Phase Space of Rolling Solutions of the Tippe Top
Equations of motion of an axially symmetric sphere rolling and sliding on a plane are usually taken as model of the tippe top. We study these equations in the nonsliding regime both in the vector notation and in the Euler angle variables when they admit three integrals of motion that are linear and...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2007 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147821 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Phase Space of Rolling Solutions of the Tippe Top / S.T. Glad, D. Petersson, S. Rauch-Wojciechowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862620753744101376 |
|---|---|
| author | Glad, S.T. Petersson, D. Rauch-Wojciechowski, S. |
| author_facet | Glad, S.T. Petersson, D. Rauch-Wojciechowski, S. |
| citation_txt | Phase Space of Rolling Solutions of the Tippe Top / S.T. Glad, D. Petersson, S. Rauch-Wojciechowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Equations of motion of an axially symmetric sphere rolling and sliding on a plane are usually taken as model of the tippe top. We study these equations in the nonsliding regime both in the vector notation and in the Euler angle variables when they admit three integrals of motion that are linear and quadratic in momenta. In the Euler angle variables (θ,φ,ψ) these integrals give separation equations that have the same structure as the equations of the Lagrange top. It makes it possible to describe the whole space of solutions by representing them in the space of parameters (D,λ,E) being constant values of the integrals of motion.
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| first_indexed | 2025-12-07T13:22:50Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147821 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:22:50Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Glad, S.T. Petersson, D. Rauch-Wojciechowski, S. 2019-02-16T08:52:00Z 2019-02-16T08:52:00Z 2007 Phase Space of Rolling Solutions of the Tippe Top / S.T. Glad, D. Petersson, S. Rauch-Wojciechowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 14 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 70E18; 70E40; 70F25; 70K05 https://nasplib.isofts.kiev.ua/handle/123456789/147821 Equations of motion of an axially symmetric sphere rolling and sliding on a plane are usually taken as model of the tippe top. We study these equations in the nonsliding regime both in the vector notation and in the Euler angle variables when they admit three integrals of motion that are linear and quadratic in momenta. In the Euler angle variables (θ,φ,ψ) these integrals give separation equations that have the same structure as the equations of the Lagrange top. It makes it possible to describe the whole space of solutions by representing them in the space of parameters (D,λ,E) being constant values of the integrals of motion. This paper is a contribution to the Vadim Kuznetsov Memorial Issue ‘Integrable Systems and Related Topics’. The authors would like to thank referees for useful suggestions and pointing some references. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Phase Space of Rolling Solutions of the Tippe Top Article published earlier |
| spellingShingle | Phase Space of Rolling Solutions of the Tippe Top Glad, S.T. Petersson, D. Rauch-Wojciechowski, S. |
| title | Phase Space of Rolling Solutions of the Tippe Top |
| title_full | Phase Space of Rolling Solutions of the Tippe Top |
| title_fullStr | Phase Space of Rolling Solutions of the Tippe Top |
| title_full_unstemmed | Phase Space of Rolling Solutions of the Tippe Top |
| title_short | Phase Space of Rolling Solutions of the Tippe Top |
| title_sort | phase space of rolling solutions of the tippe top |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147821 |
| work_keys_str_mv | AT gladst phasespaceofrollingsolutionsofthetippetop AT peterssond phasespaceofrollingsolutionsofthetippetop AT rauchwojciechowskis phasespaceofrollingsolutionsofthetippetop |