Use of Roche coordinates in the problems of small oscillations of tidally-distorted stellar models

Kopal's method of Roche coordinates used by us in an earlier paper (Mohan and Singh, 1978) to study the problems of small oscillations of tidally-distorted stars has been extended further to take into account the effect of second-order terms in tidal distortion. Our results show that the effect of including terms of second order of smallness in tidal distortion in the metric coefficients of the Roche coordinates of tidally distorted stars is quite significant, especially in case of stars with extended envelopes and (or) larger values of the mass ratio of the companion star producing tidal distortion. Some of the models which were earlier found stable against small perturbations now become dynamically unstable with the inclusion of the terms of second order of smallness in tidal effects.At present on leave of absence with the department of Mathematics, College of Science, Baghdad, Iraq.