. 15 1399
[23] Ge W K 2008 Acta Phys. Sin. 57 6714 (in Chinese) [葛伟宽 2008 57 6714]
[24] Yang X F, Jia L Q 2010 Chin. Phys.B. 19 30305
[25] Xu X J, Qin M C, Mei F X 2005 Chin. Phys. 14 1287
[26] Li Y C, Xia L L,Wang X M 2009 Acta Phys. Sin. 58 6732 (in Chinese) [李元成、夏丽莉、王小明2009 58 6732]
[27] Mei F X,Wu H B 2009 Acta Phys . Sin. 58 5916 (in Chinese) [梅凤翔、吴惠彬2009 58 5916]
[28] Wu H B,Mei F X 2010 Chin. Phys.B 19 3
[29] Zhang Y 2009 Acta Phys. Sin. 58 7447 (in Chinese) [张 毅 2009 58 7447] 〖30] Zheng S W,Jia L Q 2007 Acta Phys. Sin. 56 661 (in Chinese)[郑世旺、贾利群 2007 56 661]
[30] Zheng S W,Xie J F,Jia L Q 2006 Chin. Phys. Lett. 23 2924
[31] Zheng S W,Xie J F,Jia L Q 2007 Commun. Theor. Phys. 48 43
[32] Zheng S W,Xie J F,Zhang Q H 2007 Chin. Phys. Lett. 24 2164
[33] Zheng S W,Xie J F,Chen W C 2008 Chin. Phys. Lett. 25 809
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