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The Rosenberg problem is a typical but not a too complex problem of nonholonomic mechanical systems. By using the theory of Noether symmetries of nonholonomic systems, the conserved quantities of the problem is successively deduced,and the final result is obtained.
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Keywords:
- nonholonomic systems /
- symmetries /
- conserved quantities /
- integral
[1] Li Z P 1981 Acta Phys. Sin. 30 1699 (in Chinese) [李子平 1981 30 1699]
[2] Liu D 1991 Sci. Chin. Ser. A 34 419
[3] Mei F X 1993 Sci. Chin. Ser. A 36 1456
[4] 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)]
[5] Fu J L, Chen L Q 2003 Phys. Lett. A 317 255
[6] 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)]
[7] Luo S K, Cai J L 2003 Chin. Phys. 12 357
[8] Xu X J, Mei F X,Qin M C 2004 Chin. Phys. 13 1999
[9] Wu H P, Mei F X 2006 Acta Phys. Sin. 55 3825 (in Chinese) [吴惠彬、梅凤翔 2006 55 3825]
[10] Shang M, Chen X W 2006 Chin. Phys. 15 2788
[11] Ge W K 2007 Acta Phys. Sin. 56 1 (in Chinese) [葛伟宽 2007 56 1] 〖12] Luo S K 2007 Chin. Phys. 16 3182
[12] Zhang Y 2008 Acta Phys. Sin. 57 2643 (in Chinese) [张 毅 2008 57 2643]
[13] Wu H P, Mei F X 2009 Chin. Phys.B 18 3145
[14] Jia L Q, Xie J F, Zhen S W 2008 Chin. Phys. B 17 17
[15] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[16] Rosenberg R M 1977 Analytical Dynamics of Discrete Systems (New York: Plenum Press)
[17] Novoselov V S 1966 Variational Priciple in Mechanics (Leningrad: LGV Press )(in Russian)
[18] 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)]
[19] Mei F X, Shui X P 2006 J. Beijing Institute of Technology 26 285 (in Chinese) [梅凤翔、水小平 2006北京理工大学学报 26 285]
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[1] Li Z P 1981 Acta Phys. Sin. 30 1699 (in Chinese) [李子平 1981 30 1699]
[2] Liu D 1991 Sci. Chin. Ser. A 34 419
[3] Mei F X 1993 Sci. Chin. Ser. A 36 1456
[4] 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)]
[5] Fu J L, Chen L Q 2003 Phys. Lett. A 317 255
[6] 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)]
[7] Luo S K, Cai J L 2003 Chin. Phys. 12 357
[8] Xu X J, Mei F X,Qin M C 2004 Chin. Phys. 13 1999
[9] Wu H P, Mei F X 2006 Acta Phys. Sin. 55 3825 (in Chinese) [吴惠彬、梅凤翔 2006 55 3825]
[10] Shang M, Chen X W 2006 Chin. Phys. 15 2788
[11] Ge W K 2007 Acta Phys. Sin. 56 1 (in Chinese) [葛伟宽 2007 56 1] 〖12] Luo S K 2007 Chin. Phys. 16 3182
[12] Zhang Y 2008 Acta Phys. Sin. 57 2643 (in Chinese) [张 毅 2008 57 2643]
[13] Wu H P, Mei F X 2009 Chin. Phys.B 18 3145
[14] Jia L Q, Xie J F, Zhen S W 2008 Chin. Phys. B 17 17
[15] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[16] Rosenberg R M 1977 Analytical Dynamics of Discrete Systems (New York: Plenum Press)
[17] Novoselov V S 1966 Variational Priciple in Mechanics (Leningrad: LGV Press )(in Russian)
[18] 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)]
[19] Mei F X, Shui X P 2006 J. Beijing Institute of Technology 26 285 (in Chinese) [梅凤翔、水小平 2006北京理工大学学报 26 285]
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