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Under the infinitesimal transformations of Lie group, Noether-Lie symmetry of Nielsen equations for a singular variable mass nonholonomic system with unilateral constraints is studied. Differential equations of motion for Nielsen equations of the system are established. The definition, criteria and propositions for Nielsen equations of the system are given. Noether conserved quantity as well as generalized Hojman quantity is obtained. An example is given to illustrate the application of the results.
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Keywords:
- singular variable mass system /
- nonholonomic unilateral constraints /
- Nielsen equations /
- Noether-Lie symmetry
[1] Noether A E 1918 Math. Phys. KI II 235
[2] Li Z P 1993 Classical and Quantal Dynamics of Con-strained 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)]
[3] Zhao Y Y, Mei F X 1999 Symmetries and Invariants of Mechanical Systems (Beijing: Science Press) (in Chinese) [赵跃宇, 梅凤翔 1999 力学系统的对称性与不变量 (北京: 科学出版社)]
[4] Zhang Y, Mei F X 2004 Acta Phys. Sin. 53 2419 (in Chinese) [张毅, 梅凤翔 2004 53 2491]
[5] Fu J L, Nie N M, Huang J F 2009 Chin. Phys. B 18 2634
[6] Mei F X, Shang M 2000 Acta Phys. Sin. 49 1901 (in Chinese) [梅凤翔, 尚玫 2000 49 1901]
[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] Luo S K 2003 Acta Phys. Sin. 52 2941 (in Chinese) [罗绍凯 2003 52 2941]
[9] Zhang H B 2002 Chin. Phys. 11 1
[10] 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]
[11] Mei F X 2000 J. Beijing Inst. Technol. 9 120
[12] Zheng S W, Xie J F, Chen W C 2008 Chin. Phys. Lett. 25 809
[13] Wu H B, Mei F X 2009 Chin. Phys. B 18 3145
[14] Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[15] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanics 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)]
[16] 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: 科学出版社)]
[17] Jing H X, Li Y C, Xia L L 2007 Acta Phys. Sin. 56 3043 (in Chinese) [荆红星, 李元成, 夏丽莉 2007 56 3043]
[18] 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]
[19] 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]
[20] Zhang M L, Sun X T, Wang X X, Xie Y L, Jia L Q 2011 Chin. Phys. B 20 110202
[21] Wu H B, Mei F X 2012 Chin. Phys. B 6 064501
[22] Cui J C, Zhang Y Y, Yang X F, Jia L Q 2010 Chin. Phys. B 19 030304
[23] Wang P, Fang J H, Zhang P Y, Ding N 2006 Commun. Theor. Phys. 46 385
[24] Hou Q B, Li Y C, Xia L L, Wang J 2007 Commun. Theor. Phys. 48 619
[25] Fang J H, Liao Y P, Zhang J 2004 Acta Phys. Sin. 53 4037 (in Chinese) [方建会, 廖永藩, 张军 2004 53 4037]
[26] Chen R, Xu X J 2012 Acta Phys. Sin. 61 021102 (in Chinese) [陈蓉, 许学军 2012 61 021102]
[27] Zhang Y, Xue Y 2001 Acta Phys. Sin. 50 816 (in Chinese) [张毅, 薛纭 2001 50 816]
[28] Li Y C, Zhang Y, Liang J H 2002 Acta Phys. Sin. 51 2186 (in Chinese) [李元成, 张毅, 梁景辉 2002 51 2186]
[29] Mei F X, Zhu H P 2000 J. Beijing Inst. Technol. 9 11
[30] Luo S K 2004 Acta Phys. Sin. 53 5 (in Chinese) [罗绍凯 2004 53 5]
[31] Li Y C, Wang J, Xia L L, Hou Q B, Jing H X Chin. Phys. 16 2841
[32] Ding N, Fang J H 2006 Commun. Theor. Phys. 46 265
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[1] Noether A E 1918 Math. Phys. KI II 235
[2] Li Z P 1993 Classical and Quantal Dynamics of Con-strained 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)]
[3] Zhao Y Y, Mei F X 1999 Symmetries and Invariants of Mechanical Systems (Beijing: Science Press) (in Chinese) [赵跃宇, 梅凤翔 1999 力学系统的对称性与不变量 (北京: 科学出版社)]
[4] Zhang Y, Mei F X 2004 Acta Phys. Sin. 53 2419 (in Chinese) [张毅, 梅凤翔 2004 53 2491]
[5] Fu J L, Nie N M, Huang J F 2009 Chin. Phys. B 18 2634
[6] Mei F X, Shang M 2000 Acta Phys. Sin. 49 1901 (in Chinese) [梅凤翔, 尚玫 2000 49 1901]
[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] Luo S K 2003 Acta Phys. Sin. 52 2941 (in Chinese) [罗绍凯 2003 52 2941]
[9] Zhang H B 2002 Chin. Phys. 11 1
[10] 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]
[11] Mei F X 2000 J. Beijing Inst. Technol. 9 120
[12] Zheng S W, Xie J F, Chen W C 2008 Chin. Phys. Lett. 25 809
[13] Wu H B, Mei F X 2009 Chin. Phys. B 18 3145
[14] Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[15] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanics 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)]
[16] 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: 科学出版社)]
[17] Jing H X, Li Y C, Xia L L 2007 Acta Phys. Sin. 56 3043 (in Chinese) [荆红星, 李元成, 夏丽莉 2007 56 3043]
[18] 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]
[19] 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]
[20] Zhang M L, Sun X T, Wang X X, Xie Y L, Jia L Q 2011 Chin. Phys. B 20 110202
[21] Wu H B, Mei F X 2012 Chin. Phys. B 6 064501
[22] Cui J C, Zhang Y Y, Yang X F, Jia L Q 2010 Chin. Phys. B 19 030304
[23] Wang P, Fang J H, Zhang P Y, Ding N 2006 Commun. Theor. Phys. 46 385
[24] Hou Q B, Li Y C, Xia L L, Wang J 2007 Commun. Theor. Phys. 48 619
[25] Fang J H, Liao Y P, Zhang J 2004 Acta Phys. Sin. 53 4037 (in Chinese) [方建会, 廖永藩, 张军 2004 53 4037]
[26] Chen R, Xu X J 2012 Acta Phys. Sin. 61 021102 (in Chinese) [陈蓉, 许学军 2012 61 021102]
[27] Zhang Y, Xue Y 2001 Acta Phys. Sin. 50 816 (in Chinese) [张毅, 薛纭 2001 50 816]
[28] Li Y C, Zhang Y, Liang J H 2002 Acta Phys. Sin. 51 2186 (in Chinese) [李元成, 张毅, 梁景辉 2002 51 2186]
[29] Mei F X, Zhu H P 2000 J. Beijing Inst. Technol. 9 11
[30] Luo S K 2004 Acta Phys. Sin. 53 5 (in Chinese) [罗绍凯 2004 53 5]
[31] Li Y C, Wang J, Xia L L, Hou Q B, Jing H X Chin. Phys. 16 2841
[32] Ding N, Fang J H 2006 Commun. Theor. Phys. 46 265
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