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The Noether-Lie symmetry and conserved quantities of the Rosenberg problem are studied. From the study of the Rosenberg problem,the Noether symmetry and the Lie symmetry for the equation are obtained, thereby the conserved quantities are deduced. Then the definition and the criterion for Noether-Lie symmetry of the Rosenberg problem are derived. Finally,the Noether conserved quantity and the Hojman conserved quantity are deduced from the Noether-Lie symmetry.
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Keywords:
- nonholonomic systems /
- Noether-Lie symmetry /
- conserved quantity
[1] Noether A E 1918 Nachr. Akad. Wiss. Gttingen.Math. Phys. KI II 235
[2] Lutzky M 1979 J. Phys. A: Math. Gen. 12 973
[3] Mei F X 2000 J. Beijing Inst. Technol. 9 120
[4] Mei F X 2001 Chin. Phys. 10 177
[5] Li Z P 1993 Classical and quantal 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:北京工业大学出社)]
[6] 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)]
[7] Bahar L Y,Kwatny H G 1987 Int. J. Non-Linear Mech. 22 125
[8] Mei F X 2000 Acta Mech. Sin. 32 466 (in Chinese)[梅凤翔 2000 力学学报32 466]
[9] Mei F X 2003 Acta Phys. Sin. 52 1048 (in Chinese) [梅凤翔 2003 52 1048]
[10] Zhang Y 2003 Acta Phys. Sin. 52 1832 (in Chinese) [张 毅 2003 52 1832]
[11] Wang S Y, Mei F X 2001 Chin. Phys. 10 373
[12] Lou Z M 2004 Acta Phys. Sin. 53 2046 (in Chinese) [楼智美 2004 53 2046]
[13] Luo S K,Guo Y X,Mei F X 2004 Acta Phys. Sin. 53 2413 (in Chinese) [罗绍凯、郭永新、梅凤翔 2004 53 2413]
[14] Hojman S A 1992 J. Phys. A: Math. Gen. 25 L291
[15] Xu X J,Mei F X,Qin M C 2004 Chin. Phys. 13 1999
[16] Mei F X 2005 Transactions of Beijing Institute of Technology 25 283(in Chinese) [梅凤翔 2005 北京理工大学学报 25 283]
[17] 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]
[18] Rosenberg R M 1977 Analytical Dynamics of Discrete Systems (New York: Plenum Press)
[19] Ge W H,Zhang Y,Xue Y 2010 Acta Phys. Sin. 59 4434 (in Chinese) [葛伟宽、张 毅、薛 纭 2010 59 4434]
[20] Novoselov V S 1966 Variational Priciples in Mechanics (Leningrad: LGV Press) (in Russian)
[21] Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)[梅凤翔 1985 非完整力学基础 (北京:北京工业学院出版社)]
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[1] Noether A E 1918 Nachr. Akad. Wiss. Gttingen.Math. Phys. KI II 235
[2] Lutzky M 1979 J. Phys. A: Math. Gen. 12 973
[3] Mei F X 2000 J. Beijing Inst. Technol. 9 120
[4] Mei F X 2001 Chin. Phys. 10 177
[5] Li Z P 1993 Classical and quantal 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:北京工业大学出社)]
[6] 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)]
[7] Bahar L Y,Kwatny H G 1987 Int. J. Non-Linear Mech. 22 125
[8] Mei F X 2000 Acta Mech. Sin. 32 466 (in Chinese)[梅凤翔 2000 力学学报32 466]
[9] Mei F X 2003 Acta Phys. Sin. 52 1048 (in Chinese) [梅凤翔 2003 52 1048]
[10] Zhang Y 2003 Acta Phys. Sin. 52 1832 (in Chinese) [张 毅 2003 52 1832]
[11] Wang S Y, Mei F X 2001 Chin. Phys. 10 373
[12] Lou Z M 2004 Acta Phys. Sin. 53 2046 (in Chinese) [楼智美 2004 53 2046]
[13] Luo S K,Guo Y X,Mei F X 2004 Acta Phys. Sin. 53 2413 (in Chinese) [罗绍凯、郭永新、梅凤翔 2004 53 2413]
[14] Hojman S A 1992 J. Phys. A: Math. Gen. 25 L291
[15] Xu X J,Mei F X,Qin M C 2004 Chin. Phys. 13 1999
[16] Mei F X 2005 Transactions of Beijing Institute of Technology 25 283(in Chinese) [梅凤翔 2005 北京理工大学学报 25 283]
[17] 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]
[18] Rosenberg R M 1977 Analytical Dynamics of Discrete Systems (New York: Plenum Press)
[19] Ge W H,Zhang Y,Xue Y 2010 Acta Phys. Sin. 59 4434 (in Chinese) [葛伟宽、张 毅、薛 纭 2010 59 4434]
[20] Novoselov V S 1966 Variational Priciples in Mechanics (Leningrad: LGV Press) (in Russian)
[21] Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)[梅凤翔 1985 非完整力学基础 (北京:北京工业学院出版社)]
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