El-Nabulsi动力学模型下非Chetaev型非完整系统的精确不变量与绝热不变量

陈菊; 张毅

doi:10.7498/aps.64.034502

摘要

研究El-Nabulsi动力学模型下非Chetaev型非完整系统精确不变量与绝热不变量问题. 首先, 导出El-Nabulsi-d'Alembert-Lagrange原理并建立系统的运动微分方程. 其次, 建立El-Nabulsi模型下未受扰动的非Chetaev 型非完整系统的Noether对称性与Noether对称性导致的精确不变量之间的关系; 再次, 引入力学系统的绝热不变量概念, 研究受小扰动作用下非Chetaev型非完整系统Noether对称性的摄动导致绝热不变量问题, 给出了绝热不变量存在的条件及其形式. 作为特例, 本文讨论了El-Nabulsi模型下Chetaev型非完整系统的精确不变量与绝热不变量问题. 最后分别给出非Chetaev型和Chetaev型两种约束下的算例以说明结果的应用.

关键词:

Abstract

In this paper, the problem of exact invariants and adiabatic invariants for nonholonomic system in non-Chetaev's type based on the El-Nabulsi dynamical model is studied. First, the El-Nabulsi-d'Alembert-Lagrange principle is deduced and the differential equations of motion of the system are established. Then, the relation between the Noether symmetry and the exact invariant that is led directly by the symmetry for undisturbed nonholonomic system in non-Chetaev's type is given. Furthermore, by introducing the concept of high-order adiabatic invariant of a mechanical system, the conditions that the perturbation of symmetry leads to the adiabatic invariant and its formulation are studied for the nonholonomic system in non-Chetaev's type under the action of small disturbance. As a special case, the problem of the exact invariants and the adiabatic invariants for the nonholonomic system in Chetaev's type in El-Nabulsi model is discussed. At the end of the paper, two examples for the nonholonomic systems in non-Chetaev's type constraints and also the Chetaev's type constraints are given respectively to show the application of the methods and the results of this paper.

Keywords:

作者及机构信息

陈菊¹,
张毅²

1.
苏州科技学院数理学院, 苏州 215009;

2.
苏州科技学院土木工程学院, 苏州 215011

基金项目: 国家自然科学基金(批准号: 10972151, 11272227), 江苏省普通高级研究生科研创新计划(批准号: CXLX13_855) 和苏州科技学院研究生科研创新计划(批准号: SKCX13S_050)资助的课题.

Authors and contacts

Chen Ju¹,
Zhang Yi²

1.
College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;

2.
College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos.10972151, 11272227), the Scientific Research and Innovation Program for the Graduate Students in Institution of Higher Education of Jiangsu Province, China (Grant No. CXLX13-855), and the Scientific Research and Innovation Program for the Graduate Students of Suzhou University of Science and Technology, China (Grant No. SKCX13S-050).

参考文献

[1]	Mei F X 1987 Researches on Nonholonomic Dynamics (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔1987非完整动力学研究(北京: 北京工业学院出版社)]
[2]	Bugers J M 1917 Ann. Phys. 357 195
[3]	Djuki D S 1981 Int. J. Non-Linear Mech. 16 489
[4]	Bulanov S V, Shasharina S G 1992 Nucl. Fusion 32 1531
[5]	Notte J, Fajans J, Chu R, Wurtele J S 1993 Phys. Rev. Lett. 70 3900
[6]	Zhao Y Y, Mei F X 1999 Symmetries and Invariants of Mechanical Systems (Beijing: Science Press) p164 (in Chinese) [赵跃宇, 梅凤翔1999力学系统的对称性与守恒量(北京: 科学出版社)第164页]
[7]	Zhao Y Y, Mei F X 1996 Acta Mech. Sin. 28 207 (in Chinese) [赵跃宇, 梅凤翔 1996 力学学报 28 207]
[8]	Chen X W, Wang X M, Wang M Q 2004 Chin. Phys. 13 2003
[9]	Fu J L, Chen L Q 2004 Phys. Lett. A 324 95
[10]	Qiao Y F, Li R J, Sun D N 2005 Chin. Phys. 14 1919
[11]	Chen X W, Li Y M 2005 Chin. Phys. 14 663
[12]	Chen X W, Liu C M, Li Y M 2006 Chin. Phys. 15 470
[13]	Luo S K, Chen X W, Guo Y X 2007 Chin. Phys. 16 3176
[14]	Luo S k, Guo Y X 2007 Commun. Theor. Phys. 47 25
[15]	Ding N, Fang J H 2009 Acta Phys. Sin. 58 7440 (in Chinese) [丁宁, 方建会 2009 物理学报 58 7440]
[16]	El-Nabulsi A R 2005 Fizika A 14 289
[17]	El-Nabulsi A R 2005 Int. J. Appl. Math. 17 299
[18]	El-Nabulsi A R and Torres D F M 2008 J. Math. Phys. 49 053521
[19]	El-Nabuls A R 2007 Math. Methods Appl. Sci. 30 1931
[20]	El-Nabulsi A R 2009 Chaos Sol. Fract. 42 52
[21]	El-Nabulsi A R, Dzenite A I, Torres D F M 2006 Bound Field Compu. Simu. 48 189
[22]	El-Nabulsi A R 2013 Qual. Theory Dyn. Syst. 12 273
[23]	El-Nabulsi A R 2007 Rom. J. Phys. 52 705
[24]	El-Nabulsi A R 2007 Rom. Rep. Phys. 59 759
[25]	Zhang Y 2013 Acta Phys. Sin. 62 164501 (in Chinese) [张毅 2013 物理学报 62 164501]
[26]	Chen J, Zhang Y 2014 Acta Phys. Sin. 63 104501 (in Chinese) [陈菊, 张毅 2014 物理学报 63 104501]
[27]	Chen J, Zhang Y 2014 Nonlinear Dyn. 77 353
[28]	Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔1985非完整系统力学基础(北京: 北京工业学院出版社)]
[29]	Mei F X, Wu H B 2009 Dynamics of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press)

施引文献

[1]	Mei F X 1987 Researches on Nonholonomic Dynamics (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔1987非完整动力学研究(北京: 北京工业学院出版社)]
[2]	Bugers J M 1917 Ann. Phys. 357 195
[3]	Djuki D S 1981 Int. J. Non-Linear Mech. 16 489
[4]	Bulanov S V, Shasharina S G 1992 Nucl. Fusion 32 1531
[5]	Notte J, Fajans J, Chu R, Wurtele J S 1993 Phys. Rev. Lett. 70 3900
[6]	Zhao Y Y, Mei F X 1999 Symmetries and Invariants of Mechanical Systems (Beijing: Science Press) p164 (in Chinese) [赵跃宇, 梅凤翔1999力学系统的对称性与守恒量(北京: 科学出版社)第164页]
[7]	Zhao Y Y, Mei F X 1996 Acta Mech. Sin. 28 207 (in Chinese) [赵跃宇, 梅凤翔 1996 力学学报 28 207]
[8]	Chen X W, Wang X M, Wang M Q 2004 Chin. Phys. 13 2003
[9]	Fu J L, Chen L Q 2004 Phys. Lett. A 324 95
[10]	Qiao Y F, Li R J, Sun D N 2005 Chin. Phys. 14 1919
[11]	Chen X W, Li Y M 2005 Chin. Phys. 14 663
[12]	Chen X W, Liu C M, Li Y M 2006 Chin. Phys. 15 470
[13]	Luo S K, Chen X W, Guo Y X 2007 Chin. Phys. 16 3176
[14]	Luo S k, Guo Y X 2007 Commun. Theor. Phys. 47 25
[15]	Ding N, Fang J H 2009 Acta Phys. Sin. 58 7440 (in Chinese) [丁宁, 方建会 2009 物理学报 58 7440]
[16]	El-Nabulsi A R 2005 Fizika A 14 289
[17]	El-Nabulsi A R 2005 Int. J. Appl. Math. 17 299
[18]	El-Nabulsi A R and Torres D F M 2008 J. Math. Phys. 49 053521
[19]	El-Nabuls A R 2007 Math. Methods Appl. Sci. 30 1931
[20]	El-Nabulsi A R 2009 Chaos Sol. Fract. 42 52
[21]	El-Nabulsi A R, Dzenite A I, Torres D F M 2006 Bound Field Compu. Simu. 48 189
[22]	El-Nabulsi A R 2013 Qual. Theory Dyn. Syst. 12 273
[23]	El-Nabulsi A R 2007 Rom. J. Phys. 52 705
[24]	El-Nabulsi A R 2007 Rom. Rep. Phys. 59 759
[25]	Zhang Y 2013 Acta Phys. Sin. 62 164501 (in Chinese) [张毅 2013 物理学报 62 164501]
[26]	Chen J, Zhang Y 2014 Acta Phys. Sin. 63 104501 (in Chinese) [陈菊, 张毅 2014 物理学报 63 104501]
[27]	Chen J, Zhang Y 2014 Nonlinear Dyn. 77 353
[28]	Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔1985非完整系统力学基础(北京: 北京工业学院出版社)]
[29]	Mei F X, Wu H B 2009 Dynamics of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press)

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