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    • A new perturbative approach to the classical anharmonic oscillator

      S S Vasan M Seetharaman

      Volume 43 Issue 6 December 1994 pp 411-420

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/043/06/0411-0420

    • Keywords

       

      Classical AHO; secular term-free perturbative solution

    • Abstract

       

      The periodic motion of the classical anharmonic oscillator characterized by the potentialV(x)=1/2x2+λ/2k x2k is considered. The period is first determined to all orders inλ in a perturbative series. Making use of this, the solution of the nonlinear equation of motion is then expressed in the form of a Fourier series. The Fourier coefficients are obtained by solving simple algebraic relations. Secular terms are inherently absent in this perturbative scheme. Explicit solution is presented for generalk up to the second order, from which the Duffing and the sextic oscillator results follow as special cases.

    • Author Affiliations

       

      S S Vasan1 M Seetharaman1

      1. Department of Theoretical Physics, University of Madras, Guindy Campus, Madras - 600 025, India

    • Dates

       
      Published
      December 1994
      Manuscript received
      8 July 1994

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