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Conformal invariance and conserved quantity for a variable mass holonomic system in relative motion have been studied. The definition and the determining equations of conformal invariance for a variable mass holonomic system in relative motion are given. The necessary and sufficient conditions that the system’s conformal invariance be of Lie symmetry are deduced. With the aid of a structure equation which the gauge function should satisfy, the system’s corresponding conserved quantity is obtained. Finally, an illustrative example is given to verify the results.
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Keywords:
- variable mass /
- relative motion /
- conformal invariance /
- conserved quantity
[1] Noether A E 1918 Math. Phys. KI, Ⅱ 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] Zhang Y, Xue Y 2009 Chinese Quarterly of Mechanics 30 216 (in Chinese) [张毅, 薛纭 2009 力学季刊 30 216]
[8] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[9] 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]
[10] 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]
[11] 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]
[12] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin. Phys. B 21 100203
[13] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[14] 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]
[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] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin Phys. B 21 100203
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[1] Noether A E 1918 Math. Phys. KI, Ⅱ 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] Zhang Y, Xue Y 2009 Chinese Quarterly of Mechanics 30 216 (in Chinese) [张毅, 薛纭 2009 力学季刊 30 216]
[8] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[9] 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]
[10] 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]
[11] 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]
[12] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin. Phys. B 21 100203
[13] Wang X X, Han Y L, Zhang M L, Jia L Q 2013 Chin. Phys. B 22 020201
[14] 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]
[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] Zhang M L, Wang X X, Han Y L, Jia L Q 2012 Chin Phys. B 21 100203
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