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The Hojman method for construction of the Birkhoffian representation is discussed. By using Hojman method, the Birkhoff symmetry is restudied. A new idea of this symmetry is presented. A new proof of the Birkhoff conserved quantity is given. It is shown that the Birkhoff symmetry depends only on the Birkhoff tensors. An example is given to show the application of the result.
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Keywords:
- Birkhoffian system /
- symmetry /
- conserved quantity /
- Hojman method
[1] ［1］Santilli R M 1983 Foundations of Theoretical Mechanics (Ⅱ) (New York: Springer-Verlag)
[2] ［2］Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoffian System (Beijing: Beijing Institute of Technology Press) (in Chinese) ［梅凤翔、史荣昌、张永发、吴惠彬 1996 Birkhoff系统动力学 （北京：北京理工大学出版社）］
[3] ［3］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）］
[4] ［4］Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) pp288—415 (in Chinese) ［罗绍凯、张永发 2008 约束系统动力学研究进展（北京：科学出版社） 第288—415页］
[5] ［5］Mei F X, Gang T Q, Xie J F 2006 Chin. Phys. 15 1678
[6] ［6］Mei F X 2009 Adv. Mech. 39 37 (in Chinese) ［梅凤翔 2009 力学进展 39 37］
[7] ［7］Mei F X 1993 Sci. China A 36 1456
[8] ［8］Zhang Y 2002 Acta Phys. Sin. 51 461 (in Chinese) ［张毅 2002 51 461］
[9] ［9］Gu S L, Zhang H B 2004 Chin. Phys. 13 979
[10] ］Zhang R C, Chen X W, Mei F X 2001 Chin. Phys. 10 12
[11] ］Xu X J, Mei F X, Qin M C 2004 Chin. Phys. 13 1999
[12] ］Zhang Y 2002 Chin. Phys. 11 437
[13] ］Hojman S, Urrutia L F 1981 J. Math. Phys. 22 1986
[14] ］Ding G T 2008 Acta Phys. Sin. 57 7415 (in Chinese) ［丁光涛 2008 57 7415］
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[1] ［1］Santilli R M 1983 Foundations of Theoretical Mechanics (Ⅱ) (New York: Springer-Verlag)
[2] ［2］Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoffian System (Beijing: Beijing Institute of Technology Press) (in Chinese) ［梅凤翔、史荣昌、张永发、吴惠彬 1996 Birkhoff系统动力学 （北京：北京理工大学出版社）］
[3] ［3］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）］
[4] ［4］Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) pp288—415 (in Chinese) ［罗绍凯、张永发 2008 约束系统动力学研究进展（北京：科学出版社） 第288—415页］
[5] ［5］Mei F X, Gang T Q, Xie J F 2006 Chin. Phys. 15 1678
[6] ［6］Mei F X 2009 Adv. Mech. 39 37 (in Chinese) ［梅凤翔 2009 力学进展 39 37］
[7] ［7］Mei F X 1993 Sci. China A 36 1456
[8] ［8］Zhang Y 2002 Acta Phys. Sin. 51 461 (in Chinese) ［张毅 2002 51 461］
[9] ［9］Gu S L, Zhang H B 2004 Chin. Phys. 13 979
[10] ］Zhang R C, Chen X W, Mei F X 2001 Chin. Phys. 10 12
[11] ］Xu X J, Mei F X, Qin M C 2004 Chin. Phys. 13 1999
[12] ］Zhang Y 2002 Chin. Phys. 11 437
[13] ］Hojman S, Urrutia L F 1981 J. Math. Phys. 22 1986
[14] ］Ding G T 2008 Acta Phys. Sin. 57 7415 (in Chinese) ［丁光涛 2008 57 7415］
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