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The generalized Pfaff-Birkhoff-dAlembert principle and the form invariance of the generalized Birkhoff s equations under the infinitesimal transformation of group are studied. The criterion of the form invariance is given and the Noether conserved quantity and a new conserved quantity are obtained by the invariance.
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Keywords:
- generalized Pfaff-Birkhoff-dAlembert principle /
- generalized Birkhoff's equations /
- Noether conserved quantity /
- form invariance
[1] Noether A E 1918 Nachr Akad. Wiss Gttingen Math. Phys. 1 235
[2] Djukic D, Vujanovic B 1975 Acta Mech. 23 17
[3] Li Z P 1981 Acta Phys. Sin. 30 1659 (in Chinese)[李子平 1981 30 1659]
[4] Liu D 1989 Acta Mech. Sin. 21 75 (in Chinese)[刘 端 1989 力学学报 21 75]
[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: 北京工业大学出版社)]
[6] 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)] 〖7] 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] Lutzky M 1979 J. Phys. A 12 973
[8] Zhao Y Y 1994 Acta Mech. Sin. 26 380 (in Chinese)[赵跃宇 1994 力学学报 26 380]
[9] Mei F X 2000 Acta Mech. 141 135
[10] Mei F X 2000 J. Beijing Inst. Techn. 9 120
[11] Wang S Y, Mei F X 2002 Chin. Phys. 11 5
[12] Mei F X, Xie J F, Gang T Q 2008 Acta Mech. Sin. 24 583 (in Chinese)[梅凤翔、 解加芳、 冮铁强 2008 24 583]
[13] Mei F X, Gang T Q, Xie J F 2006 Chin. Phys. 15 1678
[14] Ge W K, Mei F X 2009 Acta Phys. Sin. 58 699(in Chinese)[葛伟宽、 梅凤翔 2009 58 699]
[15] Mei F X, Cai J L 2008 Acta Phys. Sin. 57 4657 (in Chinese)[梅凤翔、 蔡建乐 2008 57 4657]
[16] Mei F X, Zhang Y F, He G, Gang T Q, Xie J F 2007 J. Beijing Inst. Techn. 27 1035 (in Chinese)[梅凤翔、 张永发、 何 光、 冮铁强、 解加芳 2007 北京理工大学学报 27 1035]
[17] Mei F X 1993 Sci. China 36 1456
[18] Mei F X, Shang M 2009 Chin. Phys. B 18 3155
[19] Zhang Y 2008 Chin. Phys. B 17 4365
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[1] Noether A E 1918 Nachr Akad. Wiss Gttingen Math. Phys. 1 235
[2] Djukic D, Vujanovic B 1975 Acta Mech. 23 17
[3] Li Z P 1981 Acta Phys. Sin. 30 1659 (in Chinese)[李子平 1981 30 1659]
[4] Liu D 1989 Acta Mech. Sin. 21 75 (in Chinese)[刘 端 1989 力学学报 21 75]
[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: 北京工业大学出版社)]
[6] 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)] 〖7] 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] Lutzky M 1979 J. Phys. A 12 973
[8] Zhao Y Y 1994 Acta Mech. Sin. 26 380 (in Chinese)[赵跃宇 1994 力学学报 26 380]
[9] Mei F X 2000 Acta Mech. 141 135
[10] Mei F X 2000 J. Beijing Inst. Techn. 9 120
[11] Wang S Y, Mei F X 2002 Chin. Phys. 11 5
[12] Mei F X, Xie J F, Gang T Q 2008 Acta Mech. Sin. 24 583 (in Chinese)[梅凤翔、 解加芳、 冮铁强 2008 24 583]
[13] Mei F X, Gang T Q, Xie J F 2006 Chin. Phys. 15 1678
[14] Ge W K, Mei F X 2009 Acta Phys. Sin. 58 699(in Chinese)[葛伟宽、 梅凤翔 2009 58 699]
[15] Mei F X, Cai J L 2008 Acta Phys. Sin. 57 4657 (in Chinese)[梅凤翔、 蔡建乐 2008 57 4657]
[16] Mei F X, Zhang Y F, He G, Gang T Q, Xie J F 2007 J. Beijing Inst. Techn. 27 1035 (in Chinese)[梅凤翔、 张永发、 何 光、 冮铁强、 解加芳 2007 北京理工大学学报 27 1035]
[17] Mei F X 1993 Sci. China 36 1456
[18] Mei F X, Shang M 2009 Chin. Phys. B 18 3155
[19] Zhang Y 2008 Chin. Phys. B 17 4365
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