Non-linear oscillations of some homogeneous models of stellar systems

The paper studies nonlinear oscillations of homogeneous models of star systems. Nonlinear oscillations inevitably appear in initial stages of the development of star systems, for it can hardly be expected that the virial theorem is fulfilled from the very beginning. It is known that a system which is stable in a linear approximation may be instable in a nonlinear case. The lagrangian coordinate method is used to study nonlinear radial oscillations of self-consistent models, namely, the Kamm sphere, McLoren disk and circuilar cylinder. The models are chosen from the considerations that their different layers oscillate in the phase, synchronously that considerably facilitates the analysis. The velocity diagram is anisotropic in all the models. It has been found that the cylinder is stable even in the nonlinear case, and the sphere and disk are linearly stable if the perturbation energy is lower than the parabolic limit. Thus, all the above models are stable with respect to radial pulsations even in a nonlinear case