Click here to view fulltext PDF

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

Classical AHO; secular term-free perturbative solution

The periodic motion of the classical anharmonic oscillator characterized by the potentialV(x)=1/2x²+λ/2k x^2k 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.

S S Vasan¹ M Seetharaman¹

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

Published

December 1994

Manuscript received

8 July 1994