摘要：AbstractThe classical problem of the stability of stationary stellar spherical models with purely radial motion is reconsidered. The problem is due to strong central singularity in the density distribution, resulting in not entirely rigorous proof made in the well-known Antonov's paper. To avoid this difficulty, we construct a suitable two-parametric series of models with moderately elongated and nearly radial orbits, without singularity, and pass to the limiting case of models with orbits arbitrarily close to purely radial. The stability of the series with respect to odd and even spherical harmonics is considered. The growth rates of aperiodic even modes increase indefinitely when approaching purely radial models.
