Open AccessBirkhoff symmetries and conserved quantities of generalized Birkhoffian systems
Author(s) -
Yi Zhang
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.7436
Subject(s) - conserved quantity , invertible matrix , homogeneous space , mathematics , symmetry (geometry) , integer (computer science) , property (philosophy) , mathematical physics , matrix (chemical analysis) , pure mathematics , geometry , computer science , philosophy , materials science , epistemology , composite material , programming language
The problem of Birkhoff symmetry for generalized Birkhoffian systems is studied, and the corresponding conserved quantities are given. A theorem known for nonsingular equivalent Lagrangians is generalized to the generalized Birkhoffian systems. We prove that under certain conditions the matrix Λ, which is related with the generalized Birkhoffian equations obtained from two groups of dynamical functions B,Rμ,Λμ and B,Rμ,Λμ, has the property that the traces of all its integer powers are the conserved quantities of the system. An example is given to illustrate the application of the results.