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

{"title":"将Stäckel的Benenti型哈密顿变换为多项式形式","authors":"Jean de Dieu Maniraguha, K. Marciniak, C'elestin Kurujyibwami","doi":"10.4310/atmp.2022.v26.n3.a5","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"32 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Transforming Stäckel Hamiltonians of Benenti type to polynomial form\",\"authors\":\"Jean de Dieu Maniraguha, K. Marciniak, C'elestin Kurujyibwami\",\"doi\":\"10.4310/atmp.2022.v26.n3.a5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":50848,\"journal\":{\"name\":\"Advances in Theoretical and Mathematical Physics\",\"volume\":\"32 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2021-01-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Theoretical and Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.4310/atmp.2022.v26.n3.a5\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.4310/atmp.2022.v26.n3.a5","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

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

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.