Noether’s Theorem for Nonholonomic Systems of Non-Chetaev’s Type With Unilateral Constraints in Event Space

Li Yuancheng; Zhang Yi; Liang Jinghui

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Article Navigation > Applied Mathematics and Mechanics > 2000 > 21(5): 488-493

Li Yuancheng, Zhang Yi, Liang Jinghui. Noether’s Theorem for Nonholonomic Systems of Non-Chetaev’s Type With Unilateral Constraints in Event Space[J]. Applied Mathematics and Mechanics, 2000, 21(5): 488-493.

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Noether’s Theorem for Nonholonomic Systems of Non-Chetaev’s Type With Unilateral Constraints in Event Space

1.
Department of Applied Physics, University of Petroleum, Dongying, Shandong 257062, P. R. China;
2.
Suzhou Institute of Urban Construction and Environmental Protection, Suzhou 215011, P. R. China;
3.
Department of Physics, Shanxi Normal Univer sity, Linfen, Shanxi 041004, P. R. China

Received Date: 1999-04-23
Rev Recd Date: 2000-01-06
Publish Date: 2000-05-15

Abstract

Abstract

To study the Noether's theorem of nonholonomic systems of non-Chetaev's type with unilateral constraints in event space, firstly, the principle of D' Alembert-Lagrange for the systems with unilateral constraints in event space is presented, secondly, the Noether's theorem and the Noether's inverse theorem for the nonholonomic systems of non-Chetaev' s type with unilateral constraints in event space are studied and obtained, which is based upon the invariance of the differential variational principle under the infinitesimal transformations of group, finally, an example is given to illustrate the application of the result.
- analytical mechanics,
- event space,
- unilateral constraint,
- nonholonomic system,
- Noether’s theorem,
- Noeter’s inverse theorem

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References(9)

References

[1]	Noether A E.Invariante variationsprobleme[A].In:Nachr Akad Wiss Gettingen Math-Phys KⅠ,Ⅱ[C].1918,235～257.
[2]	Vujanovic B.Conservation laws of dynamical systems via D'Alembert's principle[J].Int J Non-Linear Mech,1978,13:185～197.
[3]	Vujanovic B.A study of conservation laws of dynamical systems by means of the differential principle of Jourdain and Gauss[J].Acta Mechanic a,1986,65:63～80.
[4]	刘端.非完整非保守动力学系统的守恒律[J].力学学报,1989,21(1):75～83.
[5]	刘端.非完整非保守动力学系统的Noether定理及其逆定理[J].中国科学,A辑,1990,20(11):1189～1197.
[6]	张解放.高阶非完整非保守系统的广义Noether定理[J].科学通报,1989,34(22):1756～1757.
[7]	梅凤翔.利用Jourdain原理研究二阶非完整系统的守恒律[J].北京理工大学学报,1998,18(1):17～21.
[8]	张毅.单面约束力学系统的基本理论研究[D].博士学位论文.北京:北京理工大学,1998.
[9]	李子平.经典和量子力学约束系统及其对称性质[M].北京:北京工业大学出版社,1993.