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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2019 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2019
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210062 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| 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| id |
nasplib_isofts_kiev_ua-123456789-210062 |
|---|---|
| record_format |
dspace |
| spelling |
Chanu, C.M. Rastelli, G. 2025-12-02T09:33:37Z 2019 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. 1815-0659 2010 Mathematics Subject Classification: 70H05; 37J15; 70H06 arXiv: 1808.01889 https://nasplib.isofts.kiev.ua/handle/123456789/210062 https://doi.org/10.3842/SIGMA.2019.013 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. We are grateful to Raymond McLenaghan, Krishan Rajaratnam, and Piergiulio Tempesta for conversations useful to clarify some points of our research, and to the anonymous referees who gave a relevant contribution to the improvement of this article. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians |
| spellingShingle |
Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians Chanu, C.M. Rastelli, G. |
| title_short |
Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians |
| title_full |
Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians |
| title_fullStr |
Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians |
| title_full_unstemmed |
Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians |
| title_sort |
block-separation of variables: a form of partial separation for natural hamiltonians |
| author |
Chanu, C.M. Rastelli, G. |
| author_facet |
Chanu, C.M. Rastelli, G. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210062 |
| citation_txt |
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. |
| work_keys_str_mv |
AT chanucm blockseparationofvariablesaformofpartialseparationfornaturalhamiltonians AT rastellig blockseparationofvariablesaformofpartialseparationfornaturalhamiltonians |
| first_indexed |
2025-12-07T21:24:14Z |
| last_indexed |
2025-12-07T21:24:14Z |
| _version_ |
1850886224053534720 |