Open AccessThe study of symmetries and conserved quantities for one class of linearly coupled multidimensional freedom systems
Author(s) -
Lou Zhi-Mei
Publication year - 2007
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.56.2475
Subject(s) - conserved quantity , noether's theorem , log polar coordinates , homogeneous space , symmetry (geometry) , infinitesimal , action angle coordinates , generalized coordinates , orthogonal coordinates , bipolar coordinates , class (philosophy) , physics , lagrangian and eulerian specification of the flow field , degrees of freedom (physics and chemistry) , coordinate system , classical mechanics , conserved current , inverse , mathematical physics , spherical coordinate system , lagrangian , mathematical analysis , mathematics , computer science , quantum mechanics , geometry , artificial intelligence , eulerian path
In this paper, we eliminate the coupled terms in Lagrangian firstly by changing the coordinate scales and rotating the coordinate axes, and obtain the conserved quantities in new coordinates directly. According inverse transform of the coordinates, we can obtain the conserved quantities in original coordinates, the Noether symmetry and Lie symmetry of the infinitesimal transformations of conserve quantities are studied in this paperand an example is given to illustrate the application of the result.