旋转平衡的拉格朗日变分原理新表述：多维恒星演化
A Novel Formulation by Lagrangian Variational Principle for Rotational Equilibria: Toward Multi-Dimensional Stellar Evolutions
摘要：
我们已经开发了一种新的配方，以获得自引力，轴对称的配置在永久旋转。该公式是基于拉格朗日变分原理，并处理不仅正压，但也斜压状态方程，其中角动量分布不一定是圆柱形的。我们采用蒙特卡罗技术，这是类似于在其他领域，例如核物理，在最小化的能量泛函，这是一个三角网格上评估。这封信是一个证明的原则和详细的比较与现有的结果将报告在续集中，但一些测试计算，我们已经实现了错误的位力关系$O(10^{-4})$。我们考虑到这种方法的应用，二维计算的旋转恒星的演变，拉格朗日公式是最适合的。
英文摘要：
We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle, and treats not only barotropic but also baroclinic equations of state, for which angular momentum distributions are not necessarily cylindrical. We adopt a Monte Carlo technique, which is analogous to those employed in other fields, e.g. nuclear physics, in minimizing the energy functional, which is evaluated on a triangulated mesh. This letter is a proof of principle and detailed comparisons with existing results will be reported in the sequel, but some test calculations are presented, in which we have achieved an error of $O(10^{-4})$ in the Virial relation. We have in mind the application of this method to two-dimensional calculations of the evolutions of rotating stars, for which the Lagrangian formulation is best suited.
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