Open AccessThe third independent conserved quantity and its symmetry of the two-dimensional anisotropic harmonic oscillator
Author(s) -
Lou Zhi-Mei,
Mei Feng-Xiang
Publication year - 2012
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.61.110201
Subject(s) - noether's theorem , conserved quantity , harmonic oscillator , symmetry (geometry) , physics , anisotropy , conserved current , homogeneous space , harmonic , classical mechanics , quantum mechanics , mathematical physics , mathematics , lagrangian , geometry
The energy and the two partial energies of two-dimensional anisotropic harmonic oscillator are conserved quantities, but only two of them are independent. The system possesses the third independent conserved quantity when the 1/2 is a rational number. The extended Prelle-Singer method is used to find the third independent conserved quantity for the five typical two-dimensional anisotropic harmonic oscillators. The Noether symmetry and the Lie symmetry of the third independent conserved quantities are also discussed.