A NEW PERTURBATIVE APPROACH TO THE CLASSICAL ANHARMONIC-OSCILLATOR

The periodic motion of the classical anharmonic oscillator characteriz ed by the potential V(x) = 1/2 x(2) + lambda/2k x(2k) is considered. T he period is first determined to all orders in lambda in a perturbativ e series. Making use of this, the solution of the nonlinear equation o f motion is then expressed in the form of a Fourier series. The Fourie r coefficients are obtained by solving simple algebraic relations. Sec ular terms are inherently absent in this perturbative scheme. Explicit solution is presented for general k up to the second order, from whic h the Duffing and the sextic oscillator results follow as special case s.