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":null,"pages":null},"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\":null,\"pages\":null},\"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
分享 分享
微信好友 朋友圈 QQ好友 复制链接
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
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.
期刊最新文献
A QFT for non-semisimple TQFT Fuchsian ODEs as Seiberg dualities $K_2$ and quantum curves Topological operators, noninvertible symmetries and decomposition Energy spectrum of a constrained quantum particle and the Willmore energy of the constraining surface
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1