Open AccessOn the first integrals of linear damped oscillators
Author(s) -
Ding Guang-Tao
Publication year - 2013
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.62.064501
Subject(s) - harmonic oscillator , slater integrals , order of integration (calculus) , physics , transformation (genetics) , multiple integral , mathematical analysis , harmonic , mathematics , quantum mechanics , biochemistry , chemistry , gene
By introducing fundamental integrals of one-dimensional linear damped oscillators the other first integrals can be constructed, including time-irrelevant integrals. The above method is extended to multidimensional systems, in order to construct different integrals of two-dimensional and n-dimensional linear damped oscillators. It is proved that there are three independent time-irrelevant integrals for all kinds of two-dimensional linear damped oscillators, and 2n-1 independent time-irrelevant integrals for n-dimensional linear damped oscillators. Using the transformation of variables the first integrals of linear damped oscillator transform into ones of harmonic oscillator.