NONLINEAR PULSATIONS OF UPPER MAIN-SEQUENCE STARS .1. PERTURBATION APPROACH

The non-linear pulsations of vibrationally unstable main sequence stars of between 70 and 170 MQ are investigated using a perturbation technique, prior to using numerical methods directly in a subsequent paper. More general as well as periodic solutions are considered. It is found that the presence of resonances results in overtone involvement which causes systematic modulation of the velocity curve and leads to the possibility of limitation at fairly low values of the amplitude. Consideration of the behaviour close to resonance is given and the relationship of the periodic solutions to more general solutions discussed. © Royal Astronomical Society.