[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()

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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

Author(s):

Zhang Yi

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

Keywords:

generalized Birkhoffian system;  symmetry;  conserved quantity

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.

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.

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