标题： 变量分离和经典Steklov--Lyapunov系统的显式theta函数解：几何和代数几何背景 显示英文标题

标题： Separation of variables and explicit theta-function solution of the classical Steklov--Lyapunov systems: A geometric and algebraic geometric background

摘要： 论文通过变量分离法重新研究了经典Steklov-Lyapunov系统的显式积分，该方法最初由F. Kötter于1900年提出，但直到最近才被充分理解。我们给出了分离变量的几何解释，然后应用Weierstrass超椭圆根函数，得到了该问题的显式theta函数解。我们还分析了其在相应阿贝尔流形上的极点结构。这使我们能够获得系统的一组替代相位变量的解，该解具有特定的紧凑形式。 显示英文摘要

摘要： The paper revises the explicit integration of the classical Steklov--Lyapunov systems via separation of variables, which was first made by F. K\"otter in 1900, but was not well understood until recently. We give a geometric interpretation of the separating variables and then, applying the Weierstrass hyperelliptic root functions, obtain explicit theta-function solution to the problem. We also analyze the structure of its poles on the corresponding Abelian variety. This enables us to obtain a solution for an alternative set of phase variables of the systems that has a specific compact form.