Tippe Top Equations and Equations for the Related Mechanical Systems
The equations of motion for the rolling and gliding Tippe Top (TT) are nonintegrable and difficult to analyze. The only existing arguments about TT inversion are based on analysis of stability of asymptotic solutions and the LaSalle type theorem. They do not explain the dynamics of inversion. To app...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2012 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148412 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Tippe Top Equations and Equations for the Related Mechanical Systems / N. Rutstam // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 23 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862696479955615744 |
|---|---|
| author | Rutstam, N. |
| author_facet | Rutstam, N. |
| citation_txt | Tippe Top Equations and Equations for the Related Mechanical Systems / N. Rutstam // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 23 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The equations of motion for the rolling and gliding Tippe Top (TT) are nonintegrable and difficult to analyze. The only existing arguments about TT inversion are based on analysis of stability of asymptotic solutions and the LaSalle type theorem. They do not explain the dynamics of inversion. To approach this problem we review and analyze here the equations of motion for the rolling and gliding TT in three equivalent forms, each one providing different bits of information about motion of TT. They lead to the main equation for the TT, which describes well the oscillatory character of motion of the symmetry axis 3^ during the inversion. We show also that the equations of motion of TT give rise to equations of motion for two other simpler mechanical systems: the gliding heavy symmetric top and the gliding eccentric cylinder. These systems can be of aid in understanding the dynamics of the inverting TT.
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| first_indexed | 2025-12-07T16:27:44Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148412 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:27:44Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rutstam, N. 2019-02-18T11:52:55Z 2019-02-18T11:52:55Z 2012 Tippe Top Equations and Equations for the Related Mechanical Systems / N. Rutstam // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 23 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 70F40; 74M10; 70E18; 70E40; 37B25 DOI: http://dx.doi.org/10.3842/SIGMA.2012.019 https://nasplib.isofts.kiev.ua/handle/123456789/148412 The equations of motion for the rolling and gliding Tippe Top (TT) are nonintegrable and difficult to analyze. The only existing arguments about TT inversion are based on analysis of stability of asymptotic solutions and the LaSalle type theorem. They do not explain the dynamics of inversion. To approach this problem we review and analyze here the equations of motion for the rolling and gliding TT in three equivalent forms, each one providing different bits of information about motion of TT. They lead to the main equation for the TT, which describes well the oscillatory character of motion of the symmetry axis 3^ during the inversion. We show also that the equations of motion of TT give rise to equations of motion for two other simpler mechanical systems: the gliding heavy symmetric top and the gliding eccentric cylinder. These systems can be of aid in understanding the dynamics of the inverting TT. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Tippe Top Equations and Equations for the Related Mechanical Systems Article published earlier |
| spellingShingle | Tippe Top Equations and Equations for the Related Mechanical Systems Rutstam, N. |
| title | Tippe Top Equations and Equations for the Related Mechanical Systems |
| title_full | Tippe Top Equations and Equations for the Related Mechanical Systems |
| title_fullStr | Tippe Top Equations and Equations for the Related Mechanical Systems |
| title_full_unstemmed | Tippe Top Equations and Equations for the Related Mechanical Systems |
| title_short | Tippe Top Equations and Equations for the Related Mechanical Systems |
| title_sort | tippe top equations and equations for the related mechanical systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148412 |
| work_keys_str_mv | AT rutstamn tippetopequationsandequationsfortherelatedmechanicalsystems |