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研究了完整系统Appell方程的Lie-Mei对称性与守恒量.在完整系统Appell方程的基础上,给出了Appell方程的Lie-Mei对称性的定义和判据,得到了Appell方程的Lie-Mei对称性导致的Hojman守恒量和Mei守恒量.举例说明结果的应用.
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关键词:
- 完整系统 /
- Appell方程 /
- Lie-Mei对称性 /
- 守恒量
The Lie-Mei symmetry and conserved quantities of Appell equation for a holonomic mechanical system are studied. On the basis of the Appell equation, we first obtain the Lie symmetry and the Mei symmetry for the equation and the conserved quantities deduced from them, then the definition and the criterion for Lie-Mei symmetry of Appell equation are presented. Lastly, the Mei conserved quantity and the Hojman conserved quantity are deduced from the Lie-Mei symmetry. An example is given to illustrate the application of the result.-
Keywords:
- holonomic mechanical system /
- Appell equation /
- Lie-Mei symmetry /
- conserved quantity
[1] ［1］Appell P 1899 C. R. Acad. Sci. Paris 129 317
[2] ［2］Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems (Beijing: Beijing Institute of Technology Press) p214 (in Chinese) ［梅凤翔 1985 非完整力学基础 （北京：北京工业学院出版社）第214页］
[3] ［3］Mei F X, Liu D， Luo Y 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press) p131 (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) 第131页］
[4] ［4］Xue W X 1987 Acta Mech. Sin. 19 156 (in Chinese) ［薛问西 1987 力学学报 19 156］
[5] ［5］Yuan S J， Mei F X 1987 Acta Mech. Sin. 19 165 (in Chinese) ［袁士杰、梅凤翔 1987 力学学报19 165］
[6] ［6］Luo S K 1996 Appl. Math. Mech. 17 683
[7] ［7］Luo S K 1998 Appl. Math. Mech. 19 43
[8] ［8］Noether A E 1918 Nachr. Akad. Wiss. Gttingen. Math. Phys. KI 235
[9] ［9］Li Z P 1993 Classical and Quantal Dynamics of Constrained Systems and Their Symmetrical Properties (Beijing: Beijing Polytechnic University Press) pp1—52 (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) 第1—52页］
[10] ］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)］
[11] ］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)］
[12] ］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］
[13] ］Hojman S A 1992 J. Phys. A 25 L291
[14] ］Mei F X 2000 J. Beijing Inst. Techn. 9 120
[15] ］Mei F X， Shang M 2000 Acta Phys. Sin. 49 1901 (in Chinese) ［梅凤翔、尚玫 2000 49 1901］
[16] ］Mei F X, Xu X J, Zhang Y F 2004 Acta Mech. Sin. 20 668
[17] ］Wang S Y, Mei F X 2001 Chin. Phys. 10 373
[18] ］Qiao Y F, Zhao S H, Li R J 2004 Chin. Phys. 13 292
[19] ］Mei F X 2001 Chin. Phys. 10 177
[20] ］Luo S K 2002 J. Changsha Univ. 16 1 (in Chinese) ［罗绍凯 2002 长沙大学学报 16 1］
[21] ］Li R J, Qiao Y F, Meng J 2002 Acta Phys. Sin. 51 1 (in Chinese) ［李仁杰、乔永芬、孟军 2002 51 1］
[22] ］Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese) ［罗绍凯 2002 51 712］
[23] ］Zhang Y Y, Jia L Q, Zheng S W 2007 J. Henan Normal Univ. 35 77 (in Chinese) ［张耀宇、贾利群、郑世旺 2007 河南师范大学学报 35 77］
[24] ］Jia L Q, Zhang Y Y, Zheng S W 2007 J. Yunnan Univ. 29 589 (in Chinese)［贾利群、张耀宇、郑世旺 2007 云南大学学报 29 589］
[25] ］Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16 (in Chinese) ［贾利群、崔金超、张耀宇、罗绍凯 2009 58 16］
[26] ］Jia L Q, Zhang Y Y, Cui J C 2009 J. Yunnan Univ. 31 52 ［贾利群、张耀宇、崔金超 2009 云南大学学报 31 52］
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[1] ［1］Appell P 1899 C. R. Acad. Sci. Paris 129 317
[2] ［2］Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems (Beijing: Beijing Institute of Technology Press) p214 (in Chinese) ［梅凤翔 1985 非完整力学基础 （北京：北京工业学院出版社）第214页］
[3] ［3］Mei F X, Liu D， Luo Y 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press) p131 (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) 第131页］
[4] ［4］Xue W X 1987 Acta Mech. Sin. 19 156 (in Chinese) ［薛问西 1987 力学学报 19 156］
[5] ［5］Yuan S J， Mei F X 1987 Acta Mech. Sin. 19 165 (in Chinese) ［袁士杰、梅凤翔 1987 力学学报19 165］
[6] ［6］Luo S K 1996 Appl. Math. Mech. 17 683
[7] ［7］Luo S K 1998 Appl. Math. Mech. 19 43
[8] ［8］Noether A E 1918 Nachr. Akad. Wiss. Gttingen. Math. Phys. KI 235
[9] ［9］Li Z P 1993 Classical and Quantal Dynamics of Constrained Systems and Their Symmetrical Properties (Beijing: Beijing Polytechnic University Press) pp1—52 (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) 第1—52页］
[10] ］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)］
[11] ］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)］
[12] ］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］
[13] ］Hojman S A 1992 J. Phys. A 25 L291
[14] ］Mei F X 2000 J. Beijing Inst. Techn. 9 120
[15] ］Mei F X， Shang M 2000 Acta Phys. Sin. 49 1901 (in Chinese) ［梅凤翔、尚玫 2000 49 1901］
[16] ］Mei F X, Xu X J, Zhang Y F 2004 Acta Mech. Sin. 20 668
[17] ］Wang S Y, Mei F X 2001 Chin. Phys. 10 373
[18] ］Qiao Y F, Zhao S H, Li R J 2004 Chin. Phys. 13 292
[19] ］Mei F X 2001 Chin. Phys. 10 177
[20] ］Luo S K 2002 J. Changsha Univ. 16 1 (in Chinese) ［罗绍凯 2002 长沙大学学报 16 1］
[21] ］Li R J, Qiao Y F, Meng J 2002 Acta Phys. Sin. 51 1 (in Chinese) ［李仁杰、乔永芬、孟军 2002 51 1］
[22] ］Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese) ［罗绍凯 2002 51 712］
[23] ］Zhang Y Y, Jia L Q, Zheng S W 2007 J. Henan Normal Univ. 35 77 (in Chinese) ［张耀宇、贾利群、郑世旺 2007 河南师范大学学报 35 77］
[24] ］Jia L Q, Zhang Y Y, Zheng S W 2007 J. Yunnan Univ. 29 589 (in Chinese)［贾利群、张耀宇、郑世旺 2007 云南大学学报 29 589］
[25] ］Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16 (in Chinese) ［贾利群、崔金超、张耀宇、罗绍凯 2009 58 16］
[26] ］Jia L Q, Zhang Y Y, Cui J C 2009 J. Yunnan Univ. 31 52 ［贾利群、张耀宇、崔金超 2009 云南大学学报 31 52］
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