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## 留言板

Unified symmetry and conserved quantities of Nielsen equation for a holonomic mechanical system

## Unified symmetry and conserved quantities of Nielsen equation for a holonomic mechanical system

Xia Li-Li, Li Yuan-Cheng, Wang Xiao-Ming
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• #### Abstract

The unified symmetry and conserved quantities of Nielsen equation for a holonomic mechanical system are studied. On the base of the Nielsen equation, we first give the Noether symmetry, the Lie symmetry and the Mei symmetry for the equation and the conserved quantities deduced from them, then the definition and the criterion for unified symmetry of Nielsen equation are presented, lastly, the Mei conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity deduced from the unified symmetry are obtained. An example is given to illustrate the application of the result.

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#### References

 [1] ［1］Noether A E 1918 Nachr. Akad. Wiss. Gttingen. Math. Phys. KI 235 [2] ［2］Mei F X, Liu D and Luo Y 1991 Advanced Analytical Mechanics(Beijing: Beijing Institute of Technology Press)(in Chinese)［梅凤翔、刘端、罗勇1991高等分析力学(北京：北京理工大学出版社)］ [3] ［3］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)］ [4] ［4］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)］ [5] ［5］Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanics 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] ［6］Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) (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)］ [7] ［7Hojman S A 1992 J. Phys.A:Math. Gen. 25 L291 [8] ［8］Mei F X 2000 J. Beijing Institute of Technology 9 120 [9] ［9］Mei F X, Shang M 2000 Acta Phys. Sin. 49 1901(in Chinese)［梅凤翔、尚玫 2000 物理学报 49 1901］ [10] ］Mei F X, Xu X J , Zhang Y F 2004 Acta Mech. Sin. 20 668 [11] ］Wang S Y, Mei F X 2001 Chin. Phys. 10 373 [12] ］Qiao Y F, Zhao S H, Li R J 2004 Chin. Phys. 13 292 [13] ］Xu X J, Mei F X, Qin M C 2004 Acta Phys. Sin. 53 4021(in Chinese) ［许学军、梅凤翔、秦茂昌2004 物理学报 53 4021］ [14] ］Fang J H, Xue Q Z, Zhao S Q 2002 Acta Phys. Sin. 51 2183(in Chinese) ［方建会、薛庆忠、赵嵩卿 2002 物理学报 51 2183］ [15] ］Zhang J, Fang J H, Chen P S 2005 Acta Armamentarii 26 228(in Chinese) ［张军、方建会、陈培胜2005 兵工学报 26 228］ [16] ］Hu C L, Xie J F 2007 J.Hulunbeier Coollege 15 83(in Chinese) ［胡楚勒、解加芳 2007 呼伦贝尔学院学报15 83］ [17] ］Jia L Q, Luo S K, Zhang Y Y 2008 Acta Phys.Sin. 57 2006 (in Chinese)［贾利群、罗绍凯、张耀宇 2008 物理学报 57 2006］ [18] ］Jia L Q, Zhang Y Y, Luo S K, Cui J C 2009 Acta Phys.Sin. 58 2141 (in Chinese)［贾利群、张耀宇、罗绍凯、崔金超 2009 物理学报 58 2141］ [19] ］Cui J C, Zhang Y Y, Jia L Q 2009 Chin. Phys B 18 1731 [20] ］Cui J C，Jia L Q and Zhang Y Y 2009 Commun. Theor. Phys. 52 7 [21] ］Mei F X1984 Acta Mech. Sin. 16 596 (in Chinese )［梅凤翔 1984力学学报 16 596］

#### Cited By

•  [1] ［1］Noether A E 1918 Nachr. Akad. Wiss. Gttingen. Math. Phys. KI 235 [2] ［2］Mei F X, Liu D and Luo Y 1991 Advanced Analytical Mechanics(Beijing: Beijing Institute of Technology Press)(in Chinese)［梅凤翔、刘端、罗勇1991高等分析力学(北京：北京理工大学出版社)］ [3] ［3］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)］ [4] ［4］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)］ [5] ［5］Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanics 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] ［6］Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) (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)］ [7] ［7Hojman S A 1992 J. Phys.A:Math. Gen. 25 L291 [8] ［8］Mei F X 2000 J. Beijing Institute of Technology 9 120 [9] ［9］Mei F X, Shang M 2000 Acta Phys. Sin. 49 1901(in Chinese)［梅凤翔、尚玫 2000 物理学报 49 1901］ [10] ］Mei F X, Xu X J , Zhang Y F 2004 Acta Mech. Sin. 20 668 [11] ］Wang S Y, Mei F X 2001 Chin. Phys. 10 373 [12] ］Qiao Y F, Zhao S H, Li R J 2004 Chin. Phys. 13 292 [13] ］Xu X J, Mei F X, Qin M C 2004 Acta Phys. Sin. 53 4021(in Chinese) ［许学军、梅凤翔、秦茂昌2004 物理学报 53 4021］ [14] ］Fang J H, Xue Q Z, Zhao S Q 2002 Acta Phys. Sin. 51 2183(in Chinese) ［方建会、薛庆忠、赵嵩卿 2002 物理学报 51 2183］ [15] ］Zhang J, Fang J H, Chen P S 2005 Acta Armamentarii 26 228(in Chinese) ［张军、方建会、陈培胜2005 兵工学报 26 228］ [16] ］Hu C L, Xie J F 2007 J.Hulunbeier Coollege 15 83(in Chinese) ［胡楚勒、解加芳 2007 呼伦贝尔学院学报15 83］ [17] ］Jia L Q, Luo S K, Zhang Y Y 2008 Acta Phys.Sin. 57 2006 (in Chinese)［贾利群、罗绍凯、张耀宇 2008 物理学报 57 2006］ [18] ］Jia L Q, Zhang Y Y, Luo S K, Cui J C 2009 Acta Phys.Sin. 58 2141 (in Chinese)［贾利群、张耀宇、罗绍凯、崔金超 2009 物理学报 58 2141］ [19] ］Cui J C, Zhang Y Y, Jia L Q 2009 Chin. Phys B 18 1731 [20] ］Cui J C，Jia L Q and Zhang Y Y 2009 Commun. Theor. Phys. 52 7 [21] ］Mei F X1984 Acta Mech. Sin. 16 596 (in Chinese )［梅凤翔 1984力学学报 16 596］
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•  Citation:
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• Abstract views:  3000
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##### Publishing process
• Received Date:  07 August 2009
• Accepted Date:  27 August 2009
• Published Online:  15 May 2010

## Unified symmetry and conserved quantities of Nielsen equation for a holonomic mechanical system

• 1. (1)河南教育学院物理系,郑州 450046; (2)中国石油大学(华东)物理科学与技术学院,青岛 266555

Abstract: The unified symmetry and conserved quantities of Nielsen equation for a holonomic mechanical system are studied. On the base of the Nielsen equation, we first give the Noether symmetry, the Lie symmetry and the Mei symmetry for the equation and the conserved quantities deduced from them, then the definition and the criterion for unified symmetry of Nielsen equation are presented, lastly, the Mei conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity deduced from the unified symmetry are obtained. An example is given to illustrate the application of the result.

Reference (21)

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