非球形物体抗无限倒塌的动力稳定性
Dynamic stabilization of non-spherical bodies against unlimited collapse
摘要：
我们求解方程，以简化的方式描述了自引力非旋转椭球体失去稳定性后的牛顿动力学。我们发现，收缩到一个奇点只发生在一个纯粹的球形崩溃，从球形对称性的偏差停止收缩的非线性非球形振荡的稳定作用。由于能量损失、冲击波形成或粘性，在振荡阻尼之后发生真正的崩溃。使用庞加莱映射构造的非线性振荡的详细分析。规则振荡和混沌振荡的区域被定位在这个地图上。
英文摘要：
We solve equations, describing in a simplified way the newtonian dynamics of a selfgravitating nonrotating spheroidal body after loss of stability. We find that contraction to a singularity happens only in a pure spherical collapse, and deviations from the spherical symmetry stop the contraction by the stabilising action of nonlinear nonspherical oscillations. A real collapse happens after damping of the oscillations due to energy losses, shock wave formation or viscosity. Detailed analysis of the nonlinear oscillations is performed using a Poincaré map construction. Regions of regular and chaotic oscillations are localized on this map.
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