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On the first integrals of linear damped oscillators

Ding Guang-Tao

On the first integrals of linear damped oscillators

Ding Guang-Tao
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  • Received Date:  24 August 2012
  • Accepted Date:  23 September 2012
  • Published Online:  20 March 2013

On the first integrals of linear damped oscillators

  • 1. College of Physics and Electronic Information, Anhui Normal University, Wuhu 241000, China

Abstract: 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.

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