FOURIER COEFFICIENTS OF NONLINEAR OSCILLATORS

A method for the determination of the Fourier coefficients of the velocity curve of nonlinear (adiabatic) oscillators without performing the numerical integration of the momentum equation is presented. The method is applied to the study of the nonlinear adiabatic one-zone model of pulsating stars (such as RR Lyrae stars), and the results are compared with those previously obtained by other authors with the application of numerical integration and Fourier decomposition. It is shown that the numerical integration and Fourier decomposition can give wrong Fourier coefficients if the techniques are not carefully applied. Our method requires long computing time and high computing precision, therefore it is advisable to use it just for checking independently the numerical results. Some merits and defects of the application of the nonlinear nonadiabatic one-zone model to the study of pulsating stars, RR Lyrae and Cepheids, are briefly discussed. In particular, the possibility of reproducing the bump Cepheid light curves with this simple model is presented along with some hints on the interpretation of Cepheid pulsation in terms of resonance between modes.