The stability of non-linear non-radial oscillations of the two-dimensional models of rotating stellar systems

The problem of nonlinear stability of a circular cylinder and Maclauren disk with respect to non-radial oscillations, which give to the stellar system an elliptical form and maintain the space density constant in the disturbed state, is discussed. Time-dependent phase invariants are determined. Under the condition of their existence the total energy of two-dimensional models is minimized. For non-linear oscillations considered, stability conditions in form of limitation from above of the centroid velocity Ω are found, viz for a cylinder Ω < 1 and for a disk Ω ≤ (125/486)^1/2 (in units of circular velocity) what coincides with the linear approximation data.

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