将Stäckel的Benenti型哈密顿变换为多项式形式

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2021-01-02 DOI:10.4310/atmp.2022.v26.n3.a5
Jean de Dieu Maniraguha, K. Marciniak, C'elestin Kurujyibwami
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引用次数: 0

摘要

本文讨论了将Benenti型可分离哈密顿量转化为多项式形式的两种正则变换:到Vi′e坐标的变换和到牛顿坐标的变换。到牛顿坐标系的变换直到最近才被应用到这些系统中,在本文中,我们给出了一个新的证明,证明了这种变换确实导致了贝尼蒂型St {{a}克尔哈密顿量的多项式形式。此外,我们给出了这些哈密顿量在牛顿和牛顿坐标系下的所有几何成分。
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Transforming Stäckel Hamiltonians of Benenti type to polynomial form
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.
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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