牛顿自引力弹性物质的多体球对称定态
Multi-body spherically symmetric steady states of Newtonian self-gravitating elastic matter
摘要：
本文研究了牛顿引力下静态、球对称、自引力弹性物质分布的问题。为此，我们首先在欧拉坐标系中引入均匀球对称（超）弹性体的新定义，即，根据身体当前的物理状态定义的物质场。我们表明，我们的定义是等价的经典文献中存在的，这是在拉格朗日坐标，即，在给定的参考状态下物体的变形方面。在我们的新公式中重新定义了一些著名的弹性体本构函数的例子之后，对Seth模型进行了详细的研究。对于这种类型的材料的存在性的单一和多体解决方案的建立。
英文摘要：
We study the problem of static, spherically symmetric, self-gravitating elastic matter distributions in Newtonian gravity. To this purpose we first introduce a new definition of homogeneous, spherically symmetric (hyper)elastic body in Euler coordinates, i.e., in terms of matter fields defined on the current physical state of the body. We show that our definition is equivalent to the classical one existing in the literature and which is given in Lagrangian coordinates, i.e., in terms of the deformation of the body from a given reference state. After a number of well-known examples of constitutive functions of elastic bodies are re-defined in our new formulation, a detailed study of the Seth model is presented. For this type of material the existence of single and multi-body solutions is established.
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