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Conformal invariance and a new type of conserved quantity in nonholonomic mechanical system are studied. The definition and determining equation of conformal invariance for the nonholonomic mechanical system are provided; and the necessary and sufficient conditions that the conformal invariance for a nonholonomic mechanical system should be of Lie symmetry are deduced. With the aid of a new structure equation that the gauge function satisfies, the system's corresponding new conserved quantity is obtained. Finally an example is given to illustrate the application of the results.
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Keywords:
- nonholonomic system /
- Lie symmetry /
- conformal invariance /
- new conserved quantity
[1] Noether A E 1918 Nachr. Akad. Math. 2 235
[2] Djukić D S, Vujanovi B D 1975 Acta Mechanica 23 17
[3] Lutzky M 1979 J. Phys. A Math. Gen. 12 973
[4] Hojman S A 1992 J. Phys. A Math. Gen. 25 L291
[5] 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)]
[6] 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)
[7] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) p383 (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383页]
[8] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin. Phys. B 21 100203
[9] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[10] 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]
[11] Wang X X, Zhang M L, Han Y L, Jia L Q 2012 Acta Phys. Sin. 61 200203 (in Chinese) [王肖肖, 张美玲, 韩月林, 贾利群 2012 61 200203]
[12] Sun X T, Han Y L, Wang X X, Zhang M L, Jia L Q 2012 Acta Phys. Sin. 61 200204 (in Chinese) [孙现亭, 韩月林, 王肖肖, 张美玲, 贾利群 2012 61 200204]
[13] Zhang Y, Xue Y 2009 Chinese Quarterly of Mechanics 30 216 (in Chinese) [张毅, 薛纭 2009 力学季刊 30 216]
[14] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[15] 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]
[16] Chen R, Xu X J 2012 Acta Phys. Sin. 61 021102 (in Chinese) [陈蓉, 许学军 2012 61 021102]
[17] Chen X W, Zhao Y H, Li Y M 2009 Chin Phys. B 18 3139
[18] Huang W L, Cai J L 2012 Applied Mathematics and Mechanics. 33 1294 [黄卫立, 蔡建乐 2012 应用数学和力学 33 1294 ]
[19] Han Y L, Sun X T, Zhang Y Y, Jia L Q 2013 Acta Phys. Sin. 62 160201 (in Chinese) [韩月林, 孙现亭, 张耀宇, 贾利群 2013 62 160201]
[20] Wang T Z, Han Y L 2013 Journal of Jiangnan University (Natural Science Edition). 2 234 (in Chinese) [王廷志, 韩月林 2013 江南大学学报(自然科学版) 2 234]
[21] Wang T Z, Sun X T, Han Y L 2013 Acta Phys. Sin. 62 231101 (in Chinese) [王廷志, 孙现亭, 韩月林 2013 62 231101]
[22] Jia L Q, Sun X T, Zhang M L, Zhang Y Y, Han Y L 2014 Acta Phys. Sin. 63 010201 (in Chinese) [贾利群, 孙现亭, 张美玲, 张耀宇, 韩月林 2014 63 010201]
[23] Luo S K, Li Z J, Li L 2012 Acta Mechanica 223 2621
[24] Li Z J, Luo S K 2012 Nonlinear Dyn. 70 1117
[25] Li L, Luo S K 2013 Acta Mechanica 224 1757
[26] Li Z J, Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 445
[27] Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[28] 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 2012 59 7552]
[29] SHen Y, Zhang L T 2012 ACTA ARMAMENTARII. 11 1342 (in Chinese) [沈跃, 张令坦 2012 兵工学报 11 1342]
[30] Jia L Q, Han Y L, Zhang M L, Wang X X 2013 Journal of Pingdingsban University. 2 27 (in Chinese) [贾利群, 韩月林, 张美玲, 王肖肖 2013 平顶山学院学报 2 27]
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[1] Noether A E 1918 Nachr. Akad. Math. 2 235
[2] Djukić D S, Vujanovi B D 1975 Acta Mechanica 23 17
[3] Lutzky M 1979 J. Phys. A Math. Gen. 12 973
[4] Hojman S A 1992 J. Phys. A Math. Gen. 25 L291
[5] 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)]
[6] 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)
[7] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) p383 (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383页]
[8] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin. Phys. B 21 100203
[9] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[10] 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]
[11] Wang X X, Zhang M L, Han Y L, Jia L Q 2012 Acta Phys. Sin. 61 200203 (in Chinese) [王肖肖, 张美玲, 韩月林, 贾利群 2012 61 200203]
[12] Sun X T, Han Y L, Wang X X, Zhang M L, Jia L Q 2012 Acta Phys. Sin. 61 200204 (in Chinese) [孙现亭, 韩月林, 王肖肖, 张美玲, 贾利群 2012 61 200204]
[13] Zhang Y, Xue Y 2009 Chinese Quarterly of Mechanics 30 216 (in Chinese) [张毅, 薛纭 2009 力学季刊 30 216]
[14] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[15] 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]
[16] Chen R, Xu X J 2012 Acta Phys. Sin. 61 021102 (in Chinese) [陈蓉, 许学军 2012 61 021102]
[17] Chen X W, Zhao Y H, Li Y M 2009 Chin Phys. B 18 3139
[18] Huang W L, Cai J L 2012 Applied Mathematics and Mechanics. 33 1294 [黄卫立, 蔡建乐 2012 应用数学和力学 33 1294 ]
[19] Han Y L, Sun X T, Zhang Y Y, Jia L Q 2013 Acta Phys. Sin. 62 160201 (in Chinese) [韩月林, 孙现亭, 张耀宇, 贾利群 2013 62 160201]
[20] Wang T Z, Han Y L 2013 Journal of Jiangnan University (Natural Science Edition). 2 234 (in Chinese) [王廷志, 韩月林 2013 江南大学学报(自然科学版) 2 234]
[21] Wang T Z, Sun X T, Han Y L 2013 Acta Phys. Sin. 62 231101 (in Chinese) [王廷志, 孙现亭, 韩月林 2013 62 231101]
[22] Jia L Q, Sun X T, Zhang M L, Zhang Y Y, Han Y L 2014 Acta Phys. Sin. 63 010201 (in Chinese) [贾利群, 孙现亭, 张美玲, 张耀宇, 韩月林 2014 63 010201]
[23] Luo S K, Li Z J, Li L 2012 Acta Mechanica 223 2621
[24] Li Z J, Luo S K 2012 Nonlinear Dyn. 70 1117
[25] Li L, Luo S K 2013 Acta Mechanica 224 1757
[26] Li Z J, Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 445
[27] Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[28] 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 2012 59 7552]
[29] SHen Y, Zhang L T 2012 ACTA ARMAMENTARII. 11 1342 (in Chinese) [沈跃, 张令坦 2012 兵工学报 11 1342]
[30] Jia L Q, Han Y L, Zhang M L, Wang X X 2013 Journal of Pingdingsban University. 2 27 (in Chinese) [贾利群, 韩月林, 张美玲, 王肖肖 2013 平顶山学院学报 2 27]
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