The third independent conserved quantity and its symmetry of the two-dimensional anisotropic harmonic oscillator | Zendy

Lou Zhi-Mei | Zendy; Mei Feng-Xiang | Zendy

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The 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 -

acta physica sinica

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.

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