Analytic exact solution of one-dimensional nonautonomous classical harmonic oscillator

Peng Wang, Shun Jin Wang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


One-dimensional time-dependent classical harmonic oscillator is a nonautonomous system with an SU(1,1) dynamical symmetry. By means of algebraic dynamics method, we have obtained its exact solution for the first time. As the time-dependent stiffness of the harmonic oscillator assumes some elementary functions, such as power functions, trigonal functions, exponential functions etc., the exact solutions become analytic. The recently proposed ' analytic approximation solution' is proved to be a good approximation to the corresponding analytic solution under some conditions.

Original languageEnglish
Pages (from-to)651-656
Number of pages6
JournalKao Neng Wu Li Yu Ho Wu Li/High Energy Physics and Nuclear Physics
Issue number7
StatePublished - Jul 2005
Externally publishedYes


  • Algebraic dynamics method
  • Analytic exact solution
  • SU(1,1) nonautonomous classical harmonic oscillator


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