银河系动力学中赤道圆轨道的稳定性判据：Ⅰ.牛顿薄轨
On the stability criteria for equatorial circular orbits in Galactic Dynamics: I.Newtonian Thin Disks
摘要：
本文对牛顿模型中广泛采用的周转近似下的赤道圆轨道稳定性判据进行了修正。我们发现，对于薄圆盘模型，由于引力场的不连续性，垂直稳定性的判据必须重新表述。我们证明了，对于一个表面质量密度为$Σ$的模型，具有垂直稳定轨道的充分必要条件是$Σ>0$。另一方面，径向稳定性的标准与厚岩脉相同，即周转频率为正。
英文摘要：
We make a revision of the stability criteria for equatorial circular orbits, obtained from the epicyclic approximation, which is widely used in Newtonian models for axisymmetric galaxies. We find that, for the case of thin disk models, the criteria of vertical stability must be reformulated, due to the discontinuity in the gravitational field. We show that, for a model characterized by a surface mass density $Σ$, the necessary and sufficient condition to have vertically stable orbits is that $Σ>0$. On the other hand, the criteria for radial stability is the same as in thick diks, i.e. that the epicyclic frequency is positive.
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