Open AccessMei’s symmetry theorems for non-migrated Birkhoffian systems on a time scale
Author(s) -
Yi Zhang
Publication year - 2021
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.70.20210372
Subject(s) - symmetry (geometry) , scale (ratio) , conserved quantity , dynamic equation , dynamical systems theory , mathematical physics , dynamical system (definition) , physics , mathematics , classical mechanics , geometry , quantum mechanics , nonlinear system
The Mei symmetry and its corresponding conserved quantities for non-migrated Birkhoffian systems on a time scale are proposed and studied. Firstly, the dynamic equations of non-migrated Birkhoffian systems (including free Birkhoffian systems, generalized Birkhoffian systems and constrained Birkhoffian systems) on a time scale are derived based on the time-scale Pfaff-Birkhoff principle and time-scale generalized Birkhoff principle. Secondly, based on the fact that the dynamical functions in the non-migrated Birkhoff’s equations still satisfy the original equations after they have been transformed, the definitions of Mei symmetry on an arbitrary time scale are given, and the corresponding criterion equations are derived. Thirdly, Mei’s symmetry theorems for non-migrated Birkhoffian systems on a time scales are established and proved, and Mei conserved quantities of Birkhoffian systems on a time scale are obtained. The results are illustrated by three examples.