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[1] Zhang Yi,. Symmetries and conserved quantitiesof generalized Birkhoffian systems [J]. Journal of Southeast University (English Edition), 2010, 26 (1): 146-150. [doi:10.3969/j.issn.1003-7985.2010.01030]
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Symmetries and conserved quantitiesof generalized Birkhoffian systems()
广义Birkhoff系统的对称性与守恒量
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
26
Issue:
2010 1
Page:
146-150
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2010-03-30

Info

Title:
Symmetries and conserved quantitiesof generalized Birkhoffian systems
广义Birkhoff系统的对称性与守恒量
Author(s):
Zhang Yi
College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China
张毅
苏州科技学院土木工程学院, 苏州 215011
Keywords:
generalized Birkhoffian system symmetry conserved quantity
广义Birkhoff系统 对称性 守恒量
PACS:
O316
DOI:
10.3969/j.issn.1003-7985.2010.01030
Abstract:
Three kinds of symmetries and their corresponding conserved quantities of a generalized Birkhoffian system are studied. First, by using the invariance of the Pfaffian action under the infinitesimal transformations, the Noether theory of the generalized Birkhoffian system is established. Secondly, on the basis of the invariance of differential equations under infinitesimal transformations, the definition and the criterion of the Lie symmetry of the generalized Birkhoffian system are established, and the Hojman conserved quantity directly derived from the Lie symmetry of the system is given. Finally, by using the invariance that the dynamical functions in the differential equations of the motion of mechanical systems still satisfy the equations after undergoing the infinitesimal transformations, the definition and the criterion of the Mei symmetry of the generalized Birkhoffian system are presented, and the Mei conserved quantity directly derived from the Mei symmetry of the system is obtained. Some examples are given to illustrate the application of the results.
研究了广义Birkhoff系统的3种对称性及其相应的守恒量. 首先, 基于Pfaffian作用量在无限小变换下的不变性, 建立了广义Birkhoff系统的Noether理论; 其次, 基于微分方程在无限小变换下的不变性, 建立了广义Birkhoff系统的Lie对称性的定义和判据, 给出了由系统的Lie对称性直接导致的Hojman守恒量; 最后, 基于力学系统运动微分方程中出现的动力学函数在经历无限小变换后仍然满足原来方程的一种不变性, 建立了广义Birkhoff系统的Mei对称性的定义和判据, 给出了由系统的Mei对称性直接导致的Mei守恒量. 举例说明了结果的应用.

References:

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Memo

Memo:
Biography: Zhang Yi(1964—), male, doctor, professor, weidiezh@pub.sz.jsinfo.net.
Foundation items: The National Natural Science Foundation of China(No.10972151), the Natural Science Foundation of Higher Education Institution of Jiangsu Province of China(No.08KJB130002).
Citation: Zhang Yi. Symmetries and conserved quantities of generalized Birkhoffian systems[J]. Journal of Southeast University(English Edition), 2010, 26(1): 146-150.
Last Update: 2010-03-20