标题： 将本特尼型Stäckel哈密顿量转换为多项式形式 显示英文标题

标题： Transforming Stäckel Hamiltonians of Benenti type to polynomial form

摘要： 在本文中，我们讨论了两种规范变换，这些变换将Benenti类型的Stäckel可分离哈密顿量转化为多项式形式：转换到Viète坐标和转换到牛顿坐标。转换到牛顿坐标最近才被应用于这些系统，在本文中我们提供了一个新的证明，表明这种变换确实导致了Benenti类型的Stäckel哈密顿量的多项式形式。此外，我们在Viète坐标和牛顿坐标中都给出了这些哈密顿量的所有几何要素。 显示英文摘要

摘要： In this paper we discuss two canonical transformations that turn St\"{a}ckel separable Hamiltonians of Benenti type into polynomial form: transformation to Vi\`ete coordinates and transformation to Newton coordinates. Transformation to Newton coordinates has been applied to these systems only very recently and in this paper we present a new proof that this transformation indeed leads to polynomial form of St\"{a}ckel Hamiltonians of Benenti type. Moreover we present all geometric ingredients of these Hamiltonians in both Vi\`ete and Newton coordinates.