FOURIER COEFFICIENTS OF NONLINEAR OSCILLATORS

A method for the determination of the Fourier coefficients of the velo city curve of nonlinear (adiabatic) oscillators without performing the numerical integration of the momentum equation is presented. The meth od is applied to the study of the nonlinear adiabatic one-zone model o f pulsating stars (such as RR Lyrae stars), and the results are compar ed with those previously obtained by other authors with the applicatio n of numerical integration and Fourier decomposition. It is shown that the numerical integration and Fourier decomposition can give wrong Fo urier coefficients if the techniques are not carefully applied. Our me thod requires long computing time and high computing precision, theref ore it is advisable to use it just for checking independently the nume rical results. Some merits and defects of the application of the nonli near nonadiabatic one-zone model to the study of pulsating stars, RR L yrae and Cepheids, are briefly discussed. In particular, the possibili ty of reproducing the bump Cepheid light curves with this simple model is presented along with some hints on the interpretation of Cepheid p ulsation in terms of resonance between modes.