Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians
We study twisted products H=αʳHᵣ of natural autonomous Hamiltonians Hᵣ, each one depending on a separate set, called here a separate r-block, of variables. We show that, when the twist functions αʳ are a row of the inverse of a block-Stäckel matrix, the dynamics of H reduce to the dynamics of the Hᵣ...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2019
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210062 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians / C.M. Chanu, G. Rastelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 31 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We study twisted products H=αʳHᵣ of natural autonomous Hamiltonians Hᵣ, each one depending on a separate set, called here a separate r-block, of variables. We show that, when the twist functions αʳ are a row of the inverse of a block-Stäckel matrix, the dynamics of H reduce to the dynamics of the Hᵣ, modified by a scalar potential depending only on the variables of the corresponding r-block. It is a kind of partial separation of variables. We characterize this block-separation in an invariant way by writing in block-form classical results of Stäckel separation of variables. We classify the block-separable coordinates of E³.
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| ISSN: | 1815-0659 |