Nonlinear oscillations of some homogeneous models of stellar systems. I. the case of radial oscillations

By the method of lagrangian coordinates the non-linear radial oscillations of self-consistent models – the Camm’s sphere, the Maclaurin’s disc and the cylinder – are studied. In all these models the velocity diagram is anisotropic. It is found that the cylinder is stable even with respect to non-linear oscillations. The sphere and disc are stable in non-linear case is the energy of perturbation is less than the parabolic limit.

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