ON THE STABILITY AND NORMAL-MODES OF POLYTROPIC STELLAR-SYSTEMS USINGTHE SYMMETRIES OF LINEARIZED LIOUVILLES EQUATION

The stability and normal modes of oscillations of polytropic stellar s ystems are investigated using the symmetries of the linearized Liouvil le's equation. The O(3) symmetry of this linearized equation was utili zed to separate the angle dependence of the eigenfunctions and hence t o reduce the six dimensional phase-space problem to a two dimensional one in terms of magnitudes of position and momentum vectors. For the s implest mode of radial oscillations, the eigenvalue problem was solved numerically with a Rayleigh-Ritz variational scheme. Using 125 variat ional parameters, a high degree of convergence for the lowest eigenval ues was achieved. No negative eigenvalues were detected for any polytr ope.