On the dynamics of a spinning top under high-frequency excitation
We investigate the dynamics of a spinning top whose pivot point undergoes a small amplitude high-frequency vertical vibration. The method of Direct Partition of Motion is used to obtain an autonomous equation governing the leading order slow dynamics of the top’s nutation and to derive an approximat...
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| المؤلف الرئيسي: | |
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| التنسيق: | article |
| منشور في: |
2017
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| الوصول للمادة أونلاين: | http://hdl.handle.net/10725/7044 http://dx.doi.org/10.1007/s11071-017-3609-8 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://link.springer.com/article/10.1007/s11071-017-3609-8 |
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| _version_ | 1864513481381773312 |
|---|---|
| author | Sheheitli, Hiba |
| author_facet | Sheheitli, Hiba |
| author_role | author |
| dc.creator.none.fl_str_mv | Sheheitli, Hiba |
| dc.date.none.fl_str_mv | 2017 2018-02-07T11:38:51Z 2018-02-07T11:38:51Z 2018-02-07 |
| dc.identifier.none.fl_str_mv | 1573-269X http://hdl.handle.net/10725/7044 http://dx.doi.org/10.1007/s11071-017-3609-8 Sheheitli, H. (2017). On the dynamics of a spinning top under high-frequency excitation: part I—pivot point under vertical harmonic vibration. Nonlinear Dynamics, 90(2), 765-779. http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://link.springer.com/article/10.1007/s11071-017-3609-8 |
| dc.language.none.fl_str_mv | en |
| dc.relation.none.fl_str_mv | Nonlinear Dynamics |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.title.none.fl_str_mv | On the dynamics of a spinning top under high-frequency excitation part I—pivot point under vertical harmonic vibration |
| dc.type.none.fl_str_mv | Article info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | We investigate the dynamics of a spinning top whose pivot point undergoes a small amplitude high-frequency vertical vibration. The method of Direct Partition of Motion is used to obtain an autonomous equation governing the leading order slow dynamics of the top’s nutation and to derive an approximate closed form solution for the forced spinning top problem. We show that the fast vibration can lead to the stabilization of the “sleeping top” state and an expression for the minimum amplitude required is given in terms of system parameters. We also show the existence of a degenerate family of special solutions in which the spinning top is locked at constant nutation and precession angles; we refer to those as “skewed sleeping top” states. We derive the conditions under which these states exist and are stable. The results are verified through numerical integration of the full non-autonomous system |
| eu_rights_str_mv | openAccess |
| format | article |
| id | LAURepo_dde31b5ee8693f9affa829b6877e0fa6 |
| identifier_str_mv | 1573-269X Sheheitli, H. (2017). On the dynamics of a spinning top under high-frequency excitation: part I—pivot point under vertical harmonic vibration. Nonlinear Dynamics, 90(2), 765-779. |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/7044 |
| publishDate | 2017 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | On the dynamics of a spinning top under high-frequency excitationpart I—pivot point under vertical harmonic vibrationSheheitli, HibaWe investigate the dynamics of a spinning top whose pivot point undergoes a small amplitude high-frequency vertical vibration. The method of Direct Partition of Motion is used to obtain an autonomous equation governing the leading order slow dynamics of the top’s nutation and to derive an approximate closed form solution for the forced spinning top problem. We show that the fast vibration can lead to the stabilization of the “sleeping top” state and an expression for the minimum amplitude required is given in terms of system parameters. We also show the existence of a degenerate family of special solutions in which the spinning top is locked at constant nutation and precession angles; we refer to those as “skewed sleeping top” states. We derive the conditions under which these states exist and are stable. The results are verified through numerical integration of the full non-autonomous systemPublishedN/A2018-02-07T11:38:51Z2018-02-07T11:38:51Z20172018-02-07Articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1573-269Xhttp://hdl.handle.net/10725/7044http://dx.doi.org/10.1007/s11071-017-3609-8Sheheitli, H. (2017). On the dynamics of a spinning top under high-frequency excitation: part I—pivot point under vertical harmonic vibration. Nonlinear Dynamics, 90(2), 765-779.http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.phphttps://link.springer.com/article/10.1007/s11071-017-3609-8enNonlinear Dynamicsinfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/70442021-03-19T10:43:11Z |
| spellingShingle | On the dynamics of a spinning top under high-frequency excitation Sheheitli, Hiba |
| status_str | publishedVersion |
| title | On the dynamics of a spinning top under high-frequency excitation |
| title_full | On the dynamics of a spinning top under high-frequency excitation |
| title_fullStr | On the dynamics of a spinning top under high-frequency excitation |
| title_full_unstemmed | On the dynamics of a spinning top under high-frequency excitation |
| title_short | On the dynamics of a spinning top under high-frequency excitation |
| title_sort | On the dynamics of a spinning top under high-frequency excitation |
| url | http://hdl.handle.net/10725/7044 http://dx.doi.org/10.1007/s11071-017-3609-8 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://link.springer.com/article/10.1007/s11071-017-3609-8 |