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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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Інститут математики НАН України
2007
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/147821 |
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irk-123456789-1478212019-02-17T01:23:43Z Phase Space of Rolling Solutions of the Tippe Top Glad, S.T. Petersson, D. Rauch-Wojciechowski, S. 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. 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147821 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| language |
English |
| 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. |
| format |
Article |
| author |
Glad, S.T. Petersson, D. Rauch-Wojciechowski, S. |
| spellingShingle |
Glad, S.T. Petersson, D. Rauch-Wojciechowski, S. Phase Space of Rolling Solutions of the Tippe Top Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Glad, S.T. Petersson, D. Rauch-Wojciechowski, S. |
| author_sort |
Glad, S.T. |
| title |
Phase Space of Rolling Solutions of the Tippe Top |
| title_short |
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_sort |
phase space of rolling solutions of the tippe top |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147821 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT gladst phasespaceofrollingsolutionsofthetippetop AT peterssond phasespaceofrollingsolutionsofthetippetop AT rauchwojciechowskis phasespaceofrollingsolutionsofthetippetop |
| first_indexed |
2023-05-20T17:28:35Z |
| last_indexed |
2023-05-20T17:28:35Z |
| _version_ |
1796153372872540160 |