[1]顾书龙,计国君,张宏彬,等.受约束Vacco系统的几个Noether定理[J].东南大学学报(自然科学版),2004,34(3):418-422.[doi:10.3969/j.issn.1001-0505.2004.03.032]
 Gu Shulong,Ji Guojun,Zhang Hongbin,et al.Several Noether’s theorem of Vacco systems with constraints[J].Journal of Southeast University (Natural Science Edition),2004,34(3):418-422.[doi:10.3969/j.issn.1001-0505.2004.03.032]
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受约束Vacco系统的几个Noether定理()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
34
期数:
2004年第3期
页码:
418-422
栏目:
数学、物理学、力学
出版日期:
2004-05-20

文章信息/Info

Title:
Several Noether’s theorem of Vacco systems with constraints
作者:
顾书龙1 计国君2 张宏彬3 刘东生1
1 巢湖学院物理系, 巢湖 238000; 2 厦门大学管理学院, 厦门 361005; 3 上海大学应用数学和力学研究所, 上海 200072
Author(s):
Gu Shulong1 Ji Guojun2 Zhang Hongbin3 Liu Dongsheng1
1 Department of Physics, Chaohu College, Chaohu 238000, China
2 Management School, Xiamen University, Xiamen 361005, China
3 Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, Chi
关键词:
分析力学 单面约束Vacco系统 守恒量 对称性 Noether定理
Keywords:
analytical mechanics Vacco systems with unilateral constraints conserved quantity sym- metry Noether’s theorem
分类号:
O316
DOI:
10.3969/j.issn.1001-0505.2004.03.032
摘要:
研究受约束Vacco系统的Noether对称性.基于受约束Vacco系统在r-参数有限变换群Gr的无限小广义准对称变换下的不变性,给出了受单面约束的Vacco系统的Noether定理及其逆定理.受双面约束的Vacco系统的Neother定理为该定理的推论.最后给出一个算例说明了结果的应用.
Abstract:
The Neother symmetry for Vacco systems with constraints is studied. Noether’s theorem and its inverse theorem of Vacco systems with unilateral constraints are given, which are based upon the invariant properties by introducing the generalized quasi-symmetry of the infinitesimal transformation for the transformation group Gr of r-parameter. And Noether’s theorem dealing with the Vacco system of bilateral constraints is its corollary. An example to illustrate the application of the result is given.

参考文献/References:

[1] 张毅,梅凤翔.单面约束力学系统的Noether理论[J].应用数学和力学,2000,21(1):53-60.
  Zhang Yi,Mei Fengxiang.Noether’s theory of mechanical systems with unilateral constraints [J].Applied Mathematics and Mechanics, 2000,21(1):53-60.(in Chinese)
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[3] 陈立群.受高阶非完整约束系统的Vacco动力学方程[J].科学通报,1990,35(23):1836-1837.
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[4] 罗绍凯.非线性非完整系统Vacco动力学方程的积分方法[J].应用数学和力学,1995,16(11):981-988.
  Luo Shaokai.Vacco integral method of the nonlinear nonhonolomic dynamical systems [J].Applied Mathematics and Mecha-nics, 1995,16(11):981-988.(in Chinese)
[5] 梁立孚.非完整系统动力学中的Vakonomic模型和eTaeB模型 [J].力学进展,2000,30(3):385-387.
  Liang Lifu.The Vakonomic model and Chetaev model in analytical dynamics of nonholonomic systems [J].Advances in Mechanics, 2000,30(3):385-387.(in Chinese)
[6] Zhang Hongbin.Lie symmetries and conserved quantities of non-holonomic mechanical systems with unilateral Vacco constraints [J].Chinese Physics,2002,11(1):1-5.
[7] Zhang Hongbin,Gu Shulong.Lie symmetries and conserved quantities of Birkhoff systems with unilateral constraints[J]. Chinese Physics,2002,11(8):765-769.

相似文献/References:

[1]戴德成.分析力学中的非线性非完整约束[J].东南大学学报(自然科学版),1981,11(3):85.[doi:10.3969/j.issn.1001-0505.1981.03.011]
 Dai De-cheng.Nonlinear Nonholonomic Constraints in Analytical Mechanics[J].Journal of Southeast University (Natural Science Edition),1981,11(3):85.[doi:10.3969/j.issn.1001-0505.1981.03.011]

备注/Memo

备注/Memo:
基金项目: 安徽省高校自然科学基金资助项目(2002kj230, 2004kj294).
作者简介: 顾书龙(1958—),男,副教授, gsl2142@sohu.com.
更新日期/Last Update: 2004-05-20